(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 11.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[    160751,       3497]
NotebookOptionsPosition[    150430,       3316]
NotebookOutlinePosition[    151034,       3338]
CellTagsIndexPosition[    150991,       3335]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell["2021 Homework 1", "Title",
 CellChangeTimes->{{3.821520776097179*^9, 
  3.821520817369145*^9}},ExpressionUUID->"0a4f2521-e7c0-4fab-97e1-\
603f6ab41c1c"],

Cell[BoxData[
 RowBox[{
  RowBox[{"SetOptions", "[", 
   RowBox[{
    RowBox[{"EvaluationNotebook", "[", "]"}], ",", 
    RowBox[{"CellBracketOptions", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"\"\<Color\>\"", "\[Rule]", "Black"}], ",", 
       RowBox[{"\"\<Widths\>\"", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"20", ",", "20"}], "}"}]}], ",", 
       RowBox[{"\"\<Thickness\>\"", "\[Rule]", "3.5"}]}], "}"}]}]}], "]"}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.8203427063672333`*^9, 3.820342710366617*^9}, {
   3.820342935130333*^9, 3.820342954631484*^9}, {3.8203429969742928`*^9, 
   3.820343001387989*^9}, {3.820343450595797*^9, 3.8203434962099524`*^9}, {
   3.82133799284402*^9, 3.821337995589003*^9}, 3.821338037042634*^9, {
   3.821338104274653*^9, 3.821338118749104*^9}, 3.8213382124094257`*^9, {
   3.821338261882592*^9, 3.821338269905648*^9}, 3.821338306335579*^9, {
   3.821339170488145*^9, 3.821339195906999*^9}, {3.821520832216144*^9, 
   3.821520859848032*^9}},
 CellLabel->"In[2]:=",ExpressionUUID->"c930542e-1e83-4d3f-ba5f-7ef178df48be"],

Cell[CellGroupData[{

Cell["Problem 1", "Section",
 CellChangeTimes->{{3.727218524941128*^9, 
  3.7272185300025463`*^9}},ExpressionUUID->"4dc605cd-e9a8-4768-a180-\
9ae5fdc934b3"],

Cell["\<\
We can calculate the arithmetic-geometric mean with a one liner:\
\>", "Text",
 CellChangeTimes->{{3.727218870432279*^9, 3.727218923139374*^9}, {
  3.727218955071752*^9, 
  3.7272189680086107`*^9}},ExpressionUUID->"c82b3c96-123a-42fe-9ca6-\
29ec5a8e7055"],

Cell[BoxData[
 RowBox[{
  RowBox[{"M", "[", 
   RowBox[{"a_", ",", "b_", ",", "acc_"}], "]"}], ":=", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"FixedPoint", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{
         FractionBox["1", "2"], 
         RowBox[{"Plus", "@@", "#"}]}], ",", 
        SqrtBox[
         RowBox[{"Times", "@@", "#"}]]}], "}"}], "&"}], ",", 
     RowBox[{"N", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"a", ",", "b"}], "}"}], ",", "acc"}], "]"}]}], "]"}], 
   "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}]], "Input",
 CellChangeTimes->{{3.714033121156972*^9, 3.7140332108408813`*^9}, {
   3.714033324753533*^9, 3.7140333893154373`*^9}, {3.71403392779853*^9, 
   3.71403398268673*^9}, 3.727218508943989*^9, 3.7572401046188374`*^9},
 CellLabel->"In[3]:=",ExpressionUUID->"705ce4c6-e4d9-4465-bfb8-6bc1485e78a0"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"M", "[", 
  RowBox[{"1", ",", 
   SqrtBox["2"], ",", "100"}], "]"}]], "Input",
 CellChangeTimes->{
  3.727218508944108*^9, {3.727788233055093*^9, 3.727788233630355*^9}, 
   3.7572401046189737`*^9},
 CellLabel->"In[4]:=",ExpressionUUID->"a854a07c-8e9e-4478-b5f6-e6b9e7d0a089"],

Cell[BoxData["1.\
198140234735592207439922492280323878227212663215651558263674952946405214143915\
6708358855564897933893759072250972437`100."], "Output",
 CellChangeTimes->{3.821523454506632*^9},
 CellLabel->"Out[4]=",ExpressionUUID->"47415dbc-f0e8-4f05-9ffb-b73b051b1929"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[CurlyPi]", "=", 
  RowBox[{"2", 
   RowBox[{"Integrate", "[", 
    RowBox[{
     FractionBox["1", 
      SqrtBox[
       RowBox[{"1", "-", 
        SuperscriptBox["x", "4"]}]]], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.7140294868069983`*^9, 3.714029558964859*^9}, {
   3.714029665087759*^9, 3.7140296764896517`*^9}, {3.714029717889687*^9, 
   3.714029761983122*^9}, {3.714029865848545*^9, 3.7140298700403147`*^9}, 
   3.7272185089443398`*^9, 3.727218788540429*^9, {3.727788217005782*^9, 
   3.727788222919854*^9}, {3.727788322239369*^9, 3.727788333748684*^9}, 
   3.757240104619273*^9, {3.820579735830637*^9, 3.8205797455719957`*^9}},
 CellLabel->"In[5]:=",ExpressionUUID->"bc2d4436-06a2-4458-a3b9-dd6a9bb40c3a"],

Cell[BoxData[
 FractionBox[
  RowBox[{"2", " ", 
   SqrtBox["\[Pi]"], " ", 
   RowBox[{"Gamma", "[", 
    FractionBox["5", "4"], "]"}]}], 
  RowBox[{"Gamma", "[", 
   FractionBox["3", "4"], "]"}]]], "Output",
 CellChangeTimes->{3.821523477819022*^9},
 CellLabel->"Out[5]=",ExpressionUUID->"f7032cab-50f3-4c3f-ac37-ffb37aa9f24f"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"N", "[", 
  RowBox[{
   FractionBox["\[Pi]", "\[CurlyPi]"], ",", "100"}], "]"}]], "Input",
 CellChangeTimes->{{3.714029566825777*^9, 3.714029569965837*^9}, {
   3.7140296106136017`*^9, 3.71402962323763*^9}, {3.714033617963455*^9, 
   3.714033626212165*^9}, 3.7272185089444447`*^9, {3.727788242760344*^9, 
   3.727788245276704*^9}, 3.7572401046193943`*^9},
 CellLabel->"In[6]:=",ExpressionUUID->"34ce42ca-ebb7-4493-9547-c6a2a52aa9ef"],

Cell[BoxData["1.\
198140234735592207439922492280323878227212663215651558263674952946405214143915\
6708358855564897933893759072250973411`100."], "Output",
 CellChangeTimes->{3.821523502038021*^9},
 CellLabel->"Out[6]=",ExpressionUUID->"b02cfdab-eca3-40d8-9128-5fb896f85c48"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"%", "-", "%%%"}]], "Input",
 CellChangeTimes->{{3.820579880727614*^9, 3.820579886417603*^9}},
 CellLabel->"In[7]:=",ExpressionUUID->"40411b40-3232-436b-a615-b8a4c24aca33"],

Cell[BoxData["0``99.62046235188578"], "Output",
 CellChangeTimes->{3.821523513340323*^9},
 CellLabel->"Out[7]=",ExpressionUUID->"232ca87f-283b-4aa0-a471-d7c5e94fc51b"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Problem 2", "Section",
 CellChangeTimes->{{3.725369739903851*^9, 3.725369753264626*^9}, {
  3.7572401710284233`*^9, 
  3.7572401764402847`*^9}},ExpressionUUID->"9bbb3869-b734-41b5-bc42-\
32b607e0ac0a"],

Cell[BoxData[
 RowBox[{
  RowBox[{"F", "[", "x_", "]"}], ":=", " ", 
  RowBox[{
   SuperscriptBox["5", 
    RowBox[{"5", " ", "\[ImaginaryI]", " ", "x"}]], " ", 
   FractionBox[
    RowBox[{"Gamma", "[", 
     RowBox[{"1", "-", 
      RowBox[{"5", "\[ImaginaryI]", " ", "x"}]}], "]"}], 
    SuperscriptBox[
     RowBox[{"Gamma", "[", 
      RowBox[{"1", "-", 
       RowBox[{"\[ImaginaryI]", " ", "x"}]}], "]"}], "5"]]}]}]], "Input",
 CellChangeTimes->{{3.6835961845401077`*^9, 3.683596264279517*^9}},
 CellLabel->"In[8]:=",ExpressionUUID->"41afa58a-228c-47a3-87b0-cd8d551cf04f"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", " ", 
  RowBox[{
   RowBox[{
    FractionBox["x", 
     RowBox[{"1", "-", 
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{
        RowBox[{"-", "2"}], "\[Pi]", " ", "x"}]]}]], 
    RowBox[{"Re", "[", 
     RowBox[{"F", "[", "x", "]"}], "]"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "3"}], ",", "5"}], "}"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", "All"}], ",", " ", 
   RowBox[{"ImageSize", "\[Rule]", "500"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.683596408781349*^9, 3.683596522343719*^9}, {
   3.699947052374948*^9, 3.699947104255309*^9}, {3.725369848861844*^9, 
   3.725369883168974*^9}, 3.725372209174087*^9},
 CellLabel->"In[9]:=",ExpressionUUID->"c2b52f66-4ab8-4fec-b971-2a2e552ee097"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwVlnc0F+4Xxz/Gx05WWnZIkllI9EFSVlkhycoumyaihIaMNMxvJAkZGSGf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       "]], LineBox[CompressedData["
1:eJwVlXc41o33x808SBkZDTIyI5VCyLkTmT0aMlJCiIesMktKIfJFyQjZK+N2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       "]], LineBox[CompressedData["
1:eJwBAQL+/SFib1JlAgAAAB8AAAACAAAAWH96as2JC0CCZaUKH7yQv9o0Xxsl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       "]]},
     Annotation[#, "Charting`Private`Tag$5196#1"]& ], {}}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  ImageSize->500,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{All, All},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.8215237108215714`*^9},
 CellLabel->"Out[9]=",ExpressionUUID->"50e8e4be-a376-4f55-adc8-3d2ba9de86ae"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", " ", 
  RowBox[{
   RowBox[{
    RowBox[{
     FractionBox["x", 
      RowBox[{"1", "-", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"-", "2"}], "\[Pi]", " ", "x"}]]}]], 
     RowBox[{"Re", "[", 
      RowBox[{"F", "[", "x", "]"}], "]"}]}], "+", 
    FractionBox[
     SqrtBox["5"], 
     RowBox[{"4", 
      SuperscriptBox["\[Pi]", "2"], "x"}]]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "1", ",", "5"}], "}"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"-", "3"}], ",", "5"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"-", "0.07"}], ",", "0.18"}], "}"}]}], "}"}]}], ",", " ", 
   RowBox[{"ImageSize", "\[Rule]", "500"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.683596408781349*^9, 3.683596522343719*^9}, {
   3.699947052374948*^9, 3.699947104255309*^9}, {3.725369848861844*^9, 
   3.725369883168974*^9}, {3.725372071523806*^9, 3.7253720780590982`*^9}, 
   3.7253721283004103`*^9, {3.725372269044692*^9, 3.725372274708029*^9}, {
   3.725372306203504*^9, 3.725372349435196*^9}},
 CellLabel->"In[11]:=",ExpressionUUID->"e862fbac-b7ee-48e3-b903-1676c1c4ee07"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwV0XlczPkfB/BJh9TYbROJYoTSKdMhSq9vrkrFaMps547pPme6TPTD+IXK
XZJ+dIxVKOMo1Y/NMSJaqW2FELYVft0zU81MTcV+f398Hp/H8/F6H3+8l3C4
fpEzKBTKHvL9/38h7ptLoUix4phPXW5JGvK03vO1NKVoPzDgmpGTBoZP21uq
jhR2keyCrNQ0tHXWlBgZSMHIDhqReKXh9+HM5fYrpKClnXFZMJ4KsfEPjlEM
KTI6NlcfC0zF9Qy6/3OhFDdjEvVur0xB4v1l9S8qyHlRy1r7TFJgrWE4/22V
FLdLleN0agqqTk52famV4g3fX0u3LxkVlx6Hf28m56nrfGq9mIzilztS6TKy
vsGvfZ9JMnLtMvOL3GXozZUcL6bxkGaQu0LXQwbPMNsMuh4PYeOF9/f6yKA3
WNV57zsXDuKafg5LBnbcI5H8Phcft/Wvt0mUQTzb0CEdXNC5gaMPi0gPzahO
9UzCu2ur/QckpItKrhzJSMDjvE39oXLSsa3mf4Qk4EY6U9CukoFXXmbv7J6A
g+u4ojrNEUhTr6rxdRJg23pJQ7BwBJTGL+oXSuORNTi3zsBjBDSP+JS01jhY
W43NdSsdASOIZ1+yIRb7z29x9784glOXqjMKbWLxQvdCQtyVEbArLJsrDWOR
Mej7qLBmBILKgQGTwRg8unaZJ3lC5htZNOfCGATZBbcIJSPQy7j61xxJNHIc
GwXq7qPorr2Wk1ITha6K+SKjzaNof65BRJdFwXYet3Ol9yikSK9MPhaFl4qF
tiEBo7DTuzjvaVQUFt9O76qNHYVYp1wt2TgK9WstnKLySaubTV86GokenBpo
7hkFw7W19GVGBByGnh1t6iXtQbU4FxOBw+c0rRuHRiE8Z2Gb/HMELOV7EhqU
o6BouGxhOkeAVxU5dE13DAK3a2u/jIdj2sBFkm9PWp75zWpvOAz7v4yEZJGW
lMSL8jiIOUs7HZgzBvHRAqNdWRz8tjHYfsfxMQj5Pqe2pnMQVtaeuu0s6aKI
I1aBHJT7N4y5Xx2DXUFh0eklHKx6cEph1jGGbifXO7p1O+Fd4KKSmspB+fvw
g0Vf2Wj+K68tcIUcwo0mYSffsLHZqvfXRhs5BDGfmn5oYYNoLPAucCbN4Jet
ucmGk3SoePVWOexYhR7rMtmg+Qixb7cc3Yap6wbmsKFQ1zyk207W7+Yk3ysN
Q+q24MC0V3KIp2/d08oOg/Rctc2Hd+S+2P7JGG4YBlaFvb7+hczVzH/nE2Ho
/uW/5n6TpL+F6DX0hKKlIfZZkZkCgsELHndtQyFMbfvRbK8C4kkBveNVMA57
J+6m/5v0ElHQzsZgxC+l9rhlK8COXDCqdiMYTh1e9aw8sr9ygfGenGC00ptC
cisUoDku6tvgGgyVrKFysFUBiv7TSsvLQfDnVW64tUgJdt73p7W5gdBOPMgn
xKSfNb8v3MuCUY/b3DtNSlAUNlnvEliwDJyoWdWiBDEUt902hAXfTUnDpq+V
EJZvmaflwkK+yc+RmoNKCP4wXpQ2sQMmbVbMZ4bj6A7uiF6zewfoKzts/bnj
EBzyOt2bFYBQ2ZKv0YsmICg07rBoZCKpXDz+ZOkEaK6SOZZ1TOxj/aJrZjEB
8bHWz45XmCi9V2z32X4C7I+CGbwTTHzMNcxke5H11OTHCcFMhJnO1gtMI/Nd
67bvVfqBzRxfs+UZaf/uXRWr/RBR13bcepeK3J+0vfgVA+/H6hxXZqogHEhS
dbYwEOBQ8mGVgMwP3vRc2MjA5lvxNquPqMA+82v97esMmFdrt7qXqkBcGdbc
msNAv2g9lfVEBUqfYqrLlYHk8vojB+ZNQlyl9fLSjm3Yd7o0+3U9af3APXxn
X5gmXwjfdHeSvG+8aNzMF0+2lqP24SQo86onsuf64gedKmXe80kQvhtF7SM+
KBPURft+IvtFZz9pX/eBOPG5x+PZUxD/50SAtrkPZniqZtZETEH4Jrfzs6k3
Dk0F5BzXn4Ywfe1sf3ghP+rCRJkh6a+mNn2rvFDaPhhXYzwNSrl+T/YyL9SX
Z/l2mpG5VtLw37O80OtTrb/EZRrdNFn+zFee8CmhltSGT0OQXnTzp0RP6Ls9
qu6qJft7htV7L3qgbL9dlwXrG2gf/OZILDcjfv2C6PAz3yFcX1B9tHQDfmqW
T/nzKQR7GfVRiYc7lJNcSdx8NYLy8E675Rs3MOWhkTOfqhHilveymkgX5Jzo
4KekzCAIZkCEw35nPK0NsmfoqxMCPrfvtJkT/iUMSKl9oE4QSZK1U8P2cDHi
BB3dqUEQmdlqvy2mg8f61NSrp0mIE5p41Gg77HPsbzW4p0kIuKL/bX1tg0Kh
+v5boVoEZWj5YiOOFZb9eerWG92ZBMXaKO6khgXunliZx7tO+vws6mWqOWwG
A3Q7fbUJgeZQ7n3Gchj8KNV+rCIdvo1uLVwKzQfnbywtnkUIpmUNrxxMkeDQ
8HaWtw4hKHxLPfMnDSIvjvC+QoegLA/vWme7GH7dLk7KA7oEpWNTSl6ICf4B
DZ+aNQ==
       "]], LineBox[CompressedData["
1:eJwVzn8s1HEYB/Avn5Nfd+ecH5f5NZZy2ymzqKQ9XzchdRXKceUWpR8qnC0p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       "]]},
     Annotation[#, "Charting`Private`Tag$5894#1"]& ], {}}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  ImageSize->500,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{-3, 5}, {-0.07, 0.18}},
  PlotRangeClipping->True,
  PlotRangePadding->{{0, 0}, {0, 0}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.821523901074917*^9},
 CellLabel->"Out[11]=",ExpressionUUID->"b969c3dc-5a4c-4eaa-b683-779b8a6b90f7"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Series", "[", 
  RowBox[{
   RowBox[{"x", " ", 
    RowBox[{"F", "[", "x", "]"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "Infinity", ",", "3"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.683596655534403*^9, 3.6835966816594954`*^9}, 
   3.7249481816751547`*^9, 3.726578582695652*^9, {3.789220839539797*^9, 
   3.789220859714876*^9}},
 CellLabel->"In[10]:=",ExpressionUUID->"b13b0ff3-4bb0-4351-86c6-0ceee27c1283"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{
   RowBox[{"-", 
    FractionBox[
     SqrtBox["5"], 
     RowBox[{"4", " ", 
      SuperscriptBox["\[Pi]", "2"], " ", "x"}]]}], "+", 
   FractionBox["\[ImaginaryI]", 
    RowBox[{"2", " ", 
     SqrtBox["5"], " ", 
     SuperscriptBox["\[Pi]", "2"], " ", 
     SuperscriptBox["x", "2"]}]], "+", 
   FractionBox["1", 
    RowBox[{"10", " ", 
     SqrtBox["5"], " ", 
     SuperscriptBox["\[Pi]", "2"], " ", 
     SuperscriptBox["x", "3"]}]], "+", 
   InterpretationBox[
    SuperscriptBox[
     RowBox[{"O", "[", 
      FractionBox["1", "x"], "]"}], "4"],
    SeriesData[$CellContext`x, 
     DirectedInfinity[1], {}, 2, 8, 2],
    Editable->False]}],
  SeriesData[$CellContext`x, 
   DirectedInfinity[1], {
   Rational[-1, 4] 5^Rational[1, 2] Pi^(-2), 0, Complex[0, 
      Rational[1, 2]] 5^Rational[-1, 2] Pi^(-2), 0, Rational[1, 10] 
    5^Rational[-1, 2] Pi^(-2)}, 2, 8, 2],
  Editable->False]], "Output",
 CellChangeTimes->{3.821523741859498*^9},
 CellLabel->"Out[10]=",ExpressionUUID->"1dcbd0c0-6b42-46e2-b0ad-ff1a532d3484"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"NIntegrate", "[", 
  RowBox[{
   FractionBox[
    RowBox[{"x", " ", 
     RowBox[{"Re", "[", 
      RowBox[{"F", "[", "x", "]"}], "]"}]}], 
    RowBox[{"1", "-", 
     SuperscriptBox["\[ExponentialE]", 
      RowBox[{
       RowBox[{"-", "2"}], " ", "\[Pi]", " ", "x"}]]}]], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     RowBox[{"-", "\[Infinity]"}], ",", "1"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.683597216981227*^9, 3.683597235786333*^9}, {
  3.683597272847868*^9, 3.6835973232549753`*^9}, {3.7253698288425817`*^9, 
  3.7253698296613398`*^9}},
 CellLabel->"In[12]:=",ExpressionUUID->"33d777e5-20b0-4374-bde5-b74f996cde24"],

Cell[BoxData[
 RowBox[{"-", "0.0031306892713885183`"}]], "Output",
 CellChangeTimes->{3.821523955501384*^9},
 CellLabel->"Out[12]=",ExpressionUUID->"97d837dd-ca49-43bb-bb74-789ce1b24e0d"]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"int1", "[", "prec_", "]"}], ":=", 
  RowBox[{"NIntegrate", "[", 
   RowBox[{
    FractionBox[
     RowBox[{"x", " ", 
      RowBox[{"Re", "[", 
       RowBox[{"F", "[", "x", "]"}], "]"}]}], 
     RowBox[{"1", "-", 
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{
        RowBox[{"-", "2"}], " ", "\[Pi]", " ", "x"}]]}]], ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", 
      RowBox[{"-", "\[Infinity]"}], ",", "1"}], "}"}], ",", " ", 
    RowBox[{"WorkingPrecision", "\[Rule]", "prec"}], ",", " ", 
    RowBox[{"AccuracyGoal", "\[Rule]", 
     RowBox[{"prec", "/", "2"}]}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.683597216981227*^9, 3.683597235786333*^9}, {
   3.683597272847868*^9, 3.6835973232549753`*^9}, {3.683598078791642*^9, 
   3.683598114806438*^9}, 3.699945856514333*^9, {3.699946112544516*^9, 
   3.699946113325492*^9}, {3.699946482451354*^9, 3.699946548138876*^9}, 
   3.699946655012005*^9, {3.724948214975898*^9, 3.724948220194371*^9}, 
   3.724948279911322*^9, {3.72536990803474*^9, 3.725369932995943*^9}, {
   3.725369980439267*^9, 3.7253699992943068`*^9}},
 CellLabel->"In[13]:=",ExpressionUUID->"a9acca4f-598a-4be4-a018-565e40825c47"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"int1", "[", "50", "]"}]], "Input",
 CellChangeTimes->{{3.7253699453273993`*^9, 3.7253699616493177`*^9}},
 CellLabel->"In[14]:=",ExpressionUUID->"6457da42-bf61-4937-9829-04af6f58c39c"],

Cell[BoxData[
 RowBox[{"-", 
  "0.0031306892713853153037408493787474539124903134762509762717968947935646115\
3222`50."}]], "Output",
 CellChangeTimes->{3.821523992249916*^9},
 CellLabel->"Out[14]=",ExpressionUUID->"d05aa51a-41f9-4510-ac2e-1d608d7a7eb2"]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"int2", "[", "prec_", "]"}], ":=", 
  RowBox[{"NIntegrate", "[", 
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{"x", " ", 
       RowBox[{"Re", "[", 
        RowBox[{"F", "[", "x", "]"}], "]"}]}], 
      RowBox[{"1", "-", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"-", "2"}], " ", "\[Pi]", " ", "x"}]]}]], "+", 
     FractionBox[
      SqrtBox["5"], 
      RowBox[{"4", 
       SuperscriptBox["\[Pi]", "2"], "x"}]]}], ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", "1", ",", "\[Infinity]"}], "}"}], ",", " ", 
    RowBox[{"WorkingPrecision", "\[Rule]", "prec"}], ",", " ", 
    RowBox[{"AccuracyGoal", "\[Rule]", 
     RowBox[{"prec", "/", "2"}]}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.683597346763343*^9, 3.6835974202077208`*^9}, {
   3.6835981361662083`*^9, 3.683598150877779*^9}, 3.699945879165357*^9, {
   3.6999461265779*^9, 3.699946127027211*^9}, {3.6999462335512*^9, 
   3.6999462668161077`*^9}, {3.699946675328786*^9, 3.6999466839331827`*^9}, 
   3.69994721724868*^9, {3.7249482625117493`*^9, 3.724948293311267*^9}, {
   3.725370013945641*^9, 3.725370048373584*^9}},
 CellLabel->"In[15]:=",ExpressionUUID->"616ad8d7-5837-425a-a387-8af25a043737"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"int2", "[", "50", "]"}]], "Input",
 CellChangeTimes->{{3.789221104289892*^9, 3.7892211108123426`*^9}},
 CellLabel->"In[16]:=",ExpressionUUID->"852cb80d-d993-4b8a-806e-455e37a53903"],

Cell[BoxData["0.\
00236969163010458933676844597219261403334434675423041885457897678910708854249`\
50."], "Output",
 CellChangeTimes->{3.8215240396077547`*^9},
 CellLabel->"Out[16]=",ExpressionUUID->"b02a64a6-9d4a-4e68-a9b1-52fbb6c35c5e"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Assuming", "[", 
  RowBox[{
   RowBox[{"\[Delta]", ">", "0"}], ",", 
   RowBox[{"Integrate", "[", 
    RowBox[{
     FractionBox[
      RowBox[{"Cos", "[", 
       RowBox[{"\[Delta]", " ", "x"}], "]"}], "x"], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "1", ",", "\[Infinity]"}], "}"}]}], "]"}]}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.821524129476644*^9, 3.8215241621743937`*^9}},
 CellLabel->"In[18]:=",ExpressionUUID->"d4ba3f0c-9dc5-407d-a885-df629f420872"],

Cell[BoxData[
 RowBox[{"-", 
  RowBox[{"CosIntegral", "[", "\[Delta]", "]"}]}]], "Output",
 CellChangeTimes->{3.821524097261696*^9, 3.821524164364666*^9},
 CellLabel->"Out[18]=",ExpressionUUID->"7b7f1067-27e8-42a5-83a9-34441f7de82e"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"J", "=", 
  RowBox[{
   FractionBox[
    RowBox[{"-", 
     SqrtBox["5"]}], 
    RowBox[{"4", 
     SuperscriptBox["\[Pi]", "2"]}]], 
   RowBox[{"Assuming", "[", 
    RowBox[{
     RowBox[{"\[Delta]", ">", "0"}], ",", " ", 
     RowBox[{"Integrate", "[", 
      RowBox[{
       FractionBox[
        RowBox[{"Cos", "[", 
         RowBox[{"\[Delta]", " ", "x"}], "]"}], "x"], ",", 
       RowBox[{"{", 
        RowBox[{"x", ",", "1", ",", "\[Infinity]"}], "}"}]}], "]"}]}], 
    "]"}]}]}]], "Input",
 CellChangeTimes->{{3.683597449629587*^9, 3.683597523177909*^9}, {
   3.683597571075989*^9, 3.6835975936188593`*^9}, {3.683597638104968*^9, 
   3.683597653499579*^9}, 3.6835977024851427`*^9, {3.724948365361703*^9, 
   3.724948365933737*^9}, 3.820581139493062*^9, 3.82152438284369*^9},
 CellLabel->"In[19]:=",ExpressionUUID->"81d46395-cbc5-4ee7-afed-4bcd66f7ab19"],

Cell[BoxData[
 FractionBox[
  RowBox[{
   SqrtBox["5"], " ", 
   RowBox[{"CosIntegral", "[", "\[Delta]", "]"}]}], 
  RowBox[{"4", " ", 
   SuperscriptBox["\[Pi]", "2"]}]]], "Output",
 CellChangeTimes->{3.821524414450575*^9},
 CellLabel->"Out[19]=",ExpressionUUID->"251977bd-68c8-408a-a170-44454e2b9a81"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Series", "[", 
  RowBox[{"J", ",", 
   RowBox[{"{", 
    RowBox[{"\[Delta]", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.6835977203003187`*^9, 3.683597741682925*^9}},
 CellLabel->"In[20]:=",ExpressionUUID->"cfc3778c-a80d-4fe9-a6ad-0a630de1fa6a"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SqrtBox["5"], " ", 
     RowBox[{"(", 
      RowBox[{"EulerGamma", "+", 
       RowBox[{"Log", "[", "\[Delta]", "]"}]}], ")"}]}], 
    RowBox[{"4", " ", 
     SuperscriptBox["\[Pi]", "2"]}]], "+", 
   InterpretationBox[
    SuperscriptBox[
     RowBox[{"O", "[", "\[Delta]", "]"}], "2"],
    SeriesData[$CellContext`\[Delta], 0, {}, 0, 2, 1],
    Editable->False]}],
  SeriesData[$CellContext`\[Delta], 0, {
   Rational[1, 4] 5^Rational[1, 2] 
    Pi^(-2) (EulerGamma + Log[$CellContext`\[Delta]])}, 0, 2, 1],
  Editable->False]], "Output",
 CellChangeTimes->{3.821524513910591*^9},
 CellLabel->"Out[20]=",ExpressionUUID->"7d0bb8cb-2bc6-44c6-a64b-d0bd2f039799"]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"const", "[", "prec_", "]"}], ":=", 
  RowBox[{
   RowBox[{"int1", "[", "prec", "]"}], " ", "+", " ", 
   RowBox[{"int2", "[", "prec", "]"}], " ", "+", 
   RowBox[{
    FractionBox[
     SqrtBox["5"], 
     RowBox[{"4", 
      SuperscriptBox["\[Pi]", "2"]}]], "EulerGamma"}]}]}]], "Input",
 CellChangeTimes->{{3.6835979461260138`*^9, 3.683597980897758*^9}, {
  3.7253701183141108`*^9, 3.725370147207651*^9}},
 CellLabel->"In[21]:=",ExpressionUUID->"d99bbdc3-0c10-4959-9ee4-3e07a178e6d0"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Table", "[", 
   RowBox[{
    RowBox[{"N", "[", 
     RowBox[{
      RowBox[{"int1", "[", "prec", "]"}], ",", "100"}], "]"}], ",", 
    RowBox[{"{", 
     RowBox[{"prec", ",", "100", ",", "160", ",", "10"}], "}"}]}], "]"}], "//",
   "Column"}]], "Input",
 CellChangeTimes->{{3.7249487107495728`*^9, 3.7249487933618307`*^9}, 
   3.724948905797172*^9, 3.724948938788661*^9, {3.724948997717092*^9, 
   3.7249490006862183`*^9}, {3.724951958903213*^9, 3.724951980679123*^9}, {
   3.725370192995592*^9, 3.725370214058289*^9}, {3.725370259470767*^9, 
   3.725370269396068*^9}},
 CellLabel->"In[22]:=",ExpressionUUID->"98e06414-6578-41da-b0a7-0f0c3cde4df6"],

Cell[BoxData[
 TagBox[GridBox[{
    {
     RowBox[{
     "-", "0.00313068927138531530374084937874745391246340205739641659319423337\
9462897784219389945087941345799574631971142157474`100."}]},
    {
     RowBox[{
     "-", "0.00313068927138531530374084937874745391246340205739641659319423337\
94628977842193898069756094711816570104655153906564`100."}]},
    {
     RowBox[{
     "-", "0.00313068927138531530374084937874745391246340205739641659319423337\
94628977842193898069648035428726063991474526553829`100."}]},
    {
     RowBox[{
     "-", "0.00313068927138531530374084937874745391246340205739641659319423337\
94628977842193898069648037070666743542693517874119`100."}]},
    {
     RowBox[{
     "-", "0.00313068927138531530374084937874745391246340205739641659319423337\
94628977842193898069648037070253232434058848697274`100."}]},
    {
     RowBox[{
     "-", "0.00313068927138531530374084937874745391246340205739641659319423337\
9462897784219389806964803707025312517949042824147`100."}]},
    {
     RowBox[{
     "-", "0.00313068927138531530374084937874745391246340205739641659319423337\
94628977842193898069648037070253125177054636873644`100."}]}
   },
   DefaultBaseStyle->"Column",
   GridBoxAlignment->{"Columns" -> {{Left}}},
   GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
  "Column"]], "Output",
 CellChangeTimes->{3.8215246293635817`*^9},
 CellLabel->"Out[22]=",ExpressionUUID->"3bd46017-8c8b-452b-ad48-fa00367ea398"]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Table", "[", 
   RowBox[{
    RowBox[{"N", "[", 
     RowBox[{
      RowBox[{"int2", "[", "prec", "]"}], ",", "100"}], "]"}], ",", 
    RowBox[{"{", 
     RowBox[{"prec", ",", "100", ",", "160", ",", "10"}], "}"}]}], "]"}], "//",
   "Column"}]], "Input",
 CellChangeTimes->{{3.7249487107495728`*^9, 3.7249487933618307`*^9}, 
   3.724948905797172*^9, 3.724948938788661*^9, {3.724948997717092*^9, 
   3.7249490006862183`*^9}, {3.724951958903213*^9, 3.724951980679123*^9}, {
   3.725370192995592*^9, 3.725370214058289*^9}, {3.725370259470767*^9, 
   3.725370269396068*^9}, 3.725370324692705*^9},
 CellLabel->"In[23]:=",ExpressionUUID->"4d1cdd0e-4f48-4045-ac57-b73bfb043adb"],

Cell[BoxData[
 TagBox[GridBox[{
    {"0.0023696916301045893367684459721926140333443478047086097760311776654752\
203092757373158487256717151986106498435179481`100."},
    {"0.0023696916301045893367684459721926140333443478047086097760311776654752\
203092757373159006889066430914668584362703955`100."},
    {"0.0023696916301045893367684459721926140333443478047086097760311776654752\
203092757373159006888379133742931969407332743`100."},
    {"0.0023696916301045893367684459721926140333443478047086097760311776654752\
203092757373159006888379141345957547019725421`100."},
    {"0.0023696916301045893367684459721926140333443478047086097760311776654752\
203092757373159006888379141343882355866713344`100."},
    {"0.0023696916301045893367684459721926140333443478047086097760311776654752\
203092757373159006888379141343881806168700002`100."},
    {"0.0023696916301045893367684459721926140333443478047086097760311776654752\
20309275737315900688837914134388180615634766`100."}
   },
   DefaultBaseStyle->"Column",
   GridBoxAlignment->{"Columns" -> {{Left}}},
   GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
  "Column"]], "Output",
 CellChangeTimes->{3.821524748200859*^9},
 CellLabel->"Out[23]=",ExpressionUUID->"08f25e22-ea16-4693-aef5-5b998e8eecae"]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Table", "[", 
   RowBox[{
    RowBox[{"N", "[", 
     RowBox[{
      RowBox[{"const", "[", "prec", "]"}], ",", "100"}], "]"}], ",", 
    RowBox[{"{", 
     RowBox[{"prec", ",", "100", ",", "160", ",", "10"}], "}"}]}], "]"}], "//",
   "Column"}]], "Input",
 CellChangeTimes->{{3.724950571086163*^9, 3.724950668542345*^9}, {
  3.7249507496629477`*^9, 3.724950754648986*^9}, {3.725371574968769*^9, 
  3.7253715918430862`*^9}},
 CellLabel->"In[24]:=",ExpressionUUID->"a28c7106-e41e-4009-a839-ea1fdbf01ad4"],

Cell[BoxData[
 TagBox[GridBox[{
    {"0.0319326497417670308283189005192356321594119475509534752821887555338023\
029060064807423980883055637892678952907631572`100."},
    {"0.0319326497417670308283189005192356321594119475509534752821887555338023\
029060064808805623834151095997456095102824223`100."},
    {"0.0319326497417670308283189005192356321594119475509534752821887555338023\
029060064808805731892746889331832660774805746`100."},
    {"0.0319326497417670308283189005192356321594119475509534752821887555338023\
029060064808805731891104956255307019395878134`100."},
    {"0.0319326497417670308283189005192356321594119475509534752821887555338023\
029060064808805731891105369764340462912042902`100."},
    {"0.0319326497417670308283189005192356321594119475509534752821887555338023\
029060064808805731891105369871594481634485364`100."},
    {"0.0319326497417670308283189005192356321594119475509534752821887555338023\
029060064808805731891105369871596917413500848`100."}
   },
   DefaultBaseStyle->"Column",
   GridBoxAlignment->{"Columns" -> {{Left}}},
   GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
  "Column"]], "Output",
 CellChangeTimes->{3.821524795173922*^9},
 CellLabel->"Out[24]=",ExpressionUUID->"947bb949-26a0-411a-93c5-934e6d741aaa"]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell["Problem 3", "Section",
 CellChangeTimes->{{3.725369739903851*^9, 3.725369753264626*^9}, 
   3.725372552493232*^9, {3.757240180088991*^9, 
   3.757240183728647*^9}},ExpressionUUID->"5349232d-260c-402a-84c4-\
88c8a59b01a0"],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x_", "]"}], ":=", 
   RowBox[{
    RowBox[{"Sin", "[", 
     SuperscriptBox["x", "2"], "]"}], "+", 
    SuperscriptBox[
     RowBox[{"Sin", "[", "x", "]"}], "2"]}]}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"g", "[", "x_", "]"}], ":=", 
  RowBox[{"Exp", "[", 
   FractionBox[
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"5", "-", "x"}], ")"}], "2"], "10"], "]"}]}]}], "Input",
 CellChangeTimes->{{3.612345160325829*^9, 3.612345267235836*^9}, {
  3.612345528914027*^9, 3.612345556798813*^9}},
 CellLabel->"In[25]:=",ExpressionUUID->"e15c9255-feb2-42e8-8915-5986db297514"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"f", "[", "x", "]"}], ",", 
     RowBox[{"g", "[", "x", "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "2", ",", "8"}], "}"}], ",", "\[IndentingNewLine]", 
   "         ", 
   RowBox[{"ImageSize", "\[Rule]", "600"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.6123452782951937`*^9, 3.612345380831015*^9}, 
   3.612345447166541*^9, {3.6123463216298227`*^9, 3.612346336254849*^9}, {
   3.612346373799699*^9, 3.612346374537414*^9}, {3.612348419756137*^9, 
   3.6123484307942667`*^9}, {3.61234847018513*^9, 3.612348502080276*^9}, 
   3.612348587764723*^9, 3.612348899275885*^9, 3.683414365570436*^9, {
   3.683598320701707*^9, 3.683598330053658*^9}},
 CellLabel->"In[27]:=",ExpressionUUID->"e699b49c-75c5-41ec-961e-f1a2c76ae117"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwUV3c8lf8XN6/NdV333iKrklSkaeVzkiRpURlpS5IyspJKfYWkskNlVyKK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       "]]},
     Annotation[#, "Charting`Private`Tag$19084#1"]& ], 
    TagBox[
     {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwt2Hk4VN8bAPAxU6bsM/fOpCyjbFHSVylE50UkWSKiKETqW6JNsifSIilL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       "]]},
     Annotation[#, "Charting`Private`Tag$19084#2"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{2., 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  ImageSize->600,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{2, 8}, {-0.9711700723320591, 2.4596029304514255`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.821525051469986*^9},
 CellLabel->"Out[27]=",ExpressionUUID->"ebc66c5b-281e-4509-a41e-b4683c0b198b"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"f", "[", "x", "]"}], ",", 
     RowBox[{"g", "[", "x", "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "7", ",", "7.7"}], "}"}], ",", "\[IndentingNewLine]", 
   "         ", 
   RowBox[{"ImageSize", "\[Rule]", "600"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.6123452782951937`*^9, 3.612345380831015*^9}, 
   3.612345447166541*^9, {3.6123463216298227`*^9, 3.612346336254849*^9}, {
   3.612346373799699*^9, 3.612346374537414*^9}, {3.612348419756137*^9, 
   3.6123484307942667`*^9}, {3.61234847018513*^9, 3.612348502080276*^9}, 
   3.612348587764723*^9, 3.612348899275885*^9, 3.683414365570436*^9, {
   3.683598320701707*^9, 3.683598330053658*^9}, 3.724958638344657*^9, {
   3.72537400065476*^9, 3.7253740024899273`*^9}},
 CellLabel->"In[28]:=",ExpressionUUID->"40ef4ed8-8556-4240-af3e-3bf5055db1ab"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwV13k8VF8UAHBboiSUKDMjaRGVREJynyVJyJZUilQoQhSypRBJKiEpO5Hs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       "]]},
     Annotation[#, "Charting`Private`Tag$19138#1"]& ], 
    TagBox[
     {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwVx3801Xccx/EPMd1Dt2Sl6fP9JJNzKMePOn4M+7xL2ZVQ7KJzGbVSQ7Fc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       "]]},
     Annotation[#, "Charting`Private`Tag$19138#2"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{7., 0},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  ImageSize->600,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{7, 7.7}, {-0.5221211875933288, 2.073006548269228}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.821525148521554*^9},
 CellLabel->"Out[28]=",ExpressionUUID->"832be5bd-4a9f-4e4e-9a17-a40028ccca54"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"f", "[", "x", "]"}], ",", 
     RowBox[{"g", "[", "x", "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "7.15", ",", "7.25"}], "}"}], ",", 
   "\[IndentingNewLine]", "         ", 
   RowBox[{"ImageSize", "\[Rule]", "600"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.6123452782951937`*^9, 3.612345380831015*^9}, 
   3.612345447166541*^9, {3.6123463216298227`*^9, 3.612346336254849*^9}, {
   3.612346373799699*^9, 3.612346374537414*^9}, {3.612348419756137*^9, 
   3.6123484307942667`*^9}, {3.61234847018513*^9, 3.612348502080276*^9}, 
   3.612348587764723*^9, 3.612348899275885*^9, 3.683414365570436*^9, {
   3.683598320701707*^9, 3.683598330053658*^9}, 3.724958638344657*^9, {
   3.724958695555275*^9, 3.72495872838299*^9}},
 CellLabel->"In[29]:=",ExpressionUUID->"057faa31-7128-46e1-b540-de122161acd1"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwV13k0Vd0bB3CilFlmnfImpMmbUkmxTwqllFSmylQplGi4C02oNCEUEf1M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       "]]},
     Annotation[#, "Charting`Private`Tag$19190#1"]& ], 
    TagBox[
     {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwV03s0FFgYAPCJ8Wh6GRmO7ba2hJGWfWh7+65tSTrtFqWtdpeS5OAURcom
ipYesmRreo1JoyymRsUQp4eVTKsi6xGVih46Y3oo7p2Y/frjnu/8zne+e8/9
7ncnrd0YEGYiEAgW4/oUpxdWyWQyQjeeLE4wrGdwmr3NV6Bf8W+jxeEMbPxd
VYXoutYna1zQ/b251yvQhePLFwWiS6dtfNWOLj02a1IR2v38pHmfHSW00/XM
vVUbGEjL93QdRTs7OwdVRjCYULvE5fgxQh0fXG/cFsVgvE7/sf4EoaqIOO+Y
WAYbkq07muSEim+csTdPYBAUnJXSqMD6C2fWpuxgsNzffpMhn9ATTq0h8bsZ
qPOcwgUFhApW/+JpmcHAwXRewVdnCX0dEQc2Bxk4q8+VBP1N6GF/jzfmuQz2
apXVK4oJNSaWdOUeZWDUF0hSVYQ+9wstkucxaEx2i993ntD0pJb1PgUM5v46
Sp5eSqik75F7YxGDCp8P49QXCa0ezohtUzPIka3LuFhGaMp8K+vEcgZJ7IH/
Uw2hT+Y5qGXVDEyUpc0Wlwmd8nF6zskaBk8vi8ItqgntCbg7w6ueQcvDaO9v
rhAq0ielrLrDwCl62ZSZ1wht86sB8X8M9lj4/hRRQ2hcTZvUp4NBsi77+6xa
QkMTTn8e/JhBq1eoV3YdoVGFCp31cwZw3GvXlXpCr5GFB3/QMRCGnbhdd4vQ
sUbXy+PeMVi7bcXT2gZC5YHNy68OMmjCt9PfIdT0wKVw/TADuVOY8l0j9tPM
NbJcyGFHtSbAsZnQAcHk6GERh/688Jt+LYTeW1kncRNzuKmX+S5sw/t51li/
tuWg8m8dHXefUPsv7DSeEzm8sTrSkdhJ6Nz599eIHTk0TL4Ym/CQ0NTMJOt7
Ug6VtGNpXhehvbRfLPHgINSmzcp/QujV38IS+zw5hATPiWjsxvlzOVDlN4eD
fcgWxf1nhNLDlbazvTlEFluean9BqIOLD1gt4HBbeLbX9BWhFt1LX4Qv5pB5
UztnpI7Q/NyHY4ICcb8jg82z9ITuH9J43VjJ4daFlO9C3hB6duePWyeEcMiZ
nZm35h2e3+q2z3w9h6gGZUDme5xH+f6ft0RxOHWLjvlrgFClesG5rbEcYiQz
snIYoS/nP4sITuAQEDlzdZWB0N/nNqVrkzhkTat2vzpE6LOyS9naVA7yohHu
9WiFKju0B62a6vtlE1opU3oK0rA/0jtu3ejZi6Jbp6NFTo+llsOExktTHRTo
tIlmjkvQyVPvVmzdw2H72MV2XehB325bp3QOew/8afsSnb89uQ/QstEtkrdo
j3MBN1ahNaJgG6ER/xuRxWeh35vHiKVoW4mq3YDeZDw0ahParGOwsCmDw86k
dtE2tGjJ+1QdOnNoomgXuuZflxDLvRxKDAWWhz7lH7nbeaF7BzRmmk/52No/
CtE8fkh4Db3669h1/6BHfvAWatGjDcu8H6Gl/VqTTvR2dZXBZh+HGZvHmfSg
reTe7R5o37eBI/rQcbKPZf7ooJgjggE0UegOhaHDXncajejIMpvNyej/ATG3
Wa4=
       "]]},
     Annotation[#, "Charting`Private`Tag$19190#2"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{7.15, 1.3369505676490774`},
  BaseStyle->{FontFamily -> "Arial"},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  ImageSize->600,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{7.15, 7.25}, {1.3369505676490774`, 1.6590580458972919`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.821525185531848*^9},
 CellLabel->"Out[29]=",ExpressionUUID->"e476d7c3-8efb-4723-b880-370009d08154"]
}, Open  ]],

Cell["NSolve does not want to solve this equation:", "Text",
 CellChangeTimes->{{3.612370273031274*^9, 
  3.6123702988284483`*^9}},ExpressionUUID->"f2483416-bd9e-4b71-b57b-\
5d6e14076ee0"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"N", "[", 
  RowBox[{
   RowBox[{"NSolve", "[", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{"f", "[", "x", "]"}], "-", 
        RowBox[{"g", "[", "x", "]"}]}], "\[Equal]", "0"}], " ", "&&", " ", 
      RowBox[{"2", "\[LessEqual]", "x", "\[LessEqual]", "8"}]}], ",", "x"}], 
    "]"}], ",", "80"}], "]"}]], "Input",
 CellChangeTimes->{{3.61234603335359*^9, 3.612346075423191*^9}, 
   3.6123461055421743`*^9, {3.726580872612814*^9, 3.726580935422851*^9}, {
   3.821525346586763*^9, 3.821525372058981*^9}},
 CellLabel->"In[34]:=",ExpressionUUID->"972c891e-8410-43c9-9ac5-2d5ed62efec6"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "3.7003907229884176`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "3.8642125274802397`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "4.360167327338848`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "4.688369967633294`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "5.022557762484828`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "5.288157488251704`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "5.676460878828054`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "5.792653949370362`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "7.192494024861237`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", "\[Rule]", "7.209401756890078`"}], "}"}]}], "}"}]], "Output",\

 CellChangeTimes->{
  3.821525259800413*^9, {3.821525358801485*^9, 3.821525372942841*^9}},
 CellLabel->"Out[34]=",ExpressionUUID->"103c0773-af67-4b76-9f81-36af9d6ae9c2"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Length", "[", "%", "]"}]], "Input",
 CellChangeTimes->{{3.8215252699834757`*^9, 3.8215252748305387`*^9}},
 CellLabel->"In[31]:=",ExpressionUUID->"5ca3d32b-faa0-4626-9b3c-fe6edaefe8c9"],

Cell[BoxData["10"], "Output",
 CellChangeTimes->{3.8215252771022463`*^9},
 CellLabel->"Out[31]=",ExpressionUUID->"c741c357-f6c2-4ff5-bade-346847ba8fdc"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"CountRoots", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"f", "[", "x", "]"}], "-", 
    RowBox[{"g", "[", "x", "]"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "2", ",", "8"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.789221976612116*^9, 3.789222045983073*^9}},
 CellLabel->"In[32]:=",ExpressionUUID->"4c785609-46cb-4390-8f98-cef3e05fa2c8"],

Cell[BoxData["10"], "Output",
 CellChangeTimes->{3.821525295404778*^9},
 CellLabel->"Out[32]=",ExpressionUUID->"3232ea83-0d98-4909-a9f0-17130feb3af6"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"x", "/.", 
  RowBox[{"FindRoot", "[", 
   RowBox[{
    RowBox[{
     SuperscriptBox["x", "2"], "-", "2"}], ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", "2"}], "}"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.68359861305161*^9, 3.6835986746085997`*^9}, {
  3.821525424892391*^9, 3.821525434043852*^9}},
 CellLabel->"In[37]:=",ExpressionUUID->"4714c13f-f101-4586-9bf4-caf6299b0225"],

Cell[BoxData["1.4142135623730951`"], "Output",
 CellChangeTimes->{{3.8215254029009333`*^9, 3.821525435489077*^9}},
 CellLabel->"Out[37]=",ExpressionUUID->"fc0036cf-084c-4bb4-a811-49b4c92740ba"]
}, Open  ]],

Cell["\<\
The diagram suggests 10 roots. This procedure finds these and also what seem \
from the diagram to be 5 spurious roots\
\>", "Text",
 CellChangeTimes->{{3.612370386762702*^9, 3.612370451917242*^9}, {
  3.6123705353857393`*^9, 
  3.612370590567416*^9}},ExpressionUUID->"7e3db950-9050-469e-8019-\
06b1cc06cd51"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"tab", "=", "\[IndentingNewLine]", 
  RowBox[{"Sort", "[", "\[IndentingNewLine]", 
   RowBox[{"DeleteDuplicates", "[", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"Table", "[", "  ", 
      RowBox[{
       RowBox[{"x", "/.", 
        RowBox[{
         RowBox[{"FindRoot", "[", 
          RowBox[{
           RowBox[{
            RowBox[{
             RowBox[{"f", "[", "x", "]"}], "-", 
             RowBox[{"g", "[", "x", "]"}]}], "\[Equal]", "0"}], ",", 
           RowBox[{"{", 
            RowBox[{"x", ",", 
             SubscriptBox["x", "0"]}], "}"}], ",", 
           RowBox[{"WorkingPrecision", "\[Rule]", "80"}]}], "]"}], 
         "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", 
       "\[IndentingNewLine]", "           ", 
       RowBox[{"{", 
        RowBox[{
         SubscriptBox["x", "0"], ",", "3.5", ",", "8", ",", "0.1"}], "}"}]}], 
      "]"}], ",", "\[IndentingNewLine]", 
     "                                      ", 
     RowBox[{
      RowBox[{
       RowBox[{"Abs", "[", 
        RowBox[{"#1", " ", "-", "#2"}], "]"}], "<", 
       SuperscriptBox["10", 
        RowBox[{"-", "75"}]]}], "&"}]}], "]"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.612346989177023*^9, 3.612347038653187*^9}, {
   3.612347146720282*^9, 3.6123471503508673`*^9}, {3.6123472046689663`*^9, 
   3.6123472768058567`*^9}, {3.6123473872533493`*^9, 3.612347400642789*^9}, {
   3.61234753885322*^9, 3.612347597385873*^9}, {3.612347673695332*^9, 
   3.6123476801020184`*^9}, {3.612347840087143*^9, 3.612347854455317*^9}, 
   3.612347905092712*^9, {3.612347940163908*^9, 3.6123479656726027`*^9}, {
   3.6123480201909943`*^9, 3.6123480216791983`*^9}, 3.612348073365309*^9, {
   3.612348130096066*^9, 3.612348158097817*^9}, 3.612348206453618*^9, {
   3.612348304603176*^9, 3.612348335951229*^9}, {3.612348369487598*^9, 
   3.612348373421918*^9}, 3.61234885090209*^9, {3.6123489498312073`*^9, 
   3.612348951811076*^9}, {3.612348998650296*^9, 3.612349006546805*^9}, 
   3.61234944902966*^9, {3.6123495258257504`*^9, 3.6123495262328873`*^9}, {
   3.68341465312024*^9, 3.683414663468586*^9}, {3.68341470709061*^9, 
   3.683414712762825*^9}, 3.6835987784578247`*^9, {3.725374161681798*^9, 
   3.7253741737869*^9}, 3.821525534776269*^9},
 CellLabel->"In[38]:=",ExpressionUUID->"696667d7-460e-496f-b64a-7e9e2276ea9f"],

Cell[BoxData[
 TemplateBox[{
  "FindRoot", "lstol", 
   "\"The line search decreased the step size to within tolerance specified \
by AccuracyGoal and PrecisionGoal but was unable to find a sufficient \
decrease in the merit function. You may need more than \
\\!\\(\\*RowBox[{\\\"80.`\\\"}]\\) digits of working precision to meet these \
tolerances.\"", 2, 38, 1, 18036342346202936749, "Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{3.821525597589595*^9},
 CellLabel->
  "During evaluation of \
In[38]:=",ExpressionUUID->"607945a0-0884-4540-ab2d-6744ad671774"],

Cell[BoxData[
 TemplateBox[{
  "FindRoot", "lstol", 
   "\"The line search decreased the step size to within tolerance specified \
by AccuracyGoal and PrecisionGoal but was unable to find a sufficient \
decrease in the merit function. You may need more than \
\\!\\(\\*RowBox[{\\\"80.`\\\"}]\\) digits of working precision to meet these \
tolerances.\"", 2, 38, 2, 18036342346202936749, "Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{3.8215255976415443`*^9},
 CellLabel->
  "During evaluation of \
In[38]:=",ExpressionUUID->"a667d08d-c462-4d02-93e8-6df804dc182d"],

Cell[BoxData[
 TemplateBox[{
  "FindRoot", "lstol", 
   "\"The line search decreased the step size to within tolerance specified \
by AccuracyGoal and PrecisionGoal but was unable to find a sufficient \
decrease in the merit function. You may need more than \
\\!\\(\\*RowBox[{\\\"80.`\\\"}]\\) digits of working precision to meet these \
tolerances.\"", 2, 38, 3, 18036342346202936749, "Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{3.8215255976457253`*^9},
 CellLabel->
  "During evaluation of \
In[38]:=",ExpressionUUID->"16c6fc94-1607-4d97-845a-7e0d4f55030a"],

Cell[BoxData[
 TemplateBox[{
  "General", "stop", 
   "\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"FindRoot\\\", \
\\\"::\\\", \\\"lstol\\\"}], \\\"MessageName\\\"]\\) will be suppressed \
during this calculation.\"", 2, 38, 4, 18036342346202936749, "Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{3.821525597650103*^9},
 CellLabel->
  "During evaluation of \
In[38]:=",ExpressionUUID->"8abe6b18-5d88-467a-b44f-cf88ce7c2731"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "3.7003907229884175923476756008533860420328495400814229565492229824124565292\
65267957177574672523465`80.", ",", 
   "3.864212527480239500021252081227729756644910143705252046608521121422454073\
161779029936826476668234`80.", ",", 
   "4.360167327338847761790045887393224622152405695493098017108833938673601746\
209553098632614621666178`80.", ",", 
   "4.688369967633294590605283895415308935686344611769950579203337033335442304\
802427589439792776972371`80.", ",", 
   "5.022557762484828024817570485879263381415046045946032223347161600974325904\
556413367067431499221123`80.", ",", 
   "5.288157488251703965844084105669702756962039037417096371048879825929494039\
360777383684353405770456`80.", ",", 
   "5.676460878828054445631740714431321582316791535875263992154054269412801216\
650811689194046862907763`80.", ",", 
   "5.792653949370362486794020335515909176172788157606518775262445983579190820\
706877561191417026319159`80.", ",", 
   "7.192494024861236467129656285222086357391491824591603750563551577035825589\
73691059888213197334667`80.", ",", 
   "7.209401756890078262330002575357501925524399393829594798127267313572738075\
01310670535937960188258`80.", ",", 
   "7.621060347071605465169582864871154479789888309348747545142238015798757610\
457307060516322093861732`80.", ",", 
   "7.621060347186328244881348676284667765669100732591487896914228806824170586\
173262062112330293113203`80.", ",", 
   "7.621060347307713399522744697045980162007643396671637235725459382848348589\
103332760653932707615432`80.", ",", 
   "7.621060347336519511754263876933652608210611631719443234478752401871489073\
223342512163145754432896`80.", ",", 
   "7.621060347404273664731839366463968274529981833982082781017053195280071990\
887399539414342820362473`80."}], "}"}]], "Output",
 CellChangeTimes->{3.821525597689885*^9},
 CellLabel->"Out[38]=",ExpressionUUID->"c10a2898-f06e-4abb-b5cd-2db15e6da63f"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Length", "[", "tab", "]"}]], "Input",
 CellChangeTimes->{{3.612348220092661*^9, 3.612348224278009*^9}, {
  3.724958955389489*^9, 3.7249589563087463`*^9}},
 CellLabel->"In[39]:=",ExpressionUUID->"47229937-a07f-43ba-8b98-91e4d3ff1e63"],

Cell[BoxData["15"], "Output",
 CellChangeTimes->{3.821525637381206*^9},
 CellLabel->"Out[39]=",ExpressionUUID->"d7c140c7-2cec-4e00-bdab-8629402dd3a6"]
}, Open  ]],

Cell["Do these numbers satisfy the the original equation?", "Text",
 CellChangeTimes->{{3.7253742683469067`*^9, 3.725374315759952*^9}, 
   3.7253743501862392`*^9},ExpressionUUID->"ed9168f9-076c-4605-a2a8-\
3a66efdc58e0"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"f", "[", "#", "]"}], "-", 
    RowBox[{"g", "[", "#", "]"}]}], "&"}], "/@", "tab"}]], "Input",
 CellChangeTimes->{{3.612348773736421*^9, 3.612348804881391*^9}, 
   3.612349046867207*^9, {3.724958964733115*^9, 3.724958965593693*^9}},
 CellLabel->"In[40]:=",ExpressionUUID->"797fe3c2-c723-4656-a846-7a7c52aba7f1"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "0``78.78951729851902", ",", "0``78.58251390721144", ",", 
   "0``78.38793403666588", ",", "0``78.35184039459473", ",", 
   "0``78.27429370846349", ",", "0``78.23354673658136", ",", 
   "0``78.29474039543072", ",", "0``78.37778443325898", ",", 
   "0``78.64119198568866", ",", "0``78.57612277340667", ",", 
   RowBox[{
   "-", "0.0417697978352653930069717736023035706934393015846336632932038157691\
70760862234409471712388132278`77.41995149723434"}], ",", 
   RowBox[{
   "-", "0.0417697978352653904611439513467233910937964365285486175159406623173\
11656527922339767302013650184`77.41995150279621"}], ",", 
   RowBox[{
   "-", "0.0417697978352653911321447353077109898384304674316543509562213868456\
3436029762765093528137848689`77.41995150868104"}], ",", 
   RowBox[{
   "-", "0.0417697978352653917993020698754604937848036184494502932406352733262\
15383361914372492238939531113`77.41995151007761"}], ",", 
   RowBox[{
   "-", "0.0417697978352653941365773024490464918390717689280160525824634701247\
89424566342129631511580442807`77.41995151336238"}]}], "}"}]], "Output",
 CellChangeTimes->{3.82152565727997*^9},
 CellLabel->"Out[40]=",ExpressionUUID->"5d8b7e2f-95e4-4338-9a0b-7c8407f69ab2"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"solns", " ", "=", 
  RowBox[{"Select", "[", 
   RowBox[{"tab", ",", 
    RowBox[{
     RowBox[{
      RowBox[{"Abs", "[", 
       RowBox[{
        RowBox[{"f", "[", "#", "]"}], "-", 
        RowBox[{"g", "[", "#", "]"}]}], "]"}], "<", " ", 
      SuperscriptBox["10", 
       RowBox[{"-", "78"}]]}], "&"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.683414792175013*^9, 3.683414896815982*^9}},
 CellLabel->"In[41]:=",ExpressionUUID->"4306108b-7077-48cc-a6fd-d4eb144e7027"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "3.7003907229884175923476756008533860420328495400814229565492229824124565292\
65267957177574672523465`80.", ",", 
   "3.864212527480239500021252081227729756644910143705252046608521121422454073\
161779029936826476668234`80.", ",", 
   "4.360167327338847761790045887393224622152405695493098017108833938673601746\
209553098632614621666178`80.", ",", 
   "4.688369967633294590605283895415308935686344611769950579203337033335442304\
802427589439792776972371`80.", ",", 
   "5.022557762484828024817570485879263381415046045946032223347161600974325904\
556413367067431499221123`80.", ",", 
   "5.288157488251703965844084105669702756962039037417096371048879825929494039\
360777383684353405770456`80.", ",", 
   "5.676460878828054445631740714431321582316791535875263992154054269412801216\
650811689194046862907763`80.", ",", 
   "5.792653949370362486794020335515909176172788157606518775262445983579190820\
706877561191417026319159`80.", ",", 
   "7.192494024861236467129656285222086357391491824591603750563551577035825589\
73691059888213197334667`80.", ",", 
   "7.209401756890078262330002575357501925524399393829594798127267313572738075\
01310670535937960188258`80."}], "}"}]], "Output",
 CellChangeTimes->{3.8215257648545027`*^9},
 CellLabel->"Out[41]=",ExpressionUUID->"2d8cfe58-2f42-471b-9266-5809d1615558"]
}, Open  ]],

Cell["This solves the problem in one go:", "Text",
 CellChangeTimes->{{3.789136023201459*^9, 
  3.7891360405474977`*^9}},ExpressionUUID->"7f4e63b2-ef76-40fd-ba21-\
9e7ff3f04439"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"N", "[", 
  RowBox[{
   RowBox[{"Reduce", "[", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"f", "[", "x", "]"}], "\[Equal]", 
       RowBox[{"g", "[", "x", "]"}]}], "&&", " ", 
      RowBox[{"2", "\[LessEqual]", " ", "x", "\[LessEqual]", "8"}]}], ",", 
     "x"}], "]"}], ",", "80"}], "]"}]], "Input",
 CellChangeTimes->{{3.726580656825857*^9, 3.726580720180031*^9}, {
  3.726580769064518*^9, 3.726580824957019*^9}},
 CellLabel->"In[42]:=",ExpressionUUID->"af0f118f-bef6-42de-a921-ddf50f1b1094"],

Cell[BoxData[
 RowBox[{
  RowBox[{
  "x", "\[Equal]", 
   "3.700390722988417592347675600853386042032849540081422956549222982412456529\
265267957177574672523465`80."}], "||", 
  RowBox[{
  "x", "\[Equal]", 
   "3.864212527480239500021252081227729756644910143705252046608521121422454073\
161779029936826476668234`80."}], "||", 
  RowBox[{
  "x", "\[Equal]", 
   "4.360167327338847761790045887393224622152405695493098017108833938673601746\
209553098632614621666178`80."}], "||", 
  RowBox[{
  "x", "\[Equal]", 
   "4.688369967633294590605283895415308935686344611769950579203337033335442304\
80242758943979277697237`80."}], "||", 
  RowBox[{
  "x", "\[Equal]", 
   "5.022557762484828024817570485879263381415046045946032223347161600974325904\
556413367067431499221123`80."}], "||", 
  RowBox[{
  "x", "\[Equal]", 
   "5.288157488251703965844084105669702756962039037417096371048879825929494039\
360777383684353405770457`80."}], "||", 
  RowBox[{
  "x", "\[Equal]", 
   "5.676460878828054445631740714431321582316791535875263992154054269412801216\
650811689194046862907764`80."}], "||", 
  RowBox[{
  "x", "\[Equal]", 
   "5.792653949370362486794020335515909176172788157606518775262445983579190820\
706877561191417026319159`80."}], "||", 
  RowBox[{
  "x", "\[Equal]", 
   "7.192494024861236467129656285222086357391491824591603750563551577035825589\
736910598864150738284518`80."}], "||", 
  RowBox[{
  "x", "\[Equal]", 
   "7.209401756890078262330002575357501925524399393829594798127267313572738075\
01310670535937960188258`80."}]}]], "Output",
 CellChangeTimes->{3.821525812813465*^9},
 CellLabel->"Out[42]=",ExpressionUUID->"a677d275-b630-4efd-a324-a1c22567766b"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"?", "Reduce"}]], "Input",
 CellChangeTimes->{{3.726580841152046*^9, 
  3.726580844219343*^9}},ExpressionUUID->"7374bbb4-6993-40c9-8086-\
4c5f63831f9e"]
}, Closed]],

Cell[CellGroupData[{

Cell["Problem 4", "Section",
 CellChangeTimes->{{3.727218724292704*^9, 3.727218734317277*^9}, 
   3.757244389744817*^9, 
   3.820579944621138*^9},ExpressionUUID->"cbb13f6a-ec05-418a-9f9c-\
8240bc3ba96a"],

Cell[BoxData[
 RowBox[{"Clear", "[", 
  RowBox[{"x", ",", "y", ",", "n"}], "]"}]], "Input",
 CellChangeTimes->{{3.821526401429254*^9, 3.821526434721264*^9}},
 CellLabel->"In[1]:=",ExpressionUUID->"5629fab6-131d-421a-9d65-ec4d7a6921af"],

Cell[TextData[{
 "We can choose x \[LessEqual] y, so x \[LessEqual] ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{"n", "/", "2"}], ")"}], 
    RowBox[{"1", "/", "3"}]], TraditionalForm]],ExpressionUUID->
  "983971e8-8aa5-410d-8e5a-59367926333a"],
 ". We make a list of numbers ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"n", "-", 
     SuperscriptBox["x", "3"]}], " ", ","}], TraditionalForm]],ExpressionUUID->
  "bbd1a96f-fc98-497f-ac95-edcd4f0b4659"],
 " and check when these numbers are cubes."
}], "Text",
 CellChangeTimes->{{3.727219200160927*^9, 3.727219241351602*^9}, {
  3.7272193256166058`*^9, 3.7272193644696608`*^9}, {3.7272194161689367`*^9, 
  3.727219552993155*^9}},ExpressionUUID->"d9f49424-e87d-4a22-b6be-\
4f213fc41f2d"],

Cell[BoxData[
 RowBox[{
  RowBox[{"solns", "[", "n_", "]"}], ":=", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"n", "-", "#"}], ")"}], 
       RowBox[{"1", "/", "3"}]], ",", 
      SuperscriptBox["#", 
       RowBox[{"1", "/", "3"}]]}], "}"}], "&"}], "/@", 
   RowBox[{"Select", "[", 
    RowBox[{
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"n", "-", 
        SuperscriptBox["x", "3"]}], ",", 
       RowBox[{"{", 
        RowBox[{"x", ",", "1", ",", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox["n", "2"], ")"}], 
          RowBox[{"1", "/", "3"}]]}], "}"}]}], "]"}], ",", " ", 
     RowBox[{
      RowBox[{"IntegerQ", "[", 
       SuperscriptBox["#", 
        RowBox[{"1", "/", "3"}]], "]"}], "&"}]}], "]"}], 
   "            "}]}]], "Input",
 CellChangeTimes->{{3.727033147569853*^9, 3.72703316472465*^9}, {
   3.7270332174390078`*^9, 3.7270333416721363`*^9}, {3.72703337245217*^9, 
   3.727033393088139*^9}, {3.7270336106610622`*^9, 3.727033692110938*^9}, {
   3.7270337222245417`*^9, 3.7270337895517483`*^9}, {3.7270339543212423`*^9, 
   3.7270339547941628`*^9}, {3.727034078711752*^9, 3.727034079037408*^9}, {
   3.727034277349618*^9, 3.727034299193309*^9}, {3.7270343573219*^9, 
   3.727034406791998*^9}, {3.727095839760729*^9, 3.727095878667698*^9}, {
   3.727095968320889*^9, 3.7270959853829517`*^9}, {3.727096124496266*^9, 
   3.727096133678636*^9}, 3.727096212724831*^9, {3.727218632345645*^9, 
   3.727218635761333*^9}, {3.727219174105123*^9, 3.7272191803225327`*^9}, {
   3.727219288917922*^9, 3.7272192901124277`*^9}, {3.7277889422223673`*^9, 
   3.727788947034231*^9}, {3.820580009932548*^9, 3.82058001964545*^9}},
 CellLabel->"In[2]:=",ExpressionUUID->"19675129-00b5-4048-9b53-9a19f08f1ae0"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"solns", "[", "1729", "]"}]], "Input",
 CellChangeTimes->{{3.7272192979997807`*^9, 3.727219308218495*^9}},
 CellLabel->"In[3]:=",ExpressionUUID->"025c923a-204f-437d-bcb6-e6cc47dd25ad"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1", ",", "12"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"9", ",", "10"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.8215265091263037`*^9},
 CellLabel->"Out[3]=",ExpressionUUID->"e65b493e-36b3-442a-b7a7-c46deec366ed"]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"solntab", "[", "nmax_", "]"}], ":=", "\[IndentingNewLine]", 
  RowBox[{"Select", "[", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Table", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"n", ",", 
        RowBox[{"solns", "[", "n", "]"}]}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"n", ",", "1", ",", "nmax"}], "}"}]}], "]"}], ",", 
    "\[IndentingNewLine]", "             ", 
    RowBox[{
     RowBox[{
      RowBox[{"#", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "=!=", 
      RowBox[{"{", "}"}]}], "&"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.727033824190565*^9, 3.727033873659771*^9}, {
  3.727033928711788*^9, 3.727033931344543*^9}, {3.727034426050087*^9, 
  3.727034448891808*^9}, {3.7270963455503273`*^9, 3.727096416739444*^9}, {
  3.727097072866859*^9, 3.727097091549181*^9}},
 CellLabel->"In[4]:=",ExpressionUUID->"5f1f8136-89c3-4af8-8425-8237b9d1fe75"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"solntab", "[", "2000", "]"}]], "Input",
 CellChangeTimes->{{3.7270964228007803`*^9, 3.727096465744771*^9}},
 CellLabel->"In[5]:=",ExpressionUUID->"79f05c73-3bdc-49c2-b9e9-5ede12165df3"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"2", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"1", ",", "1"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"9", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"1", ",", "2"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"16", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"2", ",", "2"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"28", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"1", ",", "3"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"35", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"2", ",", "3"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"54", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"3", ",", "3"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"65", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"1", ",", "4"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"72", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"2", ",", "4"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"91", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"3", ",", "4"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"126", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"1", ",", "5"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"128", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"4", ",", "4"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"133", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"2", ",", "5"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"152", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"3", ",", "5"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"189", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"4", ",", "5"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"217", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"1", ",", "6"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"224", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"2", ",", "6"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"243", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"3", ",", "6"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"250", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"5", ",", "5"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"280", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"4", ",", "6"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"341", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"5", ",", "6"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"344", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"1", ",", "7"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"351", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"2", ",", "7"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"370", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"3", ",", "7"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"407", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"4", ",", "7"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"432", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"6", ",", "6"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"468", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"5", ",", "7"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"513", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"1", ",", "8"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"520", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"2", ",", "8"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"539", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"3", ",", "8"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"559", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"6", ",", "7"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"576", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"4", ",", "8"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"637", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"5", ",", "8"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"686", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"7", ",", "7"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"728", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"6", ",", "8"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"730", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"1", ",", "9"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"737", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"2", ",", "9"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"756", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"3", ",", "9"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"793", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"4", ",", "9"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"854", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"5", ",", "9"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"855", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"7", ",", "8"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"945", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"6", ",", "9"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1001", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"1", ",", "10"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1008", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"2", ",", "10"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1024", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"8", ",", "8"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1027", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"3", ",", "10"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1064", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"4", ",", "10"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1072", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"7", ",", "9"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1125", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"5", ",", "10"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1216", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"6", ",", "10"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1241", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"8", ",", "9"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1332", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"1", ",", "11"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1339", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"2", ",", "11"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1343", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"7", ",", "10"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1358", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"3", ",", "11"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1395", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"4", ",", "11"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1456", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"5", ",", "11"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1458", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"9", ",", "9"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1512", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"8", ",", "10"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1547", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"6", ",", "11"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1674", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"7", ",", "11"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1729", ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"1", ",", "12"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"9", ",", "10"}], "}"}]}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1736", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"2", ",", "12"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1755", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"3", ",", "12"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1792", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"4", ",", "12"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1843", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"8", ",", "11"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1853", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"5", ",", "12"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1944", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"6", ",", "12"}], "}"}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"2000", ",", 
     RowBox[{"{", 
      RowBox[{"{", 
       RowBox[{"10", ",", "10"}], "}"}], "}"}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.821526618734042*^9},
 CellLabel->"Out[5]=",ExpressionUUID->"666a3f7a-51e7-4dda-af0a-3e51246d4740"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Select", "[", 
  RowBox[{
   RowBox[{"solntab", "[", "2000", "]"}], ",", 
   RowBox[{
    RowBox[{
     RowBox[{"Length", "[", 
      RowBox[{"#", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], 
      "]"}], "\[GreaterEqual]", "2"}], "&"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7270344781210747`*^9, 3.727034543483294*^9}, {
  3.727096579614915*^9, 3.727096589366249*^9}},
 CellLabel->"In[6]:=",ExpressionUUID->"70bf3875-4b21-464f-9aa7-d34e92e7e0a3"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"1729", ",", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"1", ",", "12"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"9", ",", "10"}], "}"}]}], "}"}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.821526655359489*^9},
 CellLabel->"Out[6]=",ExpressionUUID->"5bba4ca0-b67f-4b07-afdf-b9e250843daa"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Select", "[", 
  RowBox[{
   RowBox[{"solntab", "[", "10000", "]"}], ",", 
   RowBox[{
    RowBox[{
     RowBox[{"Length", "[", 
      RowBox[{"#", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], 
      "]"}], "\[GreaterEqual]", "2"}], "&"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7270344781210747`*^9, 3.727034543483294*^9}, {
  3.727096579614915*^9, 3.7270966240382442`*^9}, {3.821527017749641*^9, 
  3.821527017967147*^9}},
 CellLabel->"In[10]:=",ExpressionUUID->"e9d6db7b-7baf-44bd-99a6-9017c695a1d0"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1729", ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"1", ",", "12"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"9", ",", "10"}], "}"}]}], "}"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"4104", ",", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"2", ",", "16"}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"9", ",", "15"}], "}"}]}], "}"}]}], "}"}]}], "}"}]], "Output",\

 CellChangeTimes->{3.821527051652841*^9},
 CellLabel->"Out[10]=",ExpressionUUID->"b28b31af-0a18-443c-b2cd-6c8cc5d0f98a"]
}, Open  ]]
}, Closed]]
},
CellGrouping->Manual,
WindowSize->{1763, 1061},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
CellBracketOptions->{"Color"->GrayLevel[0],
"Thickness"->3.5,
"Widths"->{20, 20}},
Magnification:>1.25 Inherited,
FrontEndVersion->"12.2 for Mac OS X x86 (64-bit) (December 12, 2020)",
StyleDefinitions->FrontEnd`FileName[{"Report"}, "StandardReport.nb", 
  CharacterEncoding -> "UTF-8"],
ExpressionUUID->"e27cc7e8-695f-480b-ba4e-96d29dfb6c37"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 158, 3, 121, "Title",ExpressionUUID->"0a4f2521-e7c0-4fab-97e1-603f6ab41c1c"],
Cell[719, 25, 1084, 22, 51, "Input",ExpressionUUID->"c930542e-1e83-4d3f-ba5f-7ef178df48be"],
Cell[CellGroupData[{
Cell[1828, 51, 156, 3, 87, "Section",ExpressionUUID->"4dc605cd-e9a8-4768-a180-9ae5fdc934b3"],
Cell[1987, 56, 265, 6, 41, "Text",ExpressionUUID->"c82b3c96-123a-42fe-9ca6-29ec5a8e7055"],
Cell[2255, 64, 898, 23, 95, "Input",ExpressionUUID->"705ce4c6-e4d9-4465-bfb8-6bc1485e78a0"],
Cell[CellGroupData[{
Cell[3178, 91, 299, 7, 55, "Input",ExpressionUUID->"a854a07c-8e9e-4478-b5f6-e6b9e7d0a089"],
Cell[3480, 100, 273, 4, 64, "Output",ExpressionUUID->"47415dbc-f0e8-4f05-9ffb-b73b051b1929"]
}, Open  ]],
Cell[CellGroupData[{
Cell[3790, 109, 815, 17, 78, "Input",ExpressionUUID->"bc2d4436-06a2-4458-a3b9-dd6a9bb40c3a"],
Cell[4608, 128, 328, 9, 96, "Output",ExpressionUUID->"f7032cab-50f3-4c3f-ac37-ffb37aa9f24f"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4973, 142, 457, 8, 66, "Input",ExpressionUUID->"34ce42ca-ebb7-4493-9547-c6a2a52aa9ef"],
Cell[5433, 152, 273, 4, 64, "Output",ExpressionUUID->"b02cfdab-eca3-40d8-9128-5fb896f85c48"]
}, Open  ]],
Cell[CellGroupData[{
Cell[5743, 161, 195, 3, 50, "Input",ExpressionUUID->"40411b40-3232-436b-a615-b8a4c24aca33"],
Cell[5941, 166, 167, 2, 64, "Output",ExpressionUUID->"232ca87f-283b-4aa0-a471-d7c5e94fc51b"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[6157, 174, 207, 4, 68, "Section",ExpressionUUID->"9bbb3869-b734-41b5-bc42-32b607e0ac0a"],
Cell[6367, 180, 579, 15, 74, "Input",ExpressionUUID->"41afa58a-228c-47a3-87b0-cd8d551cf04f"],
Cell[CellGroupData[{
Cell[6971, 199, 769, 19, 68, "Input",ExpressionUUID->"c2b52f66-4ab8-4fec-b971-2a2e552ee097"],
Cell[7743, 220, 18029, 318, 430, "Output",ExpressionUUID->"50e8e4be-a376-4f55-adc8-3d2ba9de86ae"]
}, Open  ]],
Cell[CellGroupData[{
Cell[25809, 543, 1240, 33, 91, "Input",ExpressionUUID->"e862fbac-b7ee-48e3-b903-1676c1c4ee07"],
Cell[27052, 578, 5222, 104, 430, "Output",ExpressionUUID->"b969c3dc-5a4c-4eaa-b683-779b8a6b90f7"]
}, Open  ]],
Cell[CellGroupData[{
Cell[32311, 687, 449, 10, 64, "Input",ExpressionUUID->"b13b0ff3-4bb0-4351-86c6-0ceee27c1283"],
Cell[32763, 699, 1075, 32, 88, "Output",ExpressionUUID->"1dcbd0c0-6b42-46e2-b0ad-ff1a532d3484"]
}, Open  ]],
Cell[CellGroupData[{
Cell[33875, 736, 666, 17, 85, "Input",ExpressionUUID->"33d777e5-20b0-4374-bde5-b74f996cde24"],
Cell[34544, 755, 187, 3, 64, "Output",ExpressionUUID->"97d837dd-ca49-43bb-bb74-789ce1b24e0d"]
}, Open  ]],
Cell[34746, 761, 1198, 26, 85, "Input",ExpressionUUID->"a9acca4f-598a-4be4-a018-565e40825c47"],
Cell[CellGroupData[{
Cell[35969, 791, 207, 3, 64, "Input",ExpressionUUID->"6457da42-bf61-4937-9829-04af6f58c39c"],
Cell[36179, 796, 253, 5, 64, "Output",ExpressionUUID->"d05aa51a-41f9-4510-ac2e-1d608d7a7eb2"]
}, Open  ]],
Cell[36447, 804, 1239, 29, 91, "Input",ExpressionUUID->"616ad8d7-5837-425a-a387-8af25a043737"],
Cell[CellGroupData[{
Cell[37711, 837, 205, 3, 64, "Input",ExpressionUUID->"852cb80d-d993-4b8a-806e-455e37a53903"],
Cell[37919, 842, 237, 4, 64, "Output",ExpressionUUID->"b02a64a6-9d4a-4e68-a9b1-52fbb6c35c5e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[38193, 851, 493, 13, 83, "Input",ExpressionUUID->"d4ba3f0c-9dc5-407d-a885-df629f420872"],
Cell[38689, 866, 233, 4, 64, "Output",ExpressionUUID->"7b7f1067-27e8-42a5-83a9-34441f7de82e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[38959, 875, 885, 23, 91, "Input",ExpressionUUID->"81d46395-cbc5-4ee7-afed-4bcd66f7ab19"],
Cell[39847, 900, 303, 8, 85, "Output",ExpressionUUID->"251977bd-68c8-408a-a170-44454e2b9a81"]
}, Open  ]],
Cell[CellGroupData[{
Cell[40187, 913, 295, 6, 64, "Input",ExpressionUUID->"cfc3778c-a80d-4fe9-a6ad-0a630de1fa6a"],
Cell[40485, 921, 740, 21, 85, "Output",ExpressionUUID->"7d0bb8cb-2bc6-44c6-a64b-d0bd2f039799"]
}, Open  ]],
Cell[41240, 945, 521, 13, 91, "Input",ExpressionUUID->"d99bbdc3-0c10-4959-9ee4-3e07a178e6d0"],
Cell[CellGroupData[{
Cell[41786, 962, 684, 15, 64, "Input",ExpressionUUID->"98e06414-6578-41da-b0a7-0f0c3cde4df6"],
Cell[42473, 979, 1461, 36, 187, "Output",ExpressionUUID->"3bd46017-8c8b-452b-ad48-fa00367ea398"]
}, Closed]],
Cell[CellGroupData[{
Cell[43971, 1020, 706, 15, 58, "Input",ExpressionUUID->"4d1cdd0e-4f48-4045-ac57-b73bfb043adb"],
Cell[44680, 1037, 1271, 22, 187, "Output",ExpressionUUID->"08f25e22-ea16-4693-aef5-5b998e8eecae"]
}, Closed]],
Cell[CellGroupData[{
Cell[45988, 1064, 537, 13, 58, "Input",ExpressionUUID->"a28c7106-e41e-4009-a839-ea1fdbf01ad4"],
Cell[46528, 1079, 1272, 22, 187, "Output",ExpressionUUID->"947bb949-26a0-411a-93c5-934e6d741aaa"]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell[47849, 1107, 227, 4, 68, "Section",ExpressionUUID->"5349232d-260c-402a-84c4-88c8a59b01a0"],
Cell[48079, 1113, 669, 19, 143, "Input",ExpressionUUID->"e15c9255-feb2-42e8-8915-5986db297514"],
Cell[CellGroupData[{
Cell[48773, 1136, 828, 17, 90, "Input",ExpressionUUID->"e699b49c-75c5-41ec-961e-f1a2c76ae117"],
Cell[49604, 1155, 41209, 698, 499, "Output",ExpressionUUID->"ebc66c5b-281e-4509-a41e-b4683c0b198b"]
}, Open  ]],
Cell[CellGroupData[{
Cell[90850, 1858, 903, 18, 90, "Input",ExpressionUUID->"40ef4ed8-8556-4240-af3e-3bf5055db1ab"],
Cell[91756, 1878, 15081, 270, 499, "Output",ExpressionUUID->"832be5bd-4a9f-4e4e-9a17-a40028ccca54"]
}, Open  ]],
Cell[CellGroupData[{
Cell[106874, 2153, 905, 18, 90, "Input",ExpressionUUID->"057faa31-7128-46e1-b540-de122161acd1"],
Cell[107782, 2173, 8543, 162, 500, "Output",ExpressionUUID->"e476d7c3-8efb-4723-b880-370009d08154"]
}, Open  ]],
Cell[116340, 2338, 188, 3, 41, "Text",ExpressionUUID->"f2483416-bd9e-4b71-b57b-5d6e14076ee0"],
Cell[CellGroupData[{
Cell[116553, 2345, 636, 15, 64, "Input",ExpressionUUID->"972c891e-8410-43c9-9ac5-2d5ed62efec6"],
Cell[117192, 2362, 1047, 26, 64, "Output",ExpressionUUID->"103c0773-af67-4b76-9f81-36af9d6ae9c2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[118276, 2393, 208, 3, 64, "Input",ExpressionUUID->"5ca3d32b-faa0-4626-9b3c-fe6edaefe8c9"],
Cell[118487, 2398, 152, 2, 64, "Output",ExpressionUUID->"c741c357-f6c2-4ff5-bade-346847ba8fdc"]
}, Open  ]],
Cell[CellGroupData[{
Cell[118676, 2405, 374, 9, 64, "Input",ExpressionUUID->"4c785609-46cb-4390-8f98-cef3e05fa2c8"],
Cell[119053, 2416, 150, 2, 64, "Output",ExpressionUUID->"3232ea83-0d98-4909-a9f0-17130feb3af6"]
}, Open  ]],
Cell[CellGroupData[{
Cell[119240, 2423, 407, 10, 68, "Input",ExpressionUUID->"4714c13f-f101-4586-9bf4-caf6299b0225"],
Cell[119650, 2435, 193, 2, 64, "Output",ExpressionUUID->"fc0036cf-084c-4bb4-a811-49b4c92740ba"]
}, Open  ]],
Cell[119858, 2440, 319, 7, 41, "Text",ExpressionUUID->"7e3db950-9050-469e-8019-06b1cc06cd51"],
Cell[CellGroupData[{
Cell[120202, 2451, 2347, 47, 203, "Input",ExpressionUUID->"696667d7-460e-496f-b64a-7e9e2276ea9f"],
Cell[122552, 2500, 584, 12, 27, "Message",ExpressionUUID->"607945a0-0884-4540-ab2d-6744ad671774"],
Cell[123139, 2514, 586, 12, 27, "Message",ExpressionUUID->"a667d08d-c462-4d02-93e8-6df804dc182d"],
Cell[123728, 2528, 586, 12, 27, "Message",ExpressionUUID->"16c6fc94-1607-4d97-845a-7e0d4f55030a"],
Cell[124317, 2542, 453, 10, 27, "Message",ExpressionUUID->"8abe6b18-5d88-467a-b44f-cf88ce7c2731"],
Cell[124773, 2554, 1926, 34, 244, "Output",ExpressionUUID->"c10a2898-f06e-4abb-b5cd-2db15e6da63f"]
}, Open  ]],
Cell[CellGroupData[{
Cell[126736, 2593, 257, 4, 64, "Input",ExpressionUUID->"47229937-a07f-43ba-8b98-91e4d3ff1e63"],
Cell[126996, 2599, 150, 2, 64, "Output",ExpressionUUID->"d7c140c7-2cec-4e00-bdab-8629402dd3a6"]
}, Open  ]],
Cell[127161, 2604, 220, 3, 41, "Text",ExpressionUUID->"ed9168f9-076c-4605-a2a8-3a66efdc58e0"],
Cell[CellGroupData[{
Cell[127406, 2611, 371, 8, 64, "Input",ExpressionUUID->"797fe3c2-c723-4656-a846-7a7c52aba7f1"],
Cell[127780, 2621, 1231, 24, 123, "Output",ExpressionUUID->"5d8b7e2f-95e4-4338-9a0b-7c8407f69ab2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[129048, 2650, 496, 13, 68, "Input",ExpressionUUID->"4306108b-7077-48cc-a6fd-d4eb144e7027"],
Cell[129547, 2665, 1343, 24, 167, "Output",ExpressionUUID->"2d8cfe58-2f42-471b-9266-5809d1615558"]
}, Open  ]],
Cell[130905, 2692, 178, 3, 41, "Text",ExpressionUUID->"7f4e63b2-ef76-40fd-ba21-9e7ff3f04439"],
Cell[CellGroupData[{
Cell[131108, 2699, 533, 13, 64, "Input",ExpressionUUID->"af0f118f-bef6-42de-a921-ddf50f1b1094"],
Cell[131644, 2714, 1658, 43, 167, "Output",ExpressionUUID->"a677d275-b630-4efd-a324-a1c22567766b"]
}, Open  ]],
Cell[133317, 2760, 175, 4, 50, "Input",ExpressionUUID->"7374bbb4-6993-40c9-8086-4c5f63831f9e"]
}, Closed]],
Cell[CellGroupData[{
Cell[133529, 2769, 203, 4, 68, "Section",ExpressionUUID->"cbb13f6a-ec05-418a-9f9c-8240bc3ba96a"],
Cell[133735, 2775, 235, 4, 50, "Input",ExpressionUUID->"5629fab6-131d-421a-9d65-ec4d7a6921af"],
Cell[133973, 2781, 779, 21, 41, "Text",ExpressionUUID->"d9f49424-e87d-4a22-b6be-4f213fc41f2d"],
Cell[134755, 2804, 1844, 42, 95, "Input",ExpressionUUID->"19675129-00b5-4048-9b53-9a19f08f1ae0"],
Cell[CellGroupData[{
Cell[136624, 2850, 207, 3, 50, "Input",ExpressionUUID->"025c923a-204f-437d-bcb6-e6cc47dd25ad"],
Cell[136834, 2855, 295, 8, 64, "Output",ExpressionUUID->"e65b493e-36b3-442a-b7a7-c46deec366ed"]
}, Open  ]],
Cell[137144, 2866, 937, 21, 128, "Input",ExpressionUUID->"5f1f8136-89c3-4af8-8425-8237b9d1fe75"],
Cell[CellGroupData[{
Cell[138106, 2891, 209, 3, 50, "Input",ExpressionUUID->"79f05c73-3bdc-49c2-b9e9-5ede12165df3"],
Cell[138318, 2896, 9956, 347, 193, "Output",ExpressionUUID->"666a3f7a-51e7-4dda-af0a-3e51246d4740"]
}, Open  ]],
Cell[CellGroupData[{
Cell[148311, 3248, 487, 11, 50, "Input",ExpressionUUID->"70bf3875-4b21-464f-9aa7-d34e92e7e0a3"],
Cell[148801, 3261, 383, 11, 64, "Output",ExpressionUUID->"5bba4ca0-b67f-4b07-afdf-b9e250843daa"]
}, Open  ]],
Cell[CellGroupData[{
Cell[149221, 3277, 540, 12, 64, "Input",ExpressionUUID->"e9d6db7b-7baf-44bd-99a6-9017c695a1d0"],
Cell[149764, 3291, 638, 21, 64, "Output",ExpressionUUID->"b28b31af-0a18-443c-b2cd-6c8cc5d0f98a"]
}, Open  ]]
}, Closed]]
}
]
*)