CSS Lab 04 Solution.nb

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

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

(* CreatedBy='Mathematica 12.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[    102115,       2389]
NotebookOptionsPosition[     92438,       2226]
NotebookOutlinePosition[     92810,       2242]
CellTagsIndexPosition[     92767,       2239]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[TextData[StyleBox["Computing Software Systems\nLaboratory 4",
 FontSize->36,
 FontColor->RGBColor[0.5, 0, 0.5],
 Background->RGBColor[0.94, 0.88, 0.94]]], "Text",
 CellChangeTimes->{{3.9077400652968483`*^9, 3.9077400922344475`*^9}},
 TextAlignment->0.5,ExpressionUUID->"d987b510-abf8-431d-adee-930b2ec8ff85"],

Cell[TextData[StyleBox["Solution of Exercise 01 (a):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.907740161936265*^9, 3.907740170201645*^9}, {
  3.9077414768844266`*^9, 3.9077414787126865`*^9}},
 TextAlignment->Center,ExpressionUUID->"ce3a1209-5540-4606-bb53-377bb60ac9db"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"a", "[", "n_", "]"}], ":=", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{"9", "-", 
      FractionBox[
       RowBox[{
        RowBox[{"8", " ", 
         SuperscriptBox["n", "2"]}], "+", "1"}], 
       SuperscriptBox["n", "2"]]}], ")"}], 
    RowBox[{"7", " ", 
     SuperscriptBox["n", "2"]}]]}], ";", 
  RowBox[{"g", "=", 
   RowBox[{"Limit", "[", 
    RowBox[{
     RowBox[{"a", "[", "n", "]"}], ",", 
     RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.9077407157267427`*^9, 3.9077407607408752`*^9}},
 CellLabel->"In[5]:=",ExpressionUUID->"a24230bb-37bc-4ba6-9692-9bf9dab0932b"],

Cell[BoxData[
 FractionBox["1", 
  SuperscriptBox["\[ExponentialE]", "7"]]], "Output",
 CellChangeTimes->{3.9077407625220613`*^9, 3.9083445762282567`*^9},
 CellLabel->"Out[5]=",ExpressionUUID->"74b6fb6d-14fd-4fc3-893e-819ae5c73b4c"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ListPlot", "[", 
    RowBox[{
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"n", ",", 
         RowBox[{"a", "[", "n", "]"}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"n", ",", "1", ",", "75"}], "}"}]}], "]"}], ",", 
     RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}], ",", 
   RowBox[{"Plot", "[", 
    RowBox[{"g", ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "1", ",", "100"}], "}"}], ",", 
     RowBox[{"PlotStyle", "\[Rule]", "Yellow"}]}], "]"}], ",", 
   RowBox[{"Background", "\[Rule]", "Black"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.907740522594919*^9, 3.9077405505938125`*^9}, {
  3.9077406405194497`*^9, 3.9077406529880314`*^9}, {3.9077407689280643`*^9, 
  3.907740890234212*^9}, {3.9077409509214797`*^9, 3.9077409513589935`*^9}, {
  3.9077410136079383`*^9, 3.907741034482455*^9}, {3.9083445389128485`*^9, 
  3.908344568618499*^9}, {3.9083446076666775`*^9, 3.908344666994492*^9}, {
  3.908344775475664*^9, 3.9083447965530443`*^9}},
 CellLabel->"In[13]:=",ExpressionUUID->"1573084d-eea4-4af7-be35-9abb5c7496a2"],

Cell[BoxData[
 GraphicsBox[{{{}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
      0.011000000000000001`], AbsoluteThickness[1.6], PointBox[CompressedData["
1:eJxVy38s1HEcx/HvKpaVpUbU/OFuZaTM4ZK7Oq/j3Plxd+7OahEVm26mUKYt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       "]]}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.011000000000000001`], AbsoluteThickness[1.6]}, {}}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.011000000000000001`], AbsoluteThickness[
       1.6]}, {}}}, {{}, {}}}, {{{}, {}, 
     TagBox[
      {RGBColor[1, 1, 0], AbsoluteThickness[1.6], Opacity[1.], 
       LineBox[CompressedData["
1:eJxTTMoPSmViYGAwAWIQ7Z0SKcfE8MG+f6XKnOyHvva7tB4qH+z+D+dPqdgi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        "]]},
      Annotation[#, "Charting`Private`Tag$3870#1"]& ]}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  Background->GrayLevel[0],
  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]],
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 75.}, {0, 0.0009113146816034999}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.907740541328549*^9, 3.907740551734414*^9}, {
   3.9077408744579315`*^9, 3.9077408922967076`*^9}, 3.907740952405842*^9, {
   3.907741016873474*^9, 3.90774103526367*^9}, 3.9083445803065615`*^9, {
   3.908344615713619*^9, 3.9083446679008093`*^9}, {3.9083447780068264`*^9, 
   3.9083447976311255`*^9}},
 CellLabel->"Out[13]=",ExpressionUUID->"39fd421e-3ba1-44d2-bfb8-8aa8e99736bd"]
}, Open  ]],

Cell[TextData[StyleBox["Solution of Exercise 01 (b):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.907741040919775*^9, 3.90774104921646*^9}, {
  3.90774148619759*^9, 3.9077414894634304`*^9}},
 TextAlignment->Center,ExpressionUUID->"0f3ec151-5db5-4439-b6ce-d72faec84f8c"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"a", "[", "n_", "]"}], ":=", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{"1", "+", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", "n"}], "+", "3"}], ")"}], 
       RowBox[{"-", "1"}]]}], ")"}], 
    RowBox[{"6", " ", "n"}]]}], ";", 
  RowBox[{"g", "=", 
   RowBox[{"Limit", "[", 
    RowBox[{
     RowBox[{"a", "[", "n", "]"}], ",", 
     RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.9077411009089174`*^9, 3.9077411285990963`*^9}},
 CellLabel->"In[15]:=",ExpressionUUID->"b8f64d3b-9fea-4e0d-8ff4-47775b0a1c47"],

Cell[BoxData[
 SuperscriptBox["\[ExponentialE]", "3"]], "Output",
 CellChangeTimes->{3.9077411362247*^9, 3.9077416305270476`*^9, 
  3.908344851363448*^9},
 CellLabel->"Out[15]=",ExpressionUUID->"350937ee-34a3-494b-b5f9-21402a162acf"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ListPlot", "[", 
    RowBox[{
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"n", ",", 
         RowBox[{"a", "[", "n", "]"}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"n", ",", "1", ",", "1000"}], "}"}]}], "]"}], ",", 
     RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}], ",", 
   RowBox[{"Plot", "[", 
    RowBox[{"g", ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "1", ",", "1000"}], "}"}], ",", 
     RowBox[{"PlotStyle", "\[Rule]", "Orange"}]}], "]"}], ",", 
   RowBox[{"Background", "\[Rule]", "Black"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.9077411554603996`*^9, 3.90774119733731*^9}, {
   3.9077413912153697`*^9, 3.907741445535515*^9}, {3.9077416121989594`*^9, 
   3.9077416396989*^9}, 3.908344696400073*^9, {3.9083448212396154`*^9, 
   3.9083448308486276`*^9}, {3.9083448694721336`*^9, 3.908344879721716*^9}},
 CellLabel->"In[18]:=",ExpressionUUID->"26daecdc-499c-4ce8-971a-fffc507379d4"],

Cell[BoxData[
 GraphicsBox[{{{}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
      0.0055000000000000005`], AbsoluteThickness[1.6], 
      PointBox[CompressedData["
1:eJw91HlcDPr/PfCxFrqEkITsyVIIIRxLKlnGllJp2lQk0z7t0zTV1FSyZx97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       "]]}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.0055000000000000005`], AbsoluteThickness[1.6]}, {}}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.0055000000000000005`], AbsoluteThickness[
       1.6]}, {}}}, {{}, {}}}, {{{}, {}, 
     TagBox[
      {RGBColor[1, 0.5, 0], AbsoluteThickness[1.6], Opacity[1.], 
       LineBox[CompressedData["
1:eJxTTMoPSmViYGAwAWIQfeLO6QRRhg/2bBvz9z8VNXGIWN7+5NVsVQcYv+dl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        "]]},
      Annotation[#, "Charting`Private`Tag$4197#1"]& ]}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  Background->GrayLevel[0],
  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]],
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 1000.}, {0, 19.980548666376766`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.908344855957017*^9, 3.9083448810341797`*^9}},
 CellLabel->"Out[18]=",ExpressionUUID->"bc77a39a-3b45-4453-82c0-f76b373a78f5"]
}, Open  ]],

Cell[TextData[StyleBox["Solution of Exercise 01 (c):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.9077414542238736`*^9, 3.907741463177821*^9}, {
  3.9077414951043873`*^9, 3.9077414974951715`*^9}},
 TextAlignment->Center,ExpressionUUID->"6d252b1e-b9e0-47bd-a25a-be2e4d0275c6"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"a", "[", "n_", "]"}], ":=", 
   FractionBox[
    RowBox[{
     RowBox[{"3", " ", 
      SuperscriptBox["2", 
       RowBox[{
        RowBox[{"2", " ", "n"}], "+", "1"}]]}], "-", "8"}], 
    RowBox[{
     SuperscriptBox["4", 
      RowBox[{"n", "-", "1"}]], "+", "3"}]]}], ";", 
  RowBox[{"g", "=", 
   RowBox[{"Limit", "[", 
    RowBox[{
     RowBox[{"a", "[", "n", "]"}], ",", 
     RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.907741543979206*^9, 3.907741577401812*^9}},
 CellLabel->"In[19]:=",ExpressionUUID->"6c4a0842-456c-4e9b-a071-305b9463da30"],

Cell[BoxData["24"], "Output",
 CellChangeTimes->{3.9077415815737376`*^9, 3.9077416917608094`*^9, 
  3.908344905720714*^9},
 CellLabel->"Out[19]=",ExpressionUUID->"4d42dec4-d15b-4016-9139-80f27981cf6f"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ListPlot", "[", 
    RowBox[{
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"n", ",", 
         RowBox[{"a", "[", "n", "]"}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"n", ",", "1", ",", "50"}], "}"}]}], "]"}], ",", 
     RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}], ",", 
   RowBox[{"Plot", "[", 
    RowBox[{"g", ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "1", ",", "100"}], "}"}], ",", 
     RowBox[{"PlotStyle", "\[Rule]", "Yellow"}]}], "]"}], ",", 
   RowBox[{"Background", "\[Rule]", "Black"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.9077417118073287`*^9, 3.907741731431919*^9}, 
   3.908344699853106*^9, {3.9083449109704905`*^9, 3.908344919485794*^9}},
 CellLabel->"In[20]:=",ExpressionUUID->"dca1b2d0-4600-476d-9c01-739381647175"],

Cell[BoxData[
 GraphicsBox[{{{}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
      0.011000000000000001`], AbsoluteThickness[1.6], PointBox[CompressedData["
1:eJxd0DtKxFAYBeCjVarEwkLEQmUQFZFxfI3POb5nwErEBQgWNroFKxdgZe0K
Ym8xpVjYCK4iMoNodXGuNzfJT/KHhMOXkxNIpi5vz66GATTclWZ29FtZjjC/
wc5DzZ1zuQM+vdx/j78ts3ju87Ednb+v5R5lZC6aX/F67jE+X7/+hEnhCd4E
Hz2YwpMMTm3YHRSeZv2vh9gWrvHXhkjEM0QfMOJZIkJ3IJ6nq2MrXmAENxcv
ciidi+su3Vy8RD8XN+jn4vS7Tckr9HPxKv1c7P5LUrZLU3aTfi7eoJ+LN5lU
vEVT8TZtxTvy3ix3lVvKrPpOGXuqV8a+6pVxoHplHKpeGUeqV8ax6pVxonpl
tFWvjI74H8k0ocs=
       "]]}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.011000000000000001`], AbsoluteThickness[1.6]}, {}}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.011000000000000001`], AbsoluteThickness[
       1.6]}, {}}}, {{}, {}}}, {{{}, {}, 
     TagBox[
      {RGBColor[1, 1, 0], AbsoluteThickness[1.6], Opacity[1.], 
       LineBox[CompressedData["
1:eJxTTMoPSmViYGAwAWIQ7Z0SKcfE8MGeAQwsHHZpPVQ+2P0fzp9SsUXkQDe7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        "]]},
      Annotation[#, "Charting`Private`Tag$4404#1"]& ]}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  Background->GrayLevel[0],
  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]],
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 50.}, {0, 24.}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.9077417021668797`*^9, 3.907741732103779*^9}, 
   3.9083449246574497`*^9},
 CellLabel->"Out[20]=",ExpressionUUID->"4baa943f-c2d4-418d-a831-39327dcf83e8"]
}, Open  ]],

Cell[TextData[StyleBox["Solution of Exercise 01 (d):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.907741736963046*^9, 3.9077417499783726`*^9}},
 TextAlignment->Center,ExpressionUUID->"5093cd0f-1583-41a5-bb1a-290407481afa"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"a", "[", "n_", "]"}], ":=", 
   FractionBox[
    RowBox[{
     SuperscriptBox["n", "6"], "+", 
     SuperscriptBox["n", "5"]}], 
    RowBox[{
     SuperscriptBox["2", "n"], "+", 
     SuperscriptBox["3", "n"]}]]}], ";", 
  RowBox[{"g", "=", 
   RowBox[{"Limit", "[", 
    RowBox[{
     RowBox[{"a", "[", "n", "]"}], ",", 
     RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.907741785883691*^9, 3.907741808383031*^9}},
 CellLabel->"In[21]:=",ExpressionUUID->"e4e20de2-c7ee-42c1-834c-378b53d21b87"],

Cell[BoxData["0"], "Output",
 CellChangeTimes->{3.907741812554783*^9, 3.9083449464378386`*^9},
 CellLabel->"Out[21]=",ExpressionUUID->"191e19b1-18ea-40c2-8fdf-6c40beddd0ab"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ListPlot", "[", 
    RowBox[{
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"n", ",", 
         RowBox[{"a", "[", "n", "]"}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"n", ",", "1", ",", "25"}], "}"}]}], "]"}], ",", 
     RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}], ",", 
   RowBox[{"Plot", "[", 
    RowBox[{"g", ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "1", ",", "300"}], "}"}], ",", 
     RowBox[{"PlotStyle", "\[Rule]", "Orange"}]}], "]"}], ",", 
   RowBox[{"Background", "\[Rule]", "Black"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.907741832507307*^9, 3.9077418487568226`*^9}, 
   3.9083447057279654`*^9, 3.9083449394693794`*^9},
 CellLabel->"In[22]:=",ExpressionUUID->"a19c0f96-81cb-48d2-953b-4d4c5e37de5d"],

Cell[BoxData[
 GraphicsBox[{{{}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
      0.012833333333333334`], AbsoluteThickness[1.6], PointBox[CompressedData["
1:eJxTTMoPSmViYGCQBGIQDQEf7GfNBIGb9lABh3k3Oufe6JR1gHA5HCJqjobX
HLWG8gUcpLbNfuqZ4gXlizj06O16sYg7EMqXcGCMiV77XwPGl3F4fLHpsAeX
L5Sv4CCUpvSmYKErlK/kcHzinQgvW1soX8XhxrZvXgv9jaB8NQc//knCzyeq
QvkaDhpKbqZemhJQvpZDwdrQewqfOaF8HYfAlEXOwk9/Qf2j5+Aerr30HMdr
KN/AIXTNasXosltQvqFDh3JzXozfSSjfyCFlwSITzq3boXxjh6Twshabc0uh
fBOHr0Vtv3fsmgzlmzr8eRet1jqtEco3c9idKnA/7kMelG/uYHW+dk7dwygo
38KBw1T5v5mEO5Rv6ZD7MdQwa7GxPQBlPGb2
       "]]}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.012833333333333334`], AbsoluteThickness[1.6]}, {}}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.012833333333333334`], AbsoluteThickness[
       1.6]}, {}}}, {{}, {}}}, {{{}, {}, 
     TagBox[
      {RGBColor[1, 0.5, 0], AbsoluteThickness[1.6], Opacity[1.], 
       LineBox[CompressedData["
1:eJxFz3ssFAAcB/Dz2BU5LdnlSOu2SBhhpaY7om7qwu0mj7O7eVdcnDvJOXlM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        "]]},
      Annotation[#, "Charting`Private`Tag$4553#1"]& ]}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0.5, 0},
  Background->GrayLevel[0],
  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]],
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0.5, 25.}, {0, 68.640605296343}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.907741823163843*^9, 3.907741849413034*^9}, 
   3.908344950062693*^9},
 CellLabel->"Out[22]=",ExpressionUUID->"af9efc6e-b5bd-4fe4-be1e-eec13d774ae2"]
}, Open  ]],

Cell[TextData[StyleBox["Solution of Exercise 01 (e):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.9077418590064783`*^9, 3.907741870193637*^9}},
 TextAlignment->Center,ExpressionUUID->"044f4b69-312e-4de4-98ba-3a6f529bea7d"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"a", "[", "n_", "]"}], ":=", 
   RowBox[{
    UnderoverscriptBox["\[Sum]", 
     RowBox[{"k", "=", "1"}], "n"], 
    FractionBox["1", 
     SqrtBox[
      RowBox[{
       SuperscriptBox["n", "2"], "+", "k"}]]]}]}], ";", 
  RowBox[{"g", "=", 
   RowBox[{"Limit", "[", 
    RowBox[{
     RowBox[{"a", "[", "n", "]"}], ",", 
     RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.9077419348561707`*^9, 3.9077419414334035`*^9}, 
   3.907741987119296*^9, {3.907742046179682*^9, 3.907742123604945*^9}},
 CellLabel->"In[23]:=",ExpressionUUID->"8e59c243-e42f-4273-88a3-29d6b71e8604"],

Cell[BoxData["1"], "Output",
 CellChangeTimes->{{3.907742106183714*^9, 3.907742127464172*^9}, 
   3.907742972544989*^9, 3.908344968749451*^9},
 CellLabel->"Out[23]=",ExpressionUUID->"47428588-23c8-4836-9f7a-4104c6446bc1"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ListPlot", "[", 
    RowBox[{
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"n", ",", 
         RowBox[{"a", "[", "n", "]"}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"n", ",", "1", ",", "100"}], "}"}]}], "]"}], ",", 
     RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}], ",", 
   RowBox[{"Plot", "[", 
    RowBox[{"g", ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "1", ",", "300"}], "}"}], ",", 
     RowBox[{"PlotStyle", "\[Rule]", "Yellow"}]}], "]"}], ",", 
   RowBox[{"Background", "\[Rule]", "Black"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.907742153728819*^9, 3.907742156056859*^9}, 
   3.9083447094153595`*^9, {3.9083449747023396`*^9, 3.9083449819520483`*^9}},
 CellLabel->"In[24]:=",ExpressionUUID->"bb9a8025-d6cf-484d-b39b-0cdf81434d7e"],

Cell[BoxData[
 GraphicsBox[{{{}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6], PointBox[CompressedData["
1:eJw9yw1M1HUAxvG/qdhEkuJKFHOKQMCoIW+mvD3yqohw3B13h5KsBAqdUEK+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       "]]}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.009166666666666668], AbsoluteThickness[1.6]}, {}}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.009166666666666668], AbsoluteThickness[
       1.6]}, {}}}, {{}, {}}}, {{{}, {}, 
     TagBox[
      {RGBColor[1, 1, 0], AbsoluteThickness[1.6], Opacity[1.], 
       LineBox[CompressedData["
1:eJxTTMoPSmViYGAwAWIQ7c3LmMbG8MGeAQw+2DvF3Tt1pZLfAcZ/LxVneLlS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        "]]},
      Annotation[#, "Charting`Private`Tag$5147#1"]& ]}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0.6909745129754596},
  Background->GrayLevel[0],
  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]],
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 100.}, {0.6909745129754596, 0.997487608986133}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.907742146604067*^9, 3.907742157088069*^9}, 
   3.9083449829520106`*^9},
 CellLabel->"Out[24]=",ExpressionUUID->"7cd2fe01-161e-4ed6-b783-6978c0c47444"]
}, Open  ]],

Cell[TextData[StyleBox["Solution of Exercise 01 (f):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.907742171680669*^9, 3.907742177727318*^9}, {
  3.9077422121479244`*^9, 3.9077422173508525`*^9}},
 TextAlignment->Center,ExpressionUUID->"3736c737-18a4-4c24-899e-25574370743d"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"a", "[", "n_", "]"}], ":=", 
   FractionBox[
    SuperscriptBox["b", "n"], 
    RowBox[{"Factorial", "[", "n", "]"}]]}], ";", 
  RowBox[{"g", "=", 
   RowBox[{"Limit", "[", 
    RowBox[{
     RowBox[{"a", "[", "n", "]"}], ",", 
     RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.9077422511620874`*^9, 3.907742269348899*^9}, {
  3.907742568007308*^9, 3.907742569788488*^9}},
 CellLabel->"In[25]:=",ExpressionUUID->"278ca9f3-d4e9-47c9-b7a8-f725aaae4c4b"],

Cell[BoxData["0"], "Output",
 CellChangeTimes->{3.9077422728643904`*^9, 3.9077425760694857`*^9, 
  3.9077427303919587`*^9, 3.907743171934404*^9, 3.9083450064667206`*^9},
 CellLabel->"Out[25]=",ExpressionUUID->"866d9124-a9ae-4af6-bcb2-4cfc5f686c0a"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"b", "=", "10"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ListPlot", "[", 
    RowBox[{
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"n", ",", 
         RowBox[{"a", "[", "n", "]"}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"n", ",", "1", ",", "50"}], "}"}]}], "]"}], ",", 
     RowBox[{"PlotRange", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"-", "100"}], ",", "3000"}], "}"}]}]}], "]"}], ",", 
   RowBox[{"Plot", "[", 
    RowBox[{"g", ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "1", ",", "100"}], "}"}], ",", 
     RowBox[{"PlotStyle", "\[Rule]", "Orange"}]}], "]"}], ",", 
   RowBox[{"Background", "\[Rule]", "Black"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.907742290754343*^9, 3.907742316862714*^9}, {
   3.9077424056052713`*^9, 3.9077425211165442`*^9}, {3.9077425850066633`*^9, 
   3.907742638585784*^9}, {3.907742669574342*^9, 3.9077428818793344`*^9}, {
   3.9077431619335427`*^9, 3.907743175028412*^9}, 3.9083447129464903`*^9, {
   3.908345012497739*^9, 3.90834504649638*^9}},
 CellLabel->"In[32]:=",ExpressionUUID->"b417f71f-3820-456f-99d6-4bf9504f4558"],

Cell[BoxData[
 GraphicsBox[{{{}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
      0.011000000000000001`], AbsoluteThickness[1.6], PointBox[CompressedData["
1:eJxTTMoPSmViYGAwAmIQDQEf7CG0igNUAEp7QmkOh1AQuJoC5Qs4rF4FBFxV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       "]]}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.011000000000000001`], AbsoluteThickness[1.6]}, {}}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.011000000000000001`], AbsoluteThickness[
       1.6]}, {}}}, {{}, {}}}, {{{}, {}, 
     TagBox[
      {RGBColor[1, 0.5, 0], AbsoluteThickness[1.6], Opacity[1.], 
       LineBox[CompressedData["
1:eJxFznssFAAcB/Dbmdm1ldclCd1lk0y3budxhlwonfM6XJdR43ZW0Ry6yY3K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        "]]},
      Annotation[#, "Charting`Private`Tag$5762#1"]& ]}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  Background->GrayLevel[0],
  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]],
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 50.}, {-100, 3000}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {0, 0}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.9077422847076764`*^9, 3.907742318206435*^9}, {
  3.9077424068864703`*^9, 3.9077424359478855`*^9}, {3.907742477180709*^9, 
  3.9077425220227633`*^9}, {3.9077426080682755`*^9, 3.9077426394140205`*^9}, {
  3.907742688435671*^9, 3.907742882504214*^9}, {3.9077431628398757`*^9, 
  3.9077431755753326`*^9}, {3.9083450192943153`*^9, 3.9083450472932034`*^9}},
 CellLabel->"Out[33]=",ExpressionUUID->"51978104-7d52-48b4-a72a-144c5cfd0e3e"]
}, Open  ]],

Cell[TextData[StyleBox["Solution of Exercise 01 (g):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.907742891629156*^9, 3.9077429204365864`*^9}},
 TextAlignment->Center,ExpressionUUID->"ebe5f6af-a8bc-4077-9745-86950ee52e06"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"a", "[", "n_", "]"}], ":=", 
   FractionBox[
    RowBox[{"Cos", "[", 
     RowBox[{"2", " ", "n", " ", "\[Pi]"}], "]"}], "n"]}], ";", 
  RowBox[{"g", "=", 
   RowBox[{"Limit", "[", 
    RowBox[{
     RowBox[{"a", "[", "n", "]"}], ",", 
     RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.907743047668023*^9, 3.907743072011073*^9}},
 CellLabel->"In[34]:=",ExpressionUUID->"14bb7d8b-d46d-448a-a4e3-26ee8b752a77"],

Cell[BoxData["0"], "Output",
 CellChangeTimes->{3.9077430812763977`*^9, 3.9077432028506327`*^9, 
  3.9083450637769365`*^9},
 CellLabel->"Out[34]=",ExpressionUUID->"e767628f-96e5-4823-959d-77af33f208b9"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ListPlot", "[", 
    RowBox[{
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"n", ",", 
         RowBox[{"a", "[", "n", "]"}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"n", ",", "1", ",", "250"}], "}"}]}], "]"}], ",", 
     RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}], ",", 
   RowBox[{"Plot", "[", 
    RowBox[{"g", ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "1", ",", "1000"}], "}"}], ",", 
     RowBox[{"PlotStyle", "\[Rule]", "Yellow"}]}], "]"}], ",", 
   RowBox[{"Background", "\[Rule]", "Black"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.907743342732117*^9, 3.907743398233223*^9}, 
   3.9083447158214216`*^9, {3.9083450689173565`*^9, 3.908345120665293*^9}},
 CellLabel->"In[37]:=",ExpressionUUID->"2644eea2-df35-41e2-a227-7c53ed3b43ab"],

Cell[BoxData[
 GraphicsBox[{{{}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.007333333333333334],
       AbsoluteThickness[1.6], PointBox[CompressedData["
1:eJxV1XtUFPcVwPFZIkLUJKjEUKNhfSVaaEOqJiKmXFAB8cVLHvKaXVh22QeC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       "]]}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.007333333333333334], AbsoluteThickness[1.6]}, {}}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.007333333333333334], AbsoluteThickness[
       1.6]}, {}}}, {{}, {}}}, {{{}, {}, 
     TagBox[
      {RGBColor[1, 1, 0], AbsoluteThickness[1.6], Opacity[1.], 
       LineBox[CompressedData["
1:eJxFz3lI03EYBvBfdphItlYqZtk8SjymzSunyRIDh3mAizLLNcVpks6c97Wp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        "]]},
      Annotation[#, "Charting`Private`Tag$6064#1"]& ]}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  Background->GrayLevel[0],
  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]],
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 250.}, {0, 1.}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.90774333356001*^9, 3.9077433990613775`*^9}, {
  3.90834507847946*^9, 3.908345121399638*^9}},
 CellLabel->"Out[37]=",ExpressionUUID->"a20d8981-c735-44c1-9956-4626e29d254a"]
}, Open  ]],

Cell[TextData[StyleBox["Solution of Exercise 01 (h):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.907743405639594*^9, 3.9077434204366484`*^9}},
 TextAlignment->Center,ExpressionUUID->"2a62a73d-2a64-418a-99e7-45f0d6055324"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"a", "[", "n_", "]"}], ":=", 
   RowBox[{
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"1", "+", 
       SuperscriptBox["n", 
        RowBox[{"-", "1"}]]}], ")"}], "n"], "*", 
    RowBox[{"Cos", "[", 
     RowBox[{"2", " ", "n", " ", "\[Pi]"}], "]"}]}]}], ";", 
  RowBox[{"g", "=", 
   RowBox[{"Limit", "[", 
    RowBox[{
     RowBox[{"a", "[", "n", "]"}], ",", 
     RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.9077434529891634`*^9, 3.907743479614249*^9}, {
  3.907743739251552*^9, 3.90774374068902*^9}},
 CellLabel->"In[38]:=",ExpressionUUID->"231526e2-3d7d-471f-8c3f-3f9997d3dbd0"],

Cell[BoxData["Indeterminate"], "Output",
 CellChangeTimes->{3.907743484254859*^9, 3.907743741720228*^9, 
  3.9083451522265167`*^9},
 CellLabel->"Out[38]=",ExpressionUUID->"80dde39e-88a4-42eb-832e-602f1f255649"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ListPlot", "[", 
    RowBox[{
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"n", ",", 
         RowBox[{"a", "[", "n", "]"}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"n", ",", "1", ",", "100"}], "}"}]}], "]"}], ",", 
     RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}], ",", 
   RowBox[{"Plot", "[", 
    RowBox[{"g", ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "0", ",", "100"}], "}"}], ",", 
     RowBox[{"PlotStyle", "\[Rule]", "Orange"}]}], "]"}], ",", 
   RowBox[{"Background", "\[Rule]", "Black"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.9077435055829525`*^9, 3.9077435176610336`*^9}, {
   3.907743674815382*^9, 3.907743714033331*^9}, {3.90774375395434*^9, 
   3.9077438566079607`*^9}, 3.908344720149414*^9, {3.9083451453049164`*^9, 
   3.9083451885688305`*^9}, {3.90834523866057*^9, 3.9083452980331917`*^9}},
 CellLabel->"In[50]:=",ExpressionUUID->"2cd2fa8e-a04a-4deb-886c-8d7f47fe71f5"],

Cell[BoxData[
 GraphicsBox[{{{}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6], PointBox[CompressedData["
1:eJxVy39Q03Ucx/GB/MqVDQ7sh1E25UdDKRAy5IevgUMEgf1gbKnJT4Uz0MAD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       "]]}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.009166666666666668], AbsoluteThickness[1.6]}, {}}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.009166666666666668], AbsoluteThickness[
       1.6]}, {}}}, {{}, {}}}, {{}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 1.9608436761432486`},
  Background->GrayLevel[0],
  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]],
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 100.}, {1.9608436761432486`, 2.7048138294215263`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.907743675721616*^9, 3.9077437145489492`*^9}, {
  3.9077437446264143`*^9, 3.9077438578266973`*^9}, {3.9083451551795206`*^9, 
  3.908345189209416*^9}, {3.9083452464727697`*^9, 3.908345298939409*^9}},
 CellLabel->"Out[50]=",ExpressionUUID->"90e93c74-67b6-45d0-b950-02de98d2a40b"]
}, Open  ]],

Cell[TextData[StyleBox["Soluiton of Exercise 01 (i):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.907743879857319*^9, 3.9077438940444155`*^9}},
 TextAlignment->Center,ExpressionUUID->"d647b1e0-96fe-43b0-9eea-bd2e50e1f35c"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"a", "[", "n_", "]"}], ":=", 
   RowBox[{
    UnderoverscriptBox["\[Sum]", 
     RowBox[{"k", "=", "1"}], "n"], 
    RowBox[{
     FractionBox["1", "n"], 
     RowBox[{"(", 
      RowBox[{"Cos", "[", 
       FractionBox[
        RowBox[{"k", " ", "\[Pi]"}], 
        RowBox[{"2", " ", "n"}]], "]"}], ")"}]}]}]}], ";", 
  RowBox[{"g", "=", 
   RowBox[{"Limit", "[", 
    RowBox[{
     RowBox[{"a", "[", "n", "]"}], ",", 
     RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.907743943936655*^9, 3.9077439769512978`*^9}, {
  3.907744174008309*^9, 3.9077442003583107`*^9}},
 CellLabel->"In[51]:=",ExpressionUUID->"e4807c6a-344f-47d8-a6a8-56992aa82622"],

Cell[BoxData[
 FractionBox["2", "\[Pi]"]], "Output",
 CellChangeTimes->{3.907743979966816*^9, 3.907744206827166*^9, 
  3.9083453267992444`*^9},
 CellLabel->"Out[51]=",ExpressionUUID->"370a22f2-5f72-406b-9b9e-c1be63a540f1"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ListPlot", "[", 
    RowBox[{
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"n", ",", 
         RowBox[{"a", "[", "n", "]"}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"n", ",", "1", ",", "200"}], "}"}]}], "]"}], ",", 
     RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}], ",", 
   RowBox[{"Plot", "[", 
    RowBox[{"g", ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "1", ",", "250"}], "}"}], ",", 
     RowBox[{"PlotStyle", "\[Rule]", "Yellow"}]}], "]"}], ",", 
   RowBox[{"Background", "\[Rule]", "Black"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.9077440211217904`*^9, 3.907744022121739*^9}, {
   3.907744214733576*^9, 3.907744246468388*^9}, 3.9083447233524413`*^9, {
   3.9083452025995245`*^9, 3.9083452298640394`*^9}, {3.908345318455329*^9, 
   3.908345323486692*^9}},
 CellLabel->"In[52]:=",ExpressionUUID->"43de5983-e6ac-4a95-bcf8-ea63352a050d"],

Cell[BoxData[
 GraphicsBox[{{{}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6], PointBox[CompressedData["
1:eJxVzQlQUwcex/GnHGKhLCo3KhERjwAeQUUR+HEfYpQbAkISIIlOW+2CINZq
UGzFi3FRR221qSjairqxsArjka2Ld60ua+tFG0CkgHQVhVURWXY2v53ZN5N5
88n3/eY/QbkiIW+4IAhXh37/ef/3eRYs/P+DHwLWqw7qfjL9b4UrTfOfxXs2
mWyHj6NCW965GU22x8SzvoWWw5pNdsatr+9UfLeHHgur9QUNnkKLySLcHJCl
fyClPRAwO1l8dwvtic6VlZsf1dNeeC2vvtvbTE/B9sN7p2uGt5o8DVUlX/Rf
Gkd7I1k/JWTSbNoXlg+u2mXE0DOQ7CbqHpTRMzHNv6mobDk9C6XueY0Jq2kJ
0i/pT1eW0n7o6EsMry2nZ+PY9gP62n30HJwqfl11/RA9F8VVaTPHHKf9Eah4
f+I3p+l5iB8j9jhUR8/H8E2dRXYGOgC2K7fpzS7TC3CstmB82Q06EPOW90qq
b9NBmJPw5lHhXToYkuip9c/v08DRbx8ne/5ishaoqL8sdWhhD4GhrnzN9Tb2
EIwV25jFdLCH4vDqCet2P2UPRcjq7mE1/2QPwz6f72Yf62EPg/3JKfJVvezh
CIz5Mn/8K/ZweLYvdq56wx6BiKWptbYD7BF4Os5/tWyQPRJlgZ9mbB322NQj
oa5e5l1pZrIQhcczusorLdij4NrQabljBHs0SnxH9+SMZI9G4znX3V7W7DFw
6ah1+dmGPQYDneP+VGjLHgsrH1m/hR17LOzrQ4I/G8W+EImB4XNejWZfiIqn
wjeZ9uxxOF+lj69xYI/DthMrmgYd2Reh7euU7mBn9kV4e6XMaZULuxTHbd1/
+8qVXYqeX3uaDW7si5GeqV5/byz7YlgtGiVpH8e+BPtuJWm6x5uMJZhf9GJj
lzu/X4KbG7c/bhaZbFgCqcap9fYE7uNxri+88awH9/G4LO4y2z+R+3jU7Uy/
WODJfTx0ttULYyZxn4D3Hjp0OXlxn4CXMV6PjLQ2AfavRsgOT+Y+AbW/1X+p
nMJ9IsZaxd53m8p9IgbXvQ25TWsToZm70VI7jftE1HV4JInF3CehZvBB8t9p
JOFKRZnfKm/uk/D8ho2TvQ/3SSi8pvA4RQvJmKr4a3GkL/fJEN+oD3pAa5Ox
tyBu5/Lp3CfjrEt/+b9oIQVXF7anlszgPgVBG5rNrWZyn4Jd/1ir30obUuBe
JCqymcV9KlzGOH+0hUYq+v9QecJCwn0qlrcMj1tHG1LhlL856yUtpEF/Uvda
7cd9GmRS44z7tDYNPU9snaJnc5+G1LiZF2poIR01SRVz3edwn45uyzsVn9Pa
dBQE/drSTRvS8eKHMX4Jc7mXoWSqz54aGjLk69KdHPy5l2Gmb1BDPm2QQeh4
W32bFjJg7RDwUDyP+wzom70yN9HaDKh/WhvQRBsy8PHLbaWS+dxnYnBncOhm
GpnweeGy/iGtzcSTw6ERPgHcZ2L9gU0HP6WFpdjilbbrJo2lmFrxaLrrAu6X
or+hrVhFG5bio7I3a/S0kAXf82kB/TSy4JXx6vuwQO6zoErZ4bKVNmRhQkp5
5B1ayEaDdFa8YxD32RjV/0fIaG02BubYux2gDUM96FD7L7Qgx99uFVS7B5ss
kiPTT78im4YcR/3j5h6k5XI8eGc98hGtlePh1bJOZ5isk0M4JmlOog1yfOgq
7SmnjXJY7un1uE4LCvw+TLTaLIT3FShwP9gXQEOB6Naxlfm0XIFLF702fEtr
FXhr9NxrpHUKfJAh73AI5X0Fzi0yWxNLGxXI7XORrqMFJc6cr1imp0VKtPuF
326locSm9x5vcgjjfSWse0ftiKS1SjRWJD4tpHVKjIhyPFxFG5RoeXfq7F3a
qETNcLmPeTjv52DEnxdbzKJFOYiYVRGWTSMHYsm0rq20PAcrSoXBM7Q2B43f
/17SSutyYP6ivtA2gvdzUOjsYvSnjTnYc/m4QUkLuSitNnfbRotysdvtyPMa
Grl4sPldZBMtH/LI/HEWkbyfi2s3k4u8aV0uYrd1pSTShlzYDS6/UEwbc1EQ
NnDqK1rIgyTqgk8DLcrDJ+Lz8zpp5GHlkbd3baN4Pw9xGfnmElqbhwVBNldS
aF0eJjVXua+hDXnIuulkd4A25mHvrSn7L9KCCn2x+y420yIVPi8dv8EsmvdV
kLTntHrSchW8pdZtEbRWBcfoE5tVtE6Fe2n3f/yMNqiQOM/xXBVtVKHXvkV6
mRbUkDacLmujRWrUWvd9aB7D+2qMvjZqwIOWq3FPkusfQmuH9jbhE7JpnRpe
Pwp1a2mDGp88aRH200Y1ltwXv/kLLWhQUuxY1UiLNEiy+9ni2f/ua6Ar+8LV
Jpb3NTh6YGvbZFo71F9fVYfROg1GqlccyqINGlx7vmtPMW3UYPL7sRG7aGEZ
jpzZd+rkkP8NQMu5eA==
       "]]}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.009166666666666668], AbsoluteThickness[1.6]}, {}}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.009166666666666668], AbsoluteThickness[
       1.6]}, {}}}, {{}, {}}}, {{{}, {}, 
     TagBox[
      {RGBColor[1, 1, 0], AbsoluteThickness[1.6], Opacity[1.], 
       LineBox[CompressedData["
1:eJxTTMoPSmViYGAwAWIQza0sHsLK8MG++cTJXIP4J/acbxbtud7D7QDjuynP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        "]]},
      Annotation[#, "Charting`Private`Tag$7365#1"]& ]}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  Background->GrayLevel[0],
  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]],
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 200.}, {0, 0.6341164998718695}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.9077440530582786`*^9, {3.907744210499126*^9, 3.9077442482184563`*^9}, 
   3.908345332455615*^9},
 CellLabel->"Out[52]=",ExpressionUUID->"6b6d4492-3d0e-4ee3-b3de-624d37d7fc86"]
}, Open  ]],

Cell[TextData[StyleBox["Solution of Exercise 01 (j):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.9077442697256575`*^9, 3.9077442871319833`*^9}},
 TextAlignment->Center,ExpressionUUID->"7e4d9fe7-4900-4c5f-921f-324cf2ab8fc6"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"a", "[", "n_", "]"}], ":=", 
   RowBox[{
    UnderoverscriptBox["\[Sum]", 
     RowBox[{"k", "=", "1"}], "n"], 
    FractionBox["1", 
     RowBox[{"Factorial", "[", 
      RowBox[{"n", "+", "n"}], "]"}]]}]}], ";", 
  RowBox[{"g", "=", 
   RowBox[{"Limit", "[", 
    RowBox[{
     RowBox[{"a", "[", "n", "]"}], ",", 
     RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{
  3.907744319741431*^9, {3.907744349866357*^9, 3.907744386709861*^9}},
 CellLabel->"In[53]:=",ExpressionUUID->"e579065e-6016-47a2-81f7-e1ab2d1f9477"],

Cell[BoxData["0"], "Output",
 CellChangeTimes->{3.9077444068346477`*^9, 3.9083454928011336`*^9},
 CellLabel->"Out[53]=",ExpressionUUID->"aa43b679-0f1e-4161-900e-a45c3c387de7"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ListPlot", "[", 
    RowBox[{
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"n", ",", 
         RowBox[{"a", "[", "n", "]"}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"n", ",", "1", ",", "50"}], "}"}]}], "]"}], ",", 
     RowBox[{"PlotRange", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"-", "0.5"}], ",", "1"}], "}"}]}]}], "]"}], ",", 
   RowBox[{"Plot", "[", 
    RowBox[{"g", ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "1", ",", "500"}], "}"}], ",", 
     RowBox[{"PlotStyle", "\[Rule]", "Orange"}]}], "]"}], ",", 
   RowBox[{"Background", "\[Rule]", "Black"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.9077444282875395`*^9, 3.9077445383794303`*^9}, {
   3.907744804112876*^9, 3.9077448632536044`*^9}, 3.9083447263835793`*^9, {
   3.9083454799107933`*^9, 3.90834555175434*^9}},
 CellLabel->"In[59]:=",ExpressionUUID->"46242c98-3e21-4a64-95b0-3474ef68bee1"],

Cell[BoxData[
 GraphicsBox[{{{}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
      0.011000000000000001`], AbsoluteThickness[1.6], PointBox[CompressedData["
1:eJwt0VtIE3AUx/EpJHZZ6BardDF1ttZcOrepcxf9zcvcfLJV3is1JDMrG/kg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       "]]}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.011000000000000001`], AbsoluteThickness[1.6]}, {}}, {
      {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
       0.011000000000000001`], AbsoluteThickness[
       1.6]}, {}}}, {{}, {}}}, {{{}, {}, 
     TagBox[
      {RGBColor[1, 0.5, 0], AbsoluteThickness[1.6], Opacity[1.], 
       LineBox[CompressedData["
1:eJxNzn0w03EcB/B5CNOjzdOuuxRWhjXaucWtFjlCLdYuKZHM2A6TWGPJdTcu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        "]]},
      Annotation[#, "Charting`Private`Tag$8111#1"]& ]}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  Background->GrayLevel[0],
  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]],
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 50.}, {-0.5, 1}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {0, 0}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.907744837238*^9, 3.9077448639410768`*^9}, {
  3.9083455006446805`*^9, 3.908345552410683*^9}},
 CellLabel->"Out[59]=",ExpressionUUID->"a785a5ac-33f4-4fc0-aff5-271e2e84bc29"]
}, Open  ]],

Cell[TextData[StyleBox["Solution of Exercise 02:",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.9077467091476927`*^9, 3.9077467424460554`*^9}},
 TextAlignment->Center,ExpressionUUID->"70c1b3fd-e4f7-4b82-8e92-cc4ac9f64630"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"m", "[", "n_", "]"}], ":=", 
   FractionBox[
    RowBox[{"(", 
     RowBox[{"n", " ", 
      SuperscriptBox["R", "2"], " ", 
      RowBox[{"Sin", "[", 
       FractionBox[
        RowBox[{"2", " ", "\[Pi]"}], "n"], "]"}]}], ")"}], "2"]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"ReqRes02", "=", 
  RowBox[{"Limit", "[", 
   RowBox[{
    RowBox[{"m", "[", "n", "]"}], ",", 
    RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}]}]}], "Input",
 CellChangeTimes->{{3.9077468034968896`*^9, 3.9077469275013943`*^9}},
 CellLabel->"In[60]:=",ExpressionUUID->"9dae81f2-b891-4686-82cf-8c0001cecb00"],

Cell[BoxData[
 RowBox[{"\[Pi]", " ", 
  SuperscriptBox["R", "2"]}]], "Output",
 CellChangeTimes->{{3.907746914454204*^9, 3.907746929313904*^9}, 
   3.908345664936757*^9},
 CellLabel->"Out[61]=",ExpressionUUID->"f19b592b-4e77-494a-b43c-72136cbc74f7"]
}, Open  ]],

Cell[TextData[StyleBox["Another Solution of Exercise 02:",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.9077469485331774`*^9, 3.907746956283183*^9}, {
  3.9077470081743345`*^9, 3.9077470140962343`*^9}},
 TextAlignment->Center,ExpressionUUID->"1ce84a75-243f-403a-9875-32a1a13730c4"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"m", "[", "n_", "]"}], ":=", 
   RowBox[{"(", 
    RowBox[{"R", " ", 
     RowBox[{"Tan", "[", 
      FractionBox["\[Pi]", "n"], "]"}], " ", "R", " ", "n"}], ")"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"AReqRes02", "=", 
  RowBox[{"Limit", "[", 
   RowBox[{
    RowBox[{"m", "[", "n", "]"}], ",", 
    RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}]}]}], "Input",
 CellChangeTimes->{{3.9077470201275034`*^9, 3.9077471061681337`*^9}, {
  3.9083456825274143`*^9, 3.9083456857462826`*^9}, {3.9083457858882265`*^9, 
  3.9083457897788496`*^9}},
 CellLabel->"In[64]:=",ExpressionUUID->"e531c743-a55d-4dbc-a9a6-593d7254674b"],

Cell[BoxData[
 RowBox[{"\[Pi]", " ", 
  SuperscriptBox["R", "2"]}]], "Output",
 CellChangeTimes->{3.907747106964955*^9, 3.9083456874182*^9, 
  3.9083457993412685`*^9},
 CellLabel->"Out[65]=",ExpressionUUID->"d6bddda3-9230-4593-b8a2-155f2dff4921"]
}, Open  ]],

Cell[TextData[StyleBox["Solution of Exercise 03:",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.9077471154180655`*^9, 3.907747124417991*^9}},
 TextAlignment->Center,ExpressionUUID->"78f5cb02-3a96-4569-9643-0f3b5aa93fad"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"t", "[", "n_", "]"}], ":=", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"r", " ", 
      RowBox[{"Sin", "[", 
       FractionBox["\[Pi]", "n"], "]"}], " ", "r", " ", 
      RowBox[{"Cos", "[", 
       FractionBox["\[Pi]", "n"], "]"}]}], ")"}], "n"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"ReqRes03", "=", 
  RowBox[{"Limit", "[", 
   RowBox[{
    RowBox[{"t", "[", "n", "]"}], ",", 
    RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}]}]}], "Input",
 CellChangeTimes->{{3.907747153652027*^9, 3.907747254838011*^9}},
 CellLabel->"In[66]:=",ExpressionUUID->"9df3e826-903c-40f6-a709-d6bb0f7b6341"],

Cell[BoxData[
 RowBox[{"\[Pi]", " ", 
  SuperscriptBox["r", "2"]}]], "Output",
 CellChangeTimes->{3.9077472562598095`*^9, 3.9083458563624115`*^9},
 CellLabel->"Out[67]=",ExpressionUUID->"4f488e91-3518-42e4-b2f6-bd688ba18278"]
}, Open  ]],

Cell[TextData[StyleBox["Solution of Exercise 04 (a):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.9077453271856065`*^9, 3.9077453601440372`*^9}, {
  3.9077455226284466`*^9, 3.9077455259252067`*^9}},
 TextAlignment->Center,ExpressionUUID->"9e452dc8-b0ca-4e23-84a0-56c04a8f8827"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"a", "[", "n_", "]"}], ":=", 
  FractionBox[
   RowBox[{
    SqrtBox["n"], "+", "7"}], 
   RowBox[{
    RowBox[{"3", " ", 
     SqrtBox["n"]}], "+", "5"}]]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Reduce", "[", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"a", "[", 
       RowBox[{"n", "+", "1"}], "]"}], "-", 
      RowBox[{"a", "[", "n", "]"}]}], "<", "0"}], ",", "n"}], "]"}], "//", 
  "N"}]}], "Input",
 CellChangeTimes->{{3.907745411552577*^9, 3.907745495769294*^9}},
 CellLabel->"In[68]:=",ExpressionUUID->"92269ca2-f7ef-49f7-9957-3cf260ffc070"],

Cell[BoxData[
 RowBox[{"n", "\[GreaterEqual]", "0.`"}]], "Output",
 CellChangeTimes->{3.9077454974254637`*^9, 3.908345862238061*^9},
 CellLabel->"Out[69]=",ExpressionUUID->"7ded1182-3052-45b4-ba78-267d147bcc1a"]
}, Open  ]],

Cell[TextData[StyleBox["Solution of Exercise 04 (b):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.9077455289875813`*^9, 3.9077455407059617`*^9}},
 TextAlignment->Center,ExpressionUUID->"bf67d681-8004-43cc-810d-f98274a5addf"],

Cell[BoxData[
 RowBox[{"Clear", "[", 
  RowBox[{"b", ",", "n"}], "]"}]], "Input",
 CellChangeTimes->{{3.9077498473358927`*^9, 3.90774985449265*^9}, {
  3.907749982044862*^9, 3.907749982482435*^9}},
 CellLabel->"In[75]:=",ExpressionUUID->"bcd2a070-8918-401e-ad68-10c985346aa3"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"b", "[", "n_", "]"}], ":=", 
   FractionBox[
    RowBox[{
     SuperscriptBox["2", "n"], "*", 
     RowBox[{"Factorial", "[", "n", "]"}]}], 
    SuperscriptBox["n", "n"]]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Reduce", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"Simplify", "[", 
      FractionBox[
       RowBox[{"b", "[", 
        RowBox[{"n", "+", "1"}], "]"}], 
       RowBox[{"b", "[", "n", "]"}]], "]"}], "<", "1"}], ",", "n", ",", 
    "Integers"}], "]"}], "//", "N"}]}], "Input",
 CellChangeTimes->{{3.907750203014904*^9, 3.9077502751858244`*^9}},
 CellLabel->"In[76]:=",ExpressionUUID->"576ddb9f-8c2e-433e-9ba2-05cf2046cd72"],

Cell[BoxData[
 TemplateBox[{
  "Reduce","fexp",
   "\"Warning: \\!\\(\\*RowBox[{\\\"Reduce\\\"}]\\) used FunctionExpand to \
transform the system. Since FunctionExpand transformation rules are only \
generically correct, the solution set might have been altered.\"",2,77,12,
   19687389629109123352,"Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{3.9083459219035606`*^9},
 CellLabel->
  "During evaluation of \
In[76]:=",ExpressionUUID->"66be2a03-daff-47b9-b906-05d4b216f1ab"],

Cell[BoxData[
 RowBox[{
  RowBox[{"(", 
   RowBox[{
    RowBox[{"n", "\[Element]", 
     TemplateBox[{},
      "Integers"]}], "&&", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"n", "\[LessEqual]", 
       RowBox[{"-", "2.`"}]}], "||", 
      RowBox[{"n", "\[GreaterEqual]", "2.`"}], "||", 
      RowBox[{"n", "\[LessEqual]", 
       RowBox[{"-", "1.`"}]}], "||", 
      RowBox[{"n", "\[GreaterEqual]", "2.`"}]}], ")"}]}], ")"}], "||", 
  RowBox[{"n", "\[Equal]", 
   RowBox[{"-", "1.`"}]}], "||", 
  RowBox[{"(", 
   RowBox[{
    RowBox[{"n", "\[Element]", 
     TemplateBox[{},
      "Integers"]}], "&&", 
    RowBox[{"n", "\[LessEqual]", 
     RowBox[{"-", "2.`"}]}]}], ")"}], "||", 
  RowBox[{"(", 
   RowBox[{
    RowBox[{"n", "\[Element]", 
     TemplateBox[{},
      "Integers"]}], "&&", 
    RowBox[{"n", "\[GreaterEqual]", "2.`"}]}], ")"}]}]], "Output",
 CellChangeTimes->{3.9083459219348154`*^9},
 CellLabel->"Out[77]=",ExpressionUUID->"e69a0fe8-fe98-4f09-b68d-aead60028094"]
}, Open  ]],

Cell[TextData[StyleBox["Solution of Exercise 05 (a):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.907746276747136*^9, 3.9077462884031763`*^9}},
 TextAlignment->Center,ExpressionUUID->"9945ec78-e466-4746-824f-0d134b6063f8"],

Cell[BoxData[
 RowBox[{"Clear", "[", 
  RowBox[{"a", ",", "n"}], "]"}]], "Input",
 CellChangeTimes->{{3.907746487863068*^9, 3.9077464922066965`*^9}},
 CellLabel->"In[78]:=",ExpressionUUID->"7725f938-a7e1-478a-9c24-efc36f71246b"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Giv05a", "=", 
  RowBox[{"RSolve", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{
       RowBox[{"a", "[", 
        RowBox[{"n", "+", "2"}], "]"}], "\[Equal]", 
       RowBox[{
        FractionBox["1", "2"], 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"a", "[", 
           RowBox[{"n", "+", "1"}], "]"}], "+", 
          RowBox[{"a", "[", "n", "]"}]}], ")"}]}]}], ",", 
      RowBox[{
       RowBox[{"a", "[", "1", "]"}], "\[Equal]", "2"}], ",", 
      RowBox[{
       RowBox[{"a", "[", "2", "]"}], "\[Equal]", "0"}]}], "}"}], ",", 
    RowBox[{"a", "[", "n", "]"}], ",", "n"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.9077463138870873`*^9, 3.907746448665268*^9}, {
  3.907748259599736*^9, 3.907748267458963*^9}},
 CellLabel->"In[79]:=",ExpressionUUID->"7df1f640-211b-4110-a61b-443d9d9a59e9"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"a", "[", "n", "]"}], "\[Rule]", 
    RowBox[{
     RowBox[{"-", 
      FractionBox["1", "3"]}], " ", 
     SuperscriptBox["2", 
      RowBox[{"1", "-", "n"}]], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"4", " ", 
        SuperscriptBox[
         RowBox[{"(", 
          RowBox[{"-", "1"}], ")"}], "n"]}], "-", 
       SuperscriptBox["2", "n"]}], ")"}]}]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{{3.9077464330093794`*^9, 3.9077464516807823`*^9}, 
   3.9077464964877906`*^9, 3.9077477989343233`*^9, {3.9077482706567526`*^9, 
   3.9077482775160007`*^9}, 3.9077483642615767`*^9, 3.9077490938440704`*^9, 
   3.9077496841005387`*^9, 3.9083459325603447`*^9},
 CellLabel->"Out[79]=",ExpressionUUID->"de6cdff7-675a-4c5e-ae8c-66b76e30be66"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"h5a", "=", 
   RowBox[{
    RowBox[{"Limit", "[", 
     RowBox[{
      RowBox[{"Giv05a", "[", 
       RowBox[{"[", 
        RowBox[{"1", ",", "1", ",", "2"}], "]"}], "]"}], ",", 
      RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}], "//", "N"}]}], 
  "\[IndentingNewLine]"}]], "Input",
 CellChangeTimes->{{3.9077478869603624`*^9, 3.907748018533577*^9}, {
  3.9077480735598893`*^9, 3.9077482060536923`*^9}, {3.9077482832815247`*^9, 
  3.907748345652668*^9}, {3.9077490755313244`*^9, 3.907749084687742*^9}, {
  3.9077496779914007`*^9, 3.907749678460081*^9}},
 CellLabel->"In[80]:=",ExpressionUUID->"bb33b3c2-5f25-4699-8b75-a9842879681c"],

Cell[BoxData["0.6666666666666666`"], "Output",
 CellChangeTimes->{
  3.907748021721072*^9, {3.9077481800540333`*^9, 3.9077482072411723`*^9}, {
   3.9077483114215684`*^9, 3.9077483694802065`*^9}, 3.9077491000629025`*^9, 
   3.9077496856473684`*^9, 3.908345935716733*^9},
 CellLabel->"Out[80]=",ExpressionUUID->"200cd96f-fe6d-4236-b194-394b84446871"]
}, Open  ]],

Cell[TextData[StyleBox["Another solution of Exercise 05 (a):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.9077496983501687`*^9, 3.9077497181151524`*^9}},
 TextAlignment->Center,ExpressionUUID->"49392367-40b8-47ee-83b3-3cb059ff3a0a"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"L", "=", 
   RowBox[{"Table", "[", 
    RowBox[{"2", ",", 
     RowBox[{"{", 
      RowBox[{"i", ",", "1", ",", "100"}], "}"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"L", "[", 
    RowBox[{"[", "2", "]"}], "]"}], "=", "0"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"For", "[", 
  RowBox[{
   RowBox[{"i", "=", "3"}], ",", 
   RowBox[{"i", "\[LessEqual]", "100"}], ",", 
   RowBox[{"i", "++"}], ",", 
   RowBox[{
    RowBox[{
     RowBox[{"L", "[", 
      RowBox[{"[", "i", "]"}], "]"}], "=", 
     RowBox[{
      FractionBox["1", "2"], 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"L", "[", 
         RowBox[{"[", 
          RowBox[{"i", "-", "2"}], "]"}], "]"}], "+", 
        RowBox[{"L", "[", 
         RowBox[{"[", 
          RowBox[{"i", "-", "1"}], "]"}], "]"}]}], ")"}]}]}], ";"}]}], 
  "]"}]}], "Input",
 CellChangeTimes->{{3.907749206547748*^9, 3.9077494973243628`*^9}, {
  3.9077495279954753`*^9, 3.9077495558072577`*^9}, {3.907749590150087*^9, 
  3.9077496102589083`*^9}, {3.907750836829531*^9, 3.907750859050001*^9}, {
  3.9077508914739103`*^9, 3.907750893817844*^9}},
 CellLabel->"In[81]:=",ExpressionUUID->"85ff338c-ca72-4614-b286-be4a6d9f2687"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"L", "//", "N"}]], "Input",
 CellChangeTimes->{
  3.907749503886753*^9, {3.9077508722540245`*^9, 3.907750872894699*^9}},
 CellLabel->"In[84]:=",ExpressionUUID->"ae151570-08ae-4f35-ad06-44350aba8720"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "2.`", ",", "0.`", ",", "1.`", ",", "0.5`", ",", "0.75`", ",", "0.625`", 
   ",", "0.6875`", ",", "0.65625`", ",", "0.671875`", ",", "0.6640625`", ",", 
   "0.66796875`", ",", "0.666015625`", ",", "0.6669921875`", ",", 
   "0.66650390625`", ",", "0.666748046875`", ",", "0.6666259765625`", ",", 
   "0.66668701171875`", ",", "0.666656494140625`", ",", "0.6666717529296875`",
    ",", "0.6666641235351562`", ",", "0.6666679382324219`", ",", 
   "0.6666660308837891`", ",", "0.6666669845581055`", ",", 
   "0.6666665077209473`", ",", "0.6666667461395264`", ",", 
   "0.6666666269302368`", ",", "0.6666666865348816`", ",", 
   "0.6666666567325592`", ",", "0.6666666716337204`", ",", 
   "0.6666666641831398`", ",", "0.6666666679084301`", ",", 
   "0.666666666045785`", ",", "0.6666666669771075`", ",", 
   "0.6666666665114462`", ",", "0.6666666667442769`", ",", 
   "0.6666666666278616`", ",", "0.6666666666860692`", ",", 
   "0.6666666666569654`", ",", "0.6666666666715173`", ",", 
   "0.6666666666642413`", ",", "0.6666666666678793`", ",", 
   "0.6666666666660603`", ",", "0.6666666666669698`", ",", 
   "0.6666666666665151`", ",", "0.6666666666667425`", ",", 
   "0.6666666666666288`", ",", "0.6666666666666856`", ",", 
   "0.6666666666666572`", ",", "0.6666666666666714`", ",", 
   "0.6666666666666643`", ",", "0.6666666666666679`", ",", 
   "0.6666666666666661`", ",", "0.666666666666667`", ",", 
   "0.6666666666666665`", ",", "0.6666666666666667`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666667`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`", ",", "0.6666666666666666`", ",", 
   "0.6666666666666666`"}], "}"}]], "Output",
 CellChangeTimes->{{3.9077508666598496`*^9, 3.9077508977086377`*^9}, 
   3.9083459454202557`*^9},
 CellLabel->"Out[84]=",ExpressionUUID->"436670cb-f063-48f7-8c8a-82ee12c025cf"]
}, Open  ]],

Cell[TextData[StyleBox["Solution of Exercise 05 (b):",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.9077465187783675`*^9, 3.9077465488556585`*^9}},
 TextAlignment->Center,ExpressionUUID->"850118fd-4dfe-450c-9136-b3486c40daee"],

Cell[BoxData[
 RowBox[{"Clear", "[", 
  RowBox[{"a", ",", "n"}], "]"}]], "Input",
 CellLabel->"In[85]:=",ExpressionUUID->"225b7811-e046-4c0e-a5ff-d3089921c386"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Giv05b", " ", "=", 
  RowBox[{"RSolve", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{
       RowBox[{"a", "[", 
        RowBox[{"n", "+", "3"}], "]"}], "\[Equal]", 
       RowBox[{
        FractionBox["1", "3"], 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"a", "[", 
           RowBox[{"n", "+", "2"}], "]"}], "+", 
          RowBox[{"a", "[", 
           RowBox[{"n", "+", "1"}], "]"}], "+", 
          RowBox[{"a", "[", "n", "]"}]}], ")"}]}]}], ",", 
      RowBox[{
       RowBox[{"a", "[", "1", "]"}], "\[Equal]", "3"}], ",", 
      RowBox[{
       RowBox[{"a", "[", "2", "]"}], "\[Equal]", "3"}], ",", 
      RowBox[{
       RowBox[{"a", "[", "3", "]"}], "\[Equal]", "3"}]}], "}"}], ",", 
    RowBox[{"a", "[", "n", "]"}], ",", "n"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.9077465914637623`*^9, 3.90774663061887*^9}, {
  3.9077496426174355`*^9, 3.9077496529764967`*^9}},
 CellLabel->"In[86]:=",ExpressionUUID->"1ebbe896-56c8-4ea3-b939-8b20c67c767a"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"a", "[", "n", "]"}], "\[Rule]", "3"}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.9077466347905636`*^9, 3.907749748848596*^9, 
  3.908345952108001*^9},
 CellLabel->"Out[86]=",ExpressionUUID->"5d86d99c-3404-4dbe-a68a-a11651cc4642"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"h5b", "=", 
  RowBox[{
   RowBox[{"Limit", "[", 
    RowBox[{
     RowBox[{"Giv05b", "[", 
      RowBox[{"[", 
       RowBox[{"1", ",", "1", ",", "2"}], "]"}], "]"}], ",", 
     RowBox[{"n", "\[Rule]", "Infinity"}]}], "]"}], "//", "N"}]}]], "Input",
 CellChangeTimes->{{3.907749008889112*^9, 3.907749062202925*^9}, {
  3.9077497285523777`*^9, 3.9077497363021545`*^9}, {3.90775055225774*^9, 
  3.9077505879597816`*^9}},
 CellLabel->"In[87]:=",ExpressionUUID->"3ba62c3a-af68-4560-a8a6-d89d47171a85"],

Cell[BoxData["3.`"], "Output",
 CellChangeTimes->{{3.907749014029845*^9, 3.9077490632498193`*^9}, 
   3.9077497505672946`*^9, {3.907750553398259*^9, 3.9077505886472607`*^9}, 
   3.908345954686208*^9},
 CellLabel->"Out[87]=",ExpressionUUID->"e61a29c9-50d3-442d-8f75-1c7b8cdfd179"]
}, Open  ]],

Cell[TextData[StyleBox["Another Solution of Exercise 05",
 FontColor->GrayLevel[1],
 Background->GrayLevel[0.5]]], "Text",
 CellChangeTimes->{{3.9083440129338284`*^9, 3.9083441169605136`*^9}},
 TextAlignment->Center,ExpressionUUID->"2384577f-5869-45c8-bf6f-d4a501ac6cf8"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"Z", "=", 
   RowBox[{"Table", "[", 
    RowBox[{"3", ",", 
     RowBox[{"{", 
      RowBox[{"i", ",", "1", ",", "100"}], "}"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Z", "[", 
    RowBox[{"[", "2", "]"}], "]"}], "=", "3"}], ";", 
  RowBox[{
   RowBox[{"Z", "[", 
    RowBox[{"[", "3", "]"}], "]"}], "=", "3"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"For", "[", 
  RowBox[{
   RowBox[{"i", "=", "4"}], ",", 
   RowBox[{"i", "\[LessEqual]", "100"}], ",", 
   RowBox[{"i", "++"}], ",", 
   RowBox[{
    RowBox[{
     RowBox[{"Z", "[", 
      RowBox[{"[", "i", "]"}], "]"}], "=", 
     RowBox[{
      FractionBox["1", "3"], 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"Z", "[", 
         RowBox[{"[", 
          RowBox[{"i", "-", "1"}], "]"}], "]"}], "+", 
        RowBox[{"Z", "[", 
         RowBox[{"[", 
          RowBox[{"i", "-", "2"}], "]"}], "]"}], "+", 
        RowBox[{"Z", "[", 
         RowBox[{"[", 
          RowBox[{"i", "-", "3"}], "]"}], "]"}]}], ")"}]}]}], ";"}]}], 
  "]"}]}], "Input",
 CellChangeTimes->{{3.9083441880826607`*^9, 3.908344215409681*^9}, {
  3.908344246486535*^9, 3.908344257892346*^9}, {3.908344299234439*^9, 
  3.908344390024803*^9}, {3.9083444333980513`*^9, 3.908344441038348*^9}},
 CellLabel->"In[88]:=",ExpressionUUID->"9cef6ece-daaf-413f-adf3-8017c7e18983"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Z", "//", "N"}]], "Input",
 CellChangeTimes->{{3.908344454225319*^9, 3.908344456834606*^9}},
 CellLabel->"In[91]:=",ExpressionUUID->"699b9f05-9f18-490f-a90a-81eff088d440"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", "3.`", ",", 
   "3.`", ",", "3.`", ",", "3.`", ",", "3.`"}], "}"}]], "Output",
 CellChangeTimes->{3.9083444582095337`*^9, 3.9083459610145473`*^9},
 CellLabel->"Out[91]=",ExpressionUUID->"f2d9b97e-7630-456c-b938-7968647487f3"]
}, Open  ]]
},
WindowSize->{894, 878},
WindowMargins->{{-8, Automatic}, {Automatic, 0}},
Magnification:>1.25 Inherited,
FrontEndVersion->"12.0 for Microsoft Windows (64-bit) (April 8, 2019)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 313, 5, 135, "Text",ExpressionUUID->"d987b510-abf8-431d-adee-930b2ec8ff85"],
Cell[874, 27, 317, 5, 43, "Text",ExpressionUUID->"ce3a1209-5540-4606-bb53-377bb60ac9db"],
Cell[CellGroupData[{
Cell[1216, 36, 672, 20, 84, "Input",ExpressionUUID->"a24230bb-37bc-4ba6-9692-9bf9dab0932b"],
Cell[1891, 58, 232, 4, 60, "Output",ExpressionUUID->"74b6fb6d-14fd-4fc3-893e-819ae5c73b4c"]
}, Open  ]],
Cell[CellGroupData[{
Cell[2160, 67, 1137, 25, 100, "Input",ExpressionUUID->"1573084d-eea4-4af7-be35-9abb5c7496a2"],
Cell[3300, 94, 3691, 79, 293, "Output",ExpressionUUID->"39fd421e-3ba1-44d2-bfb8-8aa8e99736bd"]
}, Open  ]],
Cell[7006, 176, 313, 5, 43, "Text",ExpressionUUID->"0f3ec151-5db5-4439-b6ce-d72faec84f8c"],
Cell[CellGroupData[{
Cell[7344, 185, 642, 19, 60, "Input",ExpressionUUID->"b8f64d3b-9fea-4e0d-8ff4-47775b0a1c47"],
Cell[7989, 206, 233, 4, 40, "Output",ExpressionUUID->"350937ee-34a3-494b-b5f9-21402a162acf"]
}, Open  ]],
Cell[CellGroupData[{
Cell[8259, 215, 1010, 23, 100, "Input",ExpressionUUID->"26daecdc-499c-4ce8-971a-fffc507379d4"],
Cell[9272, 240, 14272, 254, 306, "Output",ExpressionUUID->"bc77a39a-3b45-4453-82c0-f76b373a78f5"]
}, Open  ]],
Cell[23559, 497, 319, 5, 43, "Text",ExpressionUUID->"6d252b1e-b9e0-47bd-a25a-be2e4d0275c6"],
Cell[CellGroupData[{
Cell[23903, 506, 636, 19, 76, "Input",ExpressionUUID->"6c4a0842-456c-4e9b-a071-305b9463da30"],
Cell[24542, 527, 201, 3, 40, "Output",ExpressionUUID->"4d42dec4-d15b-4016-9139-80f27981cf6f"]
}, Open  ]],
Cell[CellGroupData[{
Cell[24780, 535, 856, 21, 100, "Input",ExpressionUUID->"dca1b2d0-4600-476d-9c01-739381647175"],
Cell[25639, 558, 2834, 66, 313, "Output",ExpressionUUID->"4baa943f-c2d4-418d-a831-39327dcf83e8"]
}, Open  ]],
Cell[28488, 627, 266, 4, 43, "Text",ExpressionUUID->"5093cd0f-1583-41a5-bb1a-290407481afa"],
Cell[CellGroupData[{
Cell[28779, 635, 579, 17, 75, "Input",ExpressionUUID->"e4e20de2-c7ee-42c1-834c-378b53d21b87"],
Cell[29361, 654, 173, 2, 40, "Output",ExpressionUUID->"191e19b1-18ea-40c2-8fdf-6c40beddd0ab"]
}, Open  ]],
Cell[CellGroupData[{
Cell[29571, 661, 834, 21, 100, "Input",ExpressionUUID->"a19c0f96-81cb-48d2-953b-4d4c5e37de5d"],
Cell[30408, 684, 3121, 71, 309, "Output",ExpressionUUID->"af9efc6e-b5bd-4fe4-be1e-eec13d774ae2"]
}, Open  ]],
Cell[33544, 758, 266, 4, 43, "Text",ExpressionUUID->"044f4b69-312e-4de4-98ba-3a6f529bea7d"],
Cell[CellGroupData[{
Cell[33835, 766, 654, 18, 91, "Input",ExpressionUUID->"8e59c243-e42f-4273-88a3-29d6b71e8604"],
Cell[34492, 786, 221, 3, 40, "Output",ExpressionUUID->"47428588-23c8-4836-9f7a-4104c6446bc1"]
}, Open  ]],
Cell[CellGroupData[{
Cell[34750, 794, 859, 21, 100, "Input",ExpressionUUID->"bb9a8025-d6cf-484d-b39b-0cdf81434d7e"],
Cell[35612, 817, 3785, 81, 293, "Output",ExpressionUUID->"7cd2fe01-161e-4ed6-b783-6978c0c47444"]
}, Open  ]],
Cell[39412, 901, 317, 5, 43, "Text",ExpressionUUID->"3736c737-18a4-4c24-899e-25574370743d"],
Cell[CellGroupData[{
Cell[39754, 910, 536, 14, 76, "Input",ExpressionUUID->"278ca9f3-d4e9-47c9-b7a8-f725aaae4c4b"],
Cell[40293, 926, 248, 3, 40, "Output",ExpressionUUID->"866d9124-a9ae-4af6-bcb2-4cfc5f686c0a"]
}, Open  ]],
Cell[CellGroupData[{
Cell[40578, 934, 1212, 29, 124, "Input",ExpressionUUID->"b417f71f-3820-456f-99d6-4bf9504f4558"],
Cell[41793, 965, 3695, 78, 304, "Output",ExpressionUUID->"51978104-7d52-48b4-a72a-144c5cfd0e3e"]
}, Open  ]],
Cell[45503, 1046, 266, 4, 43, "Text",ExpressionUUID->"ebe5f6af-a8bc-4077-9745-86950ee52e06"],
Cell[CellGroupData[{
Cell[45794, 1054, 493, 13, 71, "Input",ExpressionUUID->"14bb7d8b-d46d-448a-a4e3-26ee8b752a77"],
Cell[46290, 1069, 202, 3, 40, "Output",ExpressionUUID->"e767628f-96e5-4823-959d-77af33f208b9"]
}, Open  ]],
Cell[CellGroupData[{
Cell[46529, 1077, 858, 21, 100, "Input",ExpressionUUID->"2644eea2-df35-41e2-a227-7c53ed3b43ab"],
Cell[47390, 1100, 5209, 105, 305, "Output",ExpressionUUID->"a20d8981-c735-44c1-9956-4626e29d254a"]
}, Open  ]],
Cell[52614, 1208, 266, 4, 43, "Text",ExpressionUUID->"2a62a73d-2a64-418a-99e7-45f0d6055324"],
Cell[CellGroupData[{
Cell[52905, 1216, 677, 19, 58, "Input",ExpressionUUID->"231526e2-3d7d-471f-8c3f-3f9997d3dbd0"],
Cell[53585, 1237, 210, 3, 40, "Output",ExpressionUUID->"80dde39e-88a4-42eb-832e-602f1f255649"]
}, Open  ]],
Cell[CellGroupData[{
Cell[53832, 1245, 1009, 23, 100, "Input",ExpressionUUID->"2cd2fa8e-a04a-4deb-886c-8d7f47fe71f5"],
Cell[54844, 1270, 3061, 66, 297, "Output",ExpressionUUID->"90e93c74-67b6-45d0-b950-02de98d2a40b"]
}, Open  ]],
Cell[57920, 1339, 266, 4, 43, "Text",ExpressionUUID->"d647b1e0-96fe-43b0-9eea-bd2e50e1f35c"],
Cell[CellGroupData[{
Cell[58211, 1347, 729, 21, 85, "Input",ExpressionUUID->"e4807c6a-344f-47d8-a6a8-56992aa82622"],
Cell[58943, 1370, 222, 4, 58, "Output",ExpressionUUID->"370a22f2-5f72-406b-9b9e-c1be63a540f1"]
}, Open  ]],
Cell[CellGroupData[{
Cell[59202, 1379, 961, 23, 100, "Input",ExpressionUUID->"43de5983-e6ac-4a95-bcf8-ea63352a050d"],
Cell[60166, 1404, 4954, 101, 305, "Output",ExpressionUUID->"6b6d4492-3d0e-4ee3-b3de-624d37d7fc86"]
}, Open  ]],
Cell[65135, 1508, 268, 4, 43, "Text",ExpressionUUID->"7e4d9fe7-4900-4c5f-921f-324cf2ab8fc6"],
Cell[CellGroupData[{
Cell[65428, 1516, 598, 17, 85, "Input",ExpressionUUID->"e579065e-6016-47a2-81f7-e1ab2d1f9477"],
Cell[66029, 1535, 175, 2, 40, "Output",ExpressionUUID->"aa43b679-0f1e-4161-900e-a45c3c387de7"]
}, Open  ]],
Cell[CellGroupData[{
Cell[66241, 1542, 990, 25, 100, "Input",ExpressionUUID->"46242c98-3e21-4a64-95b0-3474ef68bee1"],
Cell[67234, 1569, 3495, 76, 294, "Output",ExpressionUUID->"a785a5ac-33f4-4fc0-aff5-271e2e84bc29"]
}, Open  ]],
Cell[70744, 1648, 264, 4, 43, "Text",ExpressionUUID->"70c1b3fd-e4f7-4b82-8e92-cc4ac9f64630"],
Cell[CellGroupData[{
Cell[71033, 1656, 637, 18, 109, "Input",ExpressionUUID->"9dae81f2-b891-4686-82cf-8c0001cecb00"],
Cell[71673, 1676, 249, 5, 40, "Output",ExpressionUUID->"f19b592b-4e77-494a-b43c-72136cbc74f7"]
}, Open  ]],
Cell[71937, 1684, 323, 5, 43, "Text",ExpressionUUID->"1ce84a75-243f-403a-9875-32a1a13730c4"],
Cell[CellGroupData[{
Cell[72285, 1693, 671, 17, 115, "Input",ExpressionUUID->"e531c743-a55d-4dbc-a9a6-593d7254674b"],
Cell[72959, 1712, 246, 5, 40, "Output",ExpressionUUID->"d6bddda3-9230-4593-b8a2-155f2dff4921"]
}, Open  ]],
Cell[73220, 1720, 262, 4, 43, "Text",ExpressionUUID->"78f5cb02-3a96-4569-9643-0f3b5aa93fad"],
Cell[CellGroupData[{
Cell[73507, 1728, 647, 18, 115, "Input",ExpressionUUID->"9df3e826-903c-40f6-a709-d6bb0f7b6341"],
Cell[74157, 1748, 225, 4, 40, "Output",ExpressionUUID->"4f488e91-3518-42e4-b2f6-bd688ba18278"]
}, Open  ]],
Cell[74397, 1755, 321, 5, 43, "Text",ExpressionUUID->"9e452dc8-b0ca-4e23-84a0-56c04a8f8827"],
Cell[CellGroupData[{
Cell[74743, 1764, 603, 19, 112, "Input",ExpressionUUID->"92269ca2-f7ef-49f7-9957-3cf260ffc070"],
Cell[75349, 1785, 211, 3, 40, "Output",ExpressionUUID->"7ded1182-3052-45b4-ba78-267d147bcc1a"]
}, Open  ]],
Cell[75575, 1791, 268, 4, 43, "Text",ExpressionUUID->"bf67d681-8004-43cc-810d-f98274a5addf"],
Cell[75846, 1797, 276, 5, 55, "Input",ExpressionUUID->"bcd2a070-8918-401e-ad68-10c985346aa3"],
Cell[CellGroupData[{
Cell[76147, 1806, 699, 20, 119, "Input",ExpressionUUID->"576ddb9f-8c2e-433e-9ba2-05cf2046cd72"],
Cell[76849, 1828, 498, 11, 54, "Message",ExpressionUUID->"66be2a03-daff-47b9-b906-05d4b216f1ab"],
Cell[77350, 1841, 987, 31, 65, "Output",ExpressionUUID->"e69a0fe8-fe98-4f09-b68d-aead60028094"]
}, Open  ]],
Cell[78352, 1875, 266, 4, 43, "Text",ExpressionUUID->"9945ec78-e466-4746-824f-0d134b6063f8"],
Cell[78621, 1881, 228, 4, 55, "Input",ExpressionUUID->"7725f938-a7e1-478a-9c24-efc36f71246b"],
Cell[CellGroupData[{
Cell[78874, 1889, 851, 23, 71, "Input",ExpressionUUID->"7df1f640-211b-4110-a61b-443d9d9a59e9"],
Cell[79728, 1914, 819, 21, 57, "Output",ExpressionUUID->"de6cdff7-675a-4c5e-ae8c-66b76e30be66"]
}, Open  ]],
Cell[CellGroupData[{
Cell[80584, 1940, 669, 15, 81, "Input",ExpressionUUID->"bb33b3c2-5f25-4699-8b75-a9842879681c"],
Cell[81256, 1957, 348, 5, 40, "Output",ExpressionUUID->"200cd96f-fe6d-4236-b194-394b84446871"]
}, Open  ]],
Cell[81619, 1965, 276, 4, 43, "Text",ExpressionUUID->"49392367-40b8-47ee-83b3-3cb059ff3a0a"],
Cell[81898, 1971, 1242, 36, 140, "Input",ExpressionUUID->"85ff338c-ca72-4614-b286-be4a6d9f2687"],
Cell[CellGroupData[{
Cell[83165, 2011, 222, 4, 55, "Input",ExpressionUUID->"ae151570-08ae-4f35-ad06-44350aba8720"],
Cell[83390, 2017, 3043, 51, 305, "Output",ExpressionUUID->"436670cb-f063-48f7-8c8a-82ee12c025cf"]
}, Open  ]],
Cell[86448, 2071, 268, 4, 43, "Text",ExpressionUUID->"850118fd-4dfe-450c-9136-b3486c40daee"],
Cell[86719, 2077, 160, 3, 55, "Input",ExpressionUUID->"225b7811-e046-4c0e-a5ff-d3089921c386"],
Cell[CellGroupData[{
Cell[86904, 2084, 1014, 27, 108, "Input",ExpressionUUID->"1ebbe896-56c8-4ea3-b939-8b20c67c767a"],
Cell[87921, 2113, 303, 7, 40, "Output",ExpressionUUID->"5d86d99c-3404-4dbe-a68a-a11651cc4642"]
}, Open  ]],
Cell[CellGroupData[{
Cell[88261, 2125, 521, 12, 55, "Input",ExpressionUUID->"3ba62c3a-af68-4560-a8a6-d89d47171a85"],
Cell[88785, 2139, 279, 4, 40, "Output",ExpressionUUID->"e61a29c9-50d3-442d-8f75-1c7b8cdfd179"]
}, Open  ]],
Cell[89079, 2146, 271, 4, 43, "Text",ExpressionUUID->"2384577f-5869-45c8-bf6f-d4a501ac6cf8"],
Cell[89353, 2152, 1379, 41, 140, "Input",ExpressionUUID->"9cef6ece-daaf-413f-adf3-8017c7e18983"],
Cell[CellGroupData[{
Cell[90757, 2197, 195, 3, 55, "Input",ExpressionUUID->"699b9f05-9f18-490f-a90a-81eff088d440"],
Cell[90955, 2202, 1467, 21, 137, "Output",ExpressionUUID->"f2d9b97e-7630-456c-b938-7968647487f3"]
}, Open  ]]
}
]
*)