(* Content-type: application/mathematica *)

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

(* CreatedBy='Mathematica 6.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[    103650,       1944]
NotebookOptionsPosition[    101677,       1873]
NotebookOutlinePosition[    102018,       1888]
CellTagsIndexPosition[    101975,       1885]
WindowFrame->Normal
ContainsDynamic->False*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Cobweb plots for Homework #1", "Subsubtitle",
 CellChangeTimes->{{3.416182676742502*^9, 3.416182683785748*^9}}],

Cell[CellGroupData[{

Cell["Exercise E1 cobweb plots :", "Subsubsection",
 CellChangeTimes->{{3.41618264981765*^9, 3.4161826736385517`*^9}},
 FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"cobweb", "[", 
  RowBox[{
   RowBox[{
    SuperscriptBox["#", "2"], "&"}], ",", 
   FractionBox["1", "2"], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", 
     FractionBox["1", "2"]}], "}"}], ",", "5"}], "]"}]], "Input",
 CellChangeTimes->{{3.415737991776011*^9, 3.4157380007922688`*^9}, 
   3.415738855920464*^9, {3.415739130464196*^9, 3.4157391562230263`*^9}, {
   3.41573960375106*^9, 3.415739632003776*^9}, {3.415739872890945*^9, 
   3.4157399163754997`*^9}, {3.4157399535169487`*^9, 3.415739965388153*^9}, 
   3.415740055480748*^9, {3.4157400960451727`*^9, 3.415740105412176*^9}, {
   3.415740660295156*^9, 3.415740707049574*^9}, {3.4157900159579563`*^9, 
   3.41579001645569*^9}, {3.415790184749711*^9, 3.415790198864992*^9}, {
   3.4157902296489058`*^9, 3.4157902311663847`*^9}, {3.415984706478134*^9, 
   3.415984706638113*^9}, {3.416181969783502*^9, 3.416182020069888*^9}, {
   3.416182070031765*^9, 3.4161820771197853`*^9}},
 FontSize->14],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxNxX0s1GEcAPBzEWU7jsl+Z8eOUyuaJiNKp2jK67y02K7T5CWMZLehzTij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      "]]}, 
    {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJwV1vk71QkDBXA7qRSNdC9G5aJFV4ulhe8hJCrZs3UjWaIsJUqvNZoUrQah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      "]]}}, {{}, {}, 
    {Hue[0.67, 0.6, 0.6], Dashing[{Small, Small}], 
     LineBox[{{0.5, 0.}, {0.5, 0.25}, {0.25, 0.25}, {0.25, 0.0625}, {0.0625, 
      0.0625}, {0.0625, 0.00390625}, {0.00390625, 0.00390625}, {0.00390625, 
      0.0000152587890625}, {0.0000152587890625, 0.0000152587890625}, {
      0.0000152587890625, 2.3283064365386963`*^-10}, {
      2.3283064365386963`*^-10, 2.3283064365386963`*^-10}}]}}},
  AspectRatio->1,
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->NCache[{{0, 
      Rational[1, 2]}, {0, 
      Rational[1, 2]}}, {{0, 0.5}, {0, 0.5}}],
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.4161819902613907`*^9, 3.416182021007062*^9}, 
   3.416182077862442*^9},
 ImageCache->GraphicsData["CompressedBitmap", "\<\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\
\>"]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"cobweb", "[", 
  RowBox[{
   RowBox[{
    SuperscriptBox["#", "2"], "&"}], ",", 
   RowBox[{"-", 
    FractionBox["1", "2"]}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", 
      FractionBox["1", "2"]}], ",", 
     FractionBox["1", "2"]}], "}"}], ",", "5"}], "]"}]], "Input",
 CellChangeTimes->{{3.415737991776011*^9, 3.4157380007922688`*^9}, 
   3.415738855920464*^9, {3.415739130464196*^9, 3.4157391562230263`*^9}, {
   3.41573960375106*^9, 3.415739632003776*^9}, {3.415739872890945*^9, 
   3.4157399163754997`*^9}, {3.4157399535169487`*^9, 3.415739965388153*^9}, 
   3.415740055480748*^9, {3.4157400960451727`*^9, 3.415740105412176*^9}, {
   3.415740660295156*^9, 3.415740707049574*^9}, {3.4157900159579563`*^9, 
   3.41579001645569*^9}, {3.415790184749711*^9, 3.415790198864992*^9}, {
   3.4157902296489058`*^9, 3.4157902311663847`*^9}, {3.415984706478134*^9, 
   3.415984706638113*^9}, {3.416181969783502*^9, 3.4161820366342297`*^9}, {
   3.416182082026919*^9, 3.416182098515077*^9}},
 FontSize->14],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxN1P8v1HEcwPE73Jov+bawK9dyvkxchnK3qcYKw7DcxJk6jmEjX2a+NY2L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      "]]}, 
    {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJxd2Gc8Ffz7B3Az2eOmboXbShyyUyrnoiQpq2yyCiEncex9SEa2QmYokXnI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      "]]}}, {{}, {}, 
    {Hue[0.67, 0.6, 0.6], Dashing[{Small, Small}], 
     LineBox[{{-0.5, 0.}, {-0.5, 0.25}, {0.25, 0.25}, {0.25, 0.0625}, {0.0625,
       0.0625}, {0.0625, 0.00390625}, {0.00390625, 0.00390625}, {0.00390625, 
      0.0000152587890625}, {0.0000152587890625, 0.0000152587890625}, {
      0.0000152587890625, 2.3283064365386963`*^-10}, {
      2.3283064365386963`*^-10, 2.3283064365386963`*^-10}}]}}},
  AspectRatio->1,
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->NCache[{{
      Rational[-1, 2], 
      Rational[1, 2]}, {
      Rational[-1, 2], 
      Rational[1, 2]}}, {{-0.5, 0.5}, {-0.5, 0.5}}],
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.416182037333503*^9, 3.416182099269137*^9}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Exercise E2 cobweb plots :", "Subsubsection",
 CellChangeTimes->{{3.41618264981765*^9, 3.4161826611066437`*^9}},
 FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"cobweb", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"Cos", "[", 
     RowBox[{"\[Pi]", "#"}], "]"}], "&"}], ",", 
   FractionBox["1", "2"], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "1.1"}], ",", "1.1"}], "}"}], ",", "7"}], "]"}]], "Input",
 CellChangeTimes->{{3.415737991776011*^9, 3.4157380007922688`*^9}, 
   3.415738855920464*^9, {3.415739130464196*^9, 3.4157391562230263`*^9}, {
   3.41573960375106*^9, 3.415739632003776*^9}, {3.415739872890945*^9, 
   3.4157399163754997`*^9}, {3.4157399535169487`*^9, 3.415739965388153*^9}, 
   3.415740055480748*^9, {3.4157400960451727`*^9, 3.415740105412176*^9}, {
   3.415740660295156*^9, 3.415740707049574*^9}, {3.4157900159579563`*^9, 
   3.41579001645569*^9}, {3.415790184749711*^9, 3.415790198864992*^9}, {
   3.4157902296489058`*^9, 3.4157902311663847`*^9}, {3.415984706478134*^9, 
   3.415984706638113*^9}, {3.416181969783502*^9, 3.4161820366342297`*^9}, {
   3.416182082026919*^9, 3.416182098515077*^9}, {3.416182130966316*^9, 
   3.416182178248488*^9}, {3.416182231777534*^9, 3.41618223260021*^9}},
 FontSize->14],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxN1P8v1HEcwHGTL6HY3W4sFeXbupllRH7ouEgRnbKTo1sh1nw3rN0Z1c7I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      "]]}, 
    {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJxdmnk0VW8Xx0uEBhFlak4UadKkYitFSiVlalBEpIFokJCUIamIpDKlFBKS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      "]]}}, {{}, {}, 
    {Hue[0.67, 0.6, 0.6], Dashing[{Small, Small}], 
     LineBox[{{0.5, 0.}, {0.5, 0.}, {0., 0.}, {0., 1.}, {1., 1.}, {
      1., -1.}, {-1., -1.}, {-1., -1.}, {-1., -1.}, {-1., -1.}, {-1., -1.}, \
{-1., -1.}, {-1., -1.}, {-1., -1.}, {-1., -1.}}]}}},
  AspectRatio->1,
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{-1.1, 1.1}, {-1.1, 1.1}},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.416182155323707*^9, 3.416182178796719*^9}, 
   3.416182233218677*^9},
 ImageCache->GraphicsData["CompressedBitmap", "\<\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\
\>"]]
}, Open  ]],

Cell[TextData[StyleBox["The first few line segments are obscured by the \
coordinate axes, so we can redisplay the plot with the axes suppressed :",
 FontSize->14]], "Text",
 CellChangeTimes->{{3.416182464260891*^9, 3.416182500997903*^9}},
 FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{"%", ",", 
   RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.416182212079775*^9, 3.4161822178863707`*^9}},
 FontSize->14],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxN1P8v1HEcwHGTL6HY3W4sFeXbupllRH7ouEgRnbKTo1sh1nw3rN0Z1c7I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      "]]}, 
    {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJxdmnk0VW8Xx0uEBhFlak4UadKkYitFSiVlalBEpIFokJCUIamIpDKlFBKS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      "]]}}, {{}, {}, 
    {Hue[0.67, 0.6, 0.6], Dashing[{Small, Small}], 
     LineBox[{{0.5, 0.}, {0.5, 0.}, {0., 0.}, {0., 1.}, {1., 1.}, {
      1., -1.}, {-1., -1.}, {-1., -1.}, {-1., -1.}, {-1., -1.}, {-1., -1.}, \
{-1., -1.}, {-1., -1.}, {-1., -1.}, {-1., -1.}}]}}},
  AspectRatio->1,
  Axes->False,
  AxesOrigin->{0, 0},
  PlotRange->{{-1.1, 1.1}, {-1.1, 1.1}},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.4161822184771233`*^9, 3.416182247676854*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"cobweb", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"Cos", "[", 
     RowBox[{"\[Pi]", "#"}], "]"}], "&"}], ",", 
   RowBox[{"-", 
    FractionBox["3", "4"]}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "1.1"}], ",", "1.1"}], "}"}], ",", "7"}], "]"}]], "Input",
 CellChangeTimes->{{3.415737991776011*^9, 3.4157380007922688`*^9}, 
   3.415738855920464*^9, {3.415739130464196*^9, 3.4157391562230263`*^9}, {
   3.41573960375106*^9, 3.415739632003776*^9}, {3.415739872890945*^9, 
   3.4157399163754997`*^9}, {3.4157399535169487`*^9, 3.415739965388153*^9}, 
   3.415740055480748*^9, {3.4157400960451727`*^9, 3.415740105412176*^9}, {
   3.415740660295156*^9, 3.415740707049574*^9}, {3.4157900159579563`*^9, 
   3.41579001645569*^9}, {3.415790184749711*^9, 3.415790198864992*^9}, {
   3.4157902296489058`*^9, 3.4157902311663847`*^9}, {3.415984706478134*^9, 
   3.415984706638113*^9}, {3.416181969783502*^9, 3.4161820366342297`*^9}, {
   3.416182082026919*^9, 3.416182098515077*^9}, {3.416182130966316*^9, 
   3.416182178248488*^9}, {3.416182231777534*^9, 3.41618223260021*^9}, {
   3.416182327835421*^9, 3.416182331408203*^9}},
 FontSize->14],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxN1P8v1HEcwHGTL6HY3W4sFeXbupllRH7ouEgRnbKTo1sh1nw3rN0Z1c7I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      "]]}, 
    {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJxdmnk0VW8Xx0uEBhFlak4UadKkYitFSiVlalBEpIFokJCUIamIpDKlFBKS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      "]]}}, {{}, {}, 
    {Hue[0.67, 0.6, 0.6], Dashing[{Small, Small}], 
     LineBox[{{-0.75, 
      0.}, {-0.75, -0.7071067811865475}, {-0.7071067811865475, \
-0.7071067811865475}, {-0.7071067811865475, -0.6056998670788134}, \
{-0.6056998670788134, -0.6056998670788134}, {-0.6056998670788134, \
-0.32599678886913325`}, {-0.32599678886913325`, -0.32599678886913325`}, \
{-0.32599678886913325`, 0.519825960600638}, {0.519825960600638, 
      0.519825960600638}, {
      0.519825960600638, -0.06224482818023487}, {-0.06224482818023487, \
-0.06224482818023487}, {-0.06224482818023487, 0.9809413586020264}, {
      0.9809413586020264, 0.9809413586020264}, {
      0.9809413586020264, -0.99820805828688}, {-0.99820805828688, \
-0.99820805828688}}]}}},
  AspectRatio->1,
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{-1.1, 1.1}, {-1.1, 1.1}},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.4161823319393387`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"cobweb", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"Cos", "[", 
     RowBox[{"\[Pi]", "#"}], "]"}], "&"}], ",", 
   RowBox[{"-", 
    FractionBox["4", "5"]}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "1.1"}], ",", "0"}], "}"}], ",", "7"}], "]"}]], "Input",
 CellChangeTimes->{{3.415737991776011*^9, 3.4157380007922688`*^9}, 
   3.415738855920464*^9, {3.415739130464196*^9, 3.4157391562230263`*^9}, {
   3.41573960375106*^9, 3.415739632003776*^9}, {3.415739872890945*^9, 
   3.4157399163754997`*^9}, {3.4157399535169487`*^9, 3.415739965388153*^9}, 
   3.415740055480748*^9, {3.4157400960451727`*^9, 3.415740105412176*^9}, {
   3.415740660295156*^9, 3.415740707049574*^9}, {3.4157900159579563`*^9, 
   3.41579001645569*^9}, {3.415790184749711*^9, 3.415790198864992*^9}, {
   3.4157902296489058`*^9, 3.4157902311663847`*^9}, {3.415984706478134*^9, 
   3.415984706638113*^9}, {3.416181969783502*^9, 3.4161820366342297`*^9}, {
   3.416182082026919*^9, 3.416182098515077*^9}, {3.416182130966316*^9, 
   3.416182178248488*^9}, {3.416182231777534*^9, 3.41618223260021*^9}, {
   3.416182327835421*^9, 3.416182405561441*^9}},
 FontSize->14],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxFxXswE3AcAHC5G+URqaMQGQtN1jwaJuWRM8Jy/ljn1sUdeZWTnXU6y+NQ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      "]]}, 
    {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJwtlgk0Vdsfx5GhyBCVnkRzSYaUCKFkarjGhERdlSSJBkVP4jXIi6aXoahe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      "]]}}, {{}, {}, 
    {Hue[0.67, 0.6, 0.6], Dashing[{Small, Small}], 
     LineBox[{{-0.8, 
      0.}, {-0.8, -0.8090169943749475}, {-0.8090169943749475, \
-0.8090169943749475}, {-0.8090169943749475, -0.8253408053890465}, \
{-0.8253408053890465, -0.8253408053890465}, {-0.8253408053890465, \
-0.8531990999703334}, {-0.8531990999703334, -0.8531990999703334}, \
{-0.8531990999703334, -0.89552417503377}, {-0.89552417503377, \
-0.89552417503377}, {-0.89552417503377, -0.9466174850110264}, \
{-0.9466174850110264, -0.9466174850110264}, {-0.9466174850110264, \
-0.9859702580743581}, {-0.9859702580743581, -0.9859702580743581}, \
{-0.9859702580743581, -0.9990288220673791}, {-0.9990288220673791, \
-0.9990288220673791}}]}}},
  AspectRatio->1,
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{-1.1, 0}, {-1.1, 0}},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.416182363673044*^9, 3.416182406165362*^9}}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Approximating fixed points", "Subsection",
 CellChangeTimes->{{3.41618385350388*^9, 3.4161838639791107`*^9}}],

Cell[TextData[{
 "You can use ",
 StyleBox["Mathematica'",
  FontSlant->"Italic"],
 "s FindRoot function to numerically approximate solutions of nonlinear \
equations. For example,  to approximate the fixed points of f(x) = ",
 Cell[BoxData[
  FormBox[
   FractionBox["1", 
    RowBox[{"1", "+", 
     SuperscriptBox["x", "2"]}]], TraditionalForm]]],
 ", we could plot f(x) and x and look for intersections of the graphs:"
}], "Text",
 CellChangeTimes->{{3.416183226582303*^9, 3.4161833187393217`*^9}, {
  3.416183380939476*^9, 3.416183465973333*^9}, {3.416183604585244*^9, 
  3.416183665083478*^9}},
 FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", ",", 
     FractionBox["1", 
      RowBox[{"1", "+", 
       SuperscriptBox["x", "2"]}]]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.416183469178146*^9, 3.416183585014783*^9}, {
  3.416183669405978*^9, 3.416183694699349*^9}, {3.4161838874869833`*^9, 
  3.4161838887387238`*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxNxX0s1GEcAPBzEWU7jsl+Z8eOUyuaJiNKp9iU13lbbNdp8hJGstvQZpzR
C661Zrp1yetW4lzc0ZpEXGySlwjlXnJd13FCW8eOuOoP3+f547NP7PUURhqJ
RCL/E/X/swlLA1O6tLC9WT6EKo8WbA6HEJLHgvqTcDxR1zX3IRxOJR70baZe
grkEP/i2lwIuJypvRTs0wDXE3SMSKx7c8mtd3JiUCIudQ9k8kzUsrRrSrca4
w69+C1j+4wVwv5mZkip1hAfPTIwFq3tg2UqSU13WIDySI7IJPGyAR92dbNuM
ZHisI67niskXnjg2PO5TPgZPrrYa9fdd4I8nPilVm3p4+h5ltHe5BZ7RaNae
0inwLLMhvTuzGp4ruaZpC9qA54cOSWXeXPgLY6pK1qGCF24eFc5kbcPy3vRd
y3MesNKxM4PRFAqr2IuuyfQC+GvknHXCiid6S2a1bmMPLz52Ewv7zWF1+IHP
vT7Z6I03DSkX2+BvtVpbmt4Aa0Jq9oXGdaO10vqKCyXw94rm+TAFA9Z6EzXl
fgHoaTPjhDMb/sHLU/NHDbCOGcvlmAvQMnJTt9IeXrrhH88rtoCX7dRiTisJ
PWjHFz/Kh/W5VKs7Hn3wCqXMMz+Min5dND15XA7/5GiYrCcv0Lt0qq/4Mrz6
XM5rrCiF1yIoQrpOhN4aOUWhxmDLncgWldjrOwajDL1NG1KofbFzo0USGvqP
Q0ZkvBq9c7W2WsDFLiwqrRZh89ncUi32S1d2ZiJ692CHZ0Agdue79/L92MPP
+idZ2AtVElkh2mQRI2xfxk5UZBePY+cMJOdbYpc1x6UHYbdnno7qwn4b4XVe
jz3r5ebHxNbbOXpwsE0Ga5eHe/8FusKK0A==
     "]]}, 
   {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJwV1nk4ldsXB3BjaSJTXSRkaJJUFF36FpUGkVCUISV+Uhmrk64TLreJok4n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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 1}, {0., 0.9999999999999996}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{{3.4161834978462133`*^9, 3.416183539718628*^9}, {
   3.416183573937395*^9, 3.4161835857129*^9}, {3.41618368593559*^9, 
   3.416183695261017*^9}, 3.416183889327291*^9}]
}, Open  ]],

Cell[TextData[{
 "(Since 0 < f(x) < 1 unless x = 0, we only need to look for intersections \
between 0 and 1.) \nThere is an intersection near ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    FractionBox["2", "3"], ",", " ", 
    RowBox[{
    "so", " ", "we", " ", "take", " ", "that", " ", "as", " ", "our", " ", 
     "initial", " ", "guess", " ", "for", " ", 
     RowBox[{"FindRoot", ":"}]}]}], TraditionalForm]]]
}], "Text",
 CellChangeTimes->{{3.4161837045631647`*^9, 3.416183809282963*^9}, {
  3.416183881982576*^9, 3.4161839006585608`*^9}},
 FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FindRoot", "[", 
  RowBox[{
   RowBox[{
    FractionBox["1", 
     RowBox[{"1", "+", 
      SuperscriptBox["x", "2"]}]], "==", "x"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", 
     FractionBox["2", "3"]}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.4161829855656757`*^9, 3.41618302727293*^9}, {
  3.416183814485302*^9, 3.416183831872411*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"x", "\[Rule]", "0.6823278038280193`"}], "}"}]], "Output",
 CellChangeTimes->{3.416183027976612*^9, 3.4161838349019613`*^9, 
  3.4161839631785393`*^9}]
}, Open  ]],

Cell["\<\
We can substitute this value into the derivative of f to see if we have a \
sink or source :\
\>", "Text",
 CellChangeTimes->{{3.416183927396386*^9, 3.416183947452381*^9}},
 FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"D", "[", 
   RowBox[{
    FractionBox["1", 
     RowBox[{"1", "+", 
      SuperscriptBox["x", "2"]}]], ",", "x"}], "]"}], "/.", "%"}]], "Input",
 CellChangeTimes->{{3.416183918931237*^9, 3.416183924910375*^9}, {
  3.4161839550233793`*^9, 3.416183955480589*^9}}],

Cell[BoxData[
 RowBox[{"-", "0.6353443923439613`"}]], "Output",
 CellChangeTimes->{{3.41618396068447*^9, 3.416183965749671*^9}}]
}, Open  ]],

Cell["Sink! Here's a sample cobweb plot:", "Text",
 CellChangeTimes->{{3.4161839714077883`*^9, 3.416184007508346*^9}},
 FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"cobweb", "[", 
  RowBox[{
   RowBox[{
    FractionBox["1", 
     RowBox[{"1", "+", 
      SuperscriptBox["#", "2"]}]], "&"}], ",", "1", ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "1"}], "}"}], ",", "10"}], "]"}]], "Input",
 CellChangeTimes->{{3.4161840170816717`*^9, 3.4161840392638283`*^9}}],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxNxX0s1GEcAPBzEWU7jsl+Z8eOUyuaJiNKp9iU13lbbNdp8hJGstvQZpzR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      "]]}, 
    {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData["
1:eJwV1nk4ldsXB3BjaSJTXSRkaJJUFF36FpUGkVCUISV+Uhmrk64TLreJok4n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      "]]}}, {{}, {}, 
    {Hue[0.67, 0.6, 0.6], Dashing[{Small, Small}], 
     LineBox[{{1., 0.}, {1., 0.5}, {0.5, 0.5}, {0.5, 0.8}, {0.8, 0.8}, {0.8, 
      0.6097560975609756}, {0.6097560975609756, 0.6097560975609756}, {
      0.6097560975609756, 0.7289679098005204}, {0.7289679098005204, 
      0.7289679098005204}, {0.7289679098005204, 0.6529997248077184}, {
      0.6529997248077184, 0.6529997248077184}, {0.6529997248077184, 
      0.701061372973803}, {0.701061372973803, 0.701061372973803}, {
      0.701061372973803, 0.6704717958414473}, {0.6704717958414473, 
      0.6704717958414473}, {0.6704717958414473, 0.6898776322492279}, {
      0.6898776322492279, 0.6898776322492279}, {0.6898776322492279, 
      0.6775383809122035}, {0.6775383809122035, 0.6775383809122035}, {
      0.6775383809122035, 0.6853735927163312}, {0.6853735927163312, 
      0.6853735927163312}}]}}},
  AspectRatio->1,
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{0, 1}, {0, 1}},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.416184035799983*^9, 3.4161840398966923`*^9}}]
}, Open  ]]
}, Open  ]]
}, Open  ]]
},
WindowSize->{640, 565},
WindowMargins->{{Automatic, 148}, {4, Automatic}},
FrontEndVersion->"6.0 for Mac OS X PowerPC (32-bit) (April 20, 2007)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[590, 23, 117, 1, 26, "Subsubtitle"],
Cell[CellGroupData[{
Cell[732, 28, 133, 2, 26, "Subsubsection"],
Cell[CellGroupData[{
Cell[890, 34, 971, 19, 49, "Input"],
Cell[1864, 55, 15044, 255, 372, 5018, 89, "CachedBoxData", "BoxData", \
"Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[16945, 315, 1037, 22, 49, "Input"],
Cell[17985, 339, 7612, 132, 375, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[25646, 477, 133, 2, 26, "Subsubsection"],
Cell[CellGroupData[{
Cell[25804, 483, 1098, 21, 49, "Input"],
Cell[26905, 506, 26077, 436, 375, 12685, 214, "CachedBoxData", "BoxData", \
"Output"]
}, Open  ]],
Cell[52997, 945, 254, 4, 45, "Text"],
Cell[CellGroupData[{
Cell[53276, 953, 200, 5, 29, "Input"],
Cell[53479, 960, 12754, 215, 375, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[66270, 1180, 1168, 23, 49, "Input"],
Cell[67441, 1205, 13205, 224, 375, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[80683, 1434, 1166, 23, 50, "Input"],
Cell[81852, 1459, 6133, 107, 374, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[88034, 1572, 115, 1, 34, "Subsection"],
Cell[88152, 1575, 615, 16, 73, "Text"],
Cell[CellGroupData[{
Cell[88792, 1595, 436, 12, 47, "Input"],
Cell[89231, 1609, 4702, 84, 243, "Output"]
}, Open  ]],
Cell[93948, 1696, 559, 14, 55, "Text"],
Cell[CellGroupData[{
Cell[94532, 1714, 375, 11, 47, "Input"],
Cell[94910, 1727, 190, 4, 27, "Output"]
}, Open  ]],
Cell[95115, 1734, 197, 5, 28, "Text"],
Cell[CellGroupData[{
Cell[95337, 1743, 296, 8, 47, "Input"],
Cell[95636, 1753, 128, 2, 27, "Output"]
}, Open  ]],
Cell[95779, 1758, 133, 2, 28, "Text"],
Cell[CellGroupData[{
Cell[95937, 1764, 318, 9, 47, "Input"],
Cell[96258, 1775, 5379, 93, 372, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}
]
*)

(* End of internal cache information *)