MaxRecurrenceBox.nb

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

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

(* CreatedBy='Mathematica 11.1' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     32097,        688]
NotebookOptionsPosition[     31374,        662]
NotebookOutlinePosition[     31730,        678]
CellTagsIndexPosition[     31687,        675]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[TextData[{
 "From \"Options from graphics\" documentation page :\nThe Wolfram Language \
always tries to plot functions as smooth curves.Asa result, in places where \
your function wiggles a lot, the Wolfram Language will use more \
points.Ingeneral, the Wolfram Language tries to adapt its sampling of your \
function to the form of the function.Thereis a limit, however, which you can \
set, to how finely the Wolfram Language will ever sample a function.\n\nIt is \
important to realize that since the Wolfram Language can only sample your \
function at a limited number of points, it can always miss features of the \
function. The Wolfram Language adaptively samples the functions, increasing \
the number of samples near interesting features, but it is still possible to \
miss something. By increasing ",
 Cell[BoxData[
  TemplateBox[{Cell[
     TextData["PlotPoints"]],"paclet:ref/PlotPoints"},
   "RefLink",
   BaseStyle->{"InlineFormula"}]], "InlineFormula",
  FontFamily->"Source Sans Pro",ExpressionUUID->
  "7da1cb84-dfc3-4346-9ce1-f5f8a4982ffd"],
 ", you can make the Wolfram Language sample your function at a larger number \
of points. Of course, the larger you set ",
 Cell[BoxData[
  TemplateBox[{Cell[
     TextData["PlotPoints"]],"paclet:ref/PlotPoints"},
   "RefLink",
   BaseStyle->{"InlineFormula"}]], "InlineFormula",
  FontFamily->"Source Sans Pro",ExpressionUUID->
  "c6ba7d8f-9b8c-4cc3-95c1-c934fe6edf7e"],
 " to be, the longer it will take the Wolfram Language to plot ",
 StyleBox["any",
  FontSlant->"Italic"],
 " function, even a smooth one. \nDefault value for PlotPoints: 50"
}], "Input",
 Evaluatable->False,
 CellChangeTimes->{{3.35415280193427*^9, 3.35415283120027*^9}, {
   3.35415286735699*^9, 3.35415302670278*^9}, {3.35415315682944*^9, 
   3.35415318028287*^9}, {3.35415321147077*^9, 3.35415327573721*^9}, {
   3.35415330730012*^9, 3.35415332578473*^9}, {3.35415349792756*^9, 
   3.35415357163163*^9}, {3.35415369574259*^9, 3.35415369830512*^9}, {
   3.35733197835938*^9, 3.35733197851563*^9}, {3.35742855921875*^9, 
   3.35742857132813*^9}, {3.35818313378514*^9, 3.35818313436598*^9}, {
   3.36244773887781*^9, 3.36244776869031*^9}, {3.36244817034656*^9, 
   3.36244817062781*^9}, {3.36951297854688*^9, 3.36951298003125*^9}, {
   3.3839155679511156`*^9, 3.3839155685761156`*^9}, 3.7331802128999968`*^9, {
   3.778430830421362*^9, 3.778430966698813*^9}, {3.778430998668227*^9, 
   3.778430999029628*^9}, {3.77843103707062*^9, 3.7784310461463013`*^9}},
 FormatType->"TextForm",
 CellID->1496021318,ExpressionUUID->"e575e2a6-5485-462d-aef9-57b02a7de3fb"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  RowBox[{"Manipulate", "[", 
   RowBox[{
    RowBox[{"Plot", "[", 
     RowBox[{"fun", ",", 
      RowBox[{"{", 
       RowBox[{"x", ",", "0", ",", "xmax"}], "}"}], ",", 
      RowBox[{"Mesh", "->", "All"}], ",", 
      RowBox[{"MeshStyle", "->", 
       RowBox[{"Directive", "[", 
        RowBox[{"Red", ",", 
         RowBox[{"PointSize", "[", "0.012", "]"}]}], "]"}]}], ",", 
      RowBox[{"PlotPoints", "->", "n"}], ",", 
      RowBox[{"MaxRecursion", "->", "m"}]}], "]"}], ",", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"fun", ",", 
        RowBox[{"Sin", "[", "x", "]"}], ",", "\"\<function to plot\>\""}], 
       "}"}], ",", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"Sin", "[", "x", "]"}], ",", 
        RowBox[{"Tan", "[", "x", "]"}], ",", 
        RowBox[{"Sin", "[", 
         RowBox[{"Tan", "[", "x", "]"}], "]"}], ",", 
        RowBox[{"Abs", "[", 
         RowBox[{"Sqrt", "[", 
          RowBox[{"Sin", "[", "x", "]"}], "]"}], "]"}]}], "}"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"xmax", ",", "10", ",", "\"\<range of plot\>\""}], "}"}], ",", 
      "1", ",", "40"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"n", ",", "50", ",", "\"\<initial number of points\>\""}], 
       "}"}], ",", "2", ",", "100", ",", "1"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"m", ",", "6", ",", "\"\<maximum subdivision level\>\""}], 
       "}"}], ",", "0", ",", "8", ",", "1"}], "}"}], ",", " ", 
    RowBox[{"AutorunSequencing", "->", 
     RowBox[{"{", 
      RowBox[{"2", ",", "3", ",", "4"}], "}"}]}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.35415280193427*^9, 3.35415283120027*^9}, {
   3.35415286735699*^9, 3.35415302670278*^9}, {3.35415315682944*^9, 
   3.35415318028287*^9}, {3.35415321147077*^9, 3.35415327573721*^9}, {
   3.35415330730012*^9, 3.35415332578473*^9}, {3.35415349792756*^9, 
   3.35415357163163*^9}, {3.35415369574259*^9, 3.35415369830512*^9}, {
   3.35733197835938*^9, 3.35733197851563*^9}, {3.35742855921875*^9, 
   3.35742857132813*^9}, {3.35818313378514*^9, 3.35818313436598*^9}, {
   3.36244773887781*^9, 3.36244776869031*^9}, {3.36244817034656*^9, 
   3.36244817062781*^9}, {3.36951297854688*^9, 3.36951298003125*^9}, {
   3.3839155679511156`*^9, 3.3839155685761156`*^9}, 3.7331802128999968`*^9, {
   3.778430830421362*^9, 
   3.778430836395007*^9}},ExpressionUUID->"4d900f12-0f4c-4554-86df-\
4df721d906b7"],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`fun$$ = Abs[
      Sin[$CellContext`x]]^Rational[1, 2], $CellContext`m$$ = 
    3, $CellContext`n$$ = 9, $CellContext`xmax$$ = 4.550000000000001, 
    Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, 
    Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 
    1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{
       Hold[$CellContext`fun$$], 
       Sin[$CellContext`x], "function to plot"}, {
       Sin[$CellContext`x], 
       Tan[$CellContext`x], 
       Sin[
        Tan[$CellContext`x]], Abs[
         Sin[$CellContext`x]]^Rational[1, 2]}}, {{
       Hold[$CellContext`xmax$$], 10, "range of plot"}, 1, 40}, {{
       Hold[$CellContext`n$$], 50, "initial number of points"}, 2, 100, 1}, {{
      
       Hold[$CellContext`m$$], 6, "maximum subdivision level"}, 0, 8, 1}}, 
    Typeset`size$$ = {360., {109., 113.}}, Typeset`update$$ = 0, 
    Typeset`initDone$$, Typeset`skipInitDone$$ = 
    True, $CellContext`fun$34220$$ = 0, $CellContext`xmax$34221$$ = 
    0, $CellContext`n$34222$$ = 0, $CellContext`m$34223$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`fun$$ = 
        Sin[$CellContext`x], $CellContext`m$$ = 6, $CellContext`n$$ = 
        50, $CellContext`xmax$$ = 10}, "ControllerVariables" :> {
        Hold[$CellContext`fun$$, $CellContext`fun$34220$$, 0], 
        Hold[$CellContext`xmax$$, $CellContext`xmax$34221$$, 0], 
        Hold[$CellContext`n$$, $CellContext`n$34222$$, 0], 
        Hold[$CellContext`m$$, $CellContext`m$34223$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> 
      Plot[$CellContext`fun$$, {$CellContext`x, 0, $CellContext`xmax$$}, Mesh -> 
        All, MeshStyle -> Directive[Red, 
          PointSize[0.012]], PlotPoints -> $CellContext`n$$, 
        MaxRecursion -> $CellContext`m$$], 
      "Specifications" :> {{{$CellContext`fun$$, 
          Sin[$CellContext`x], "function to plot"}, {
          Sin[$CellContext`x], 
          Tan[$CellContext`x], 
          Sin[
           Tan[$CellContext`x]], Abs[
            Sin[$CellContext`x]]^Rational[1, 2]}}, {{$CellContext`xmax$$, 10, 
          "range of plot"}, 1, 
         40}, {{$CellContext`n$$, 50, "initial number of points"}, 2, 100, 
         1}, {{$CellContext`m$$, 6, "maximum subdivision level"}, 0, 8, 1}}, 
      "Options" :> {AutorunSequencing -> {2, 3, 4}}, 
      "DefaultOptions" :> {ControllerLinking -> True}],
     ImageSizeCache->{405., {197., 203.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    SynchronousInitialization->True,
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{3.733180212900612*^9},
 CellID->683697159,ExpressionUUID->"9b4206e4-055c-403c-a31d-2983c1752314"]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"Cell", "[", 
   RowBox[{"CellGroupData", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"Cell", "[", 
        RowBox[{
         RowBox[{"BoxData", "[", 
          RowBox[{"RowBox", "[", 
           RowBox[{"{", 
            RowBox[{"\"\<Manipulate\>\"", ",", "\"\<[\>\"", ",", 
             RowBox[{"RowBox", "[", 
              RowBox[{"{", 
               RowBox[{
                RowBox[{"RowBox", "[", 
                 RowBox[{"{", 
                  RowBox[{"\"\<Plot\>\"", ",", "\"\<[\>\"", ",", 
                   RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<fun\>\"", ",", "\"\<,\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<{\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    "\"\<x\>\"", ",", "\"\<,\>\"", ",", "\"\<0\>\"", ",", 
                    "\"\<,\>\"", ",", "\"\<xmax\>\""}], "}"}], "]"}], ",", 
                    "\"\<}\>\""}], "}"}], "]"}], ",", "\"\<,\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    "\"\<Mesh\>\"", ",", "\"\<->\>\"", ",", "\"\<All\>\""}], 
                    "}"}], "]"}], ",", "\"\<,\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<MeshStyle\>\"", ",", "\"\<->\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<Directive\>\"", ",", "\"\<[\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<Red\>\"", ",", "\"\<,\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    "\"\<PointSize\>\"", ",", "\"\<[\>\"", ",", 
                    "\"\<0.012\>\"", ",", "\"\<]\>\""}], "}"}], "]"}]}], 
                    "}"}], "]"}], ",", "\"\<]\>\""}], "}"}], "]"}]}], "}"}], 
                    "]"}], ",", "\"\<,\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    "\"\<PlotPoints\>\"", ",", "\"\<->\>\"", ",", 
                    "\"\<n\>\""}], "}"}], "]"}], ",", "\"\<,\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    "\"\<MaxRecursion\>\"", ",", "\"\<->\>\"", ",", 
                    "\"\<m\>\""}], "}"}], "]"}]}], "}"}], "]"}], ",", 
                   "\"\<]\>\""}], "}"}], "]"}], ",", "\"\<,\>\"", ",", 
                RowBox[{"RowBox", "[", 
                 RowBox[{"{", 
                  RowBox[{"\"\<{\>\"", ",", 
                   RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<{\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<fun\>\"", ",", "\"\<,\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    "\"\<Sin\>\"", ",", "\"\<[\>\"", ",", "\"\<x\>\"", ",", 
                    "\"\<]\>\""}], "}"}], "]"}], ",", "\"\<,\>\"", ",", 
                    "\"\<\\\"\\<function to plot\\>\\\"\>\""}], "}"}], "]"}], 
                    ",", "\"\<}\>\""}], "}"}], "]"}], ",", "\"\<,\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<{\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    "\"\<Sin\>\"", ",", "\"\<[\>\"", ",", "\"\<x\>\"", ",", 
                    "\"\<]\>\""}], "}"}], "]"}], ",", "\"\<,\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    "\"\<Tan\>\"", ",", "\"\<[\>\"", ",", "\"\<x\>\"", ",", 
                    "\"\<]\>\""}], "}"}], "]"}], ",", "\"\<,\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<Sin\>\"", ",", "\"\<[\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    "\"\<Tan\>\"", ",", "\"\<[\>\"", ",", "\"\<x\>\"", ",", 
                    "\"\<]\>\""}], "}"}], "]"}], ",", "\"\<]\>\""}], "}"}], 
                    "]"}], ",", "\"\<,\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<Abs\>\"", ",", "\"\<[\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<Sqrt\>\"", ",", "\"\<[\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    "\"\<Sin\>\"", ",", "\"\<[\>\"", ",", "\"\<x\>\"", ",", 
                    "\"\<]\>\""}], "}"}], "]"}], ",", "\"\<]\>\""}], "}"}], 
                    "]"}], ",", "\"\<]\>\""}], "}"}], "]"}]}], "}"}], "]"}], 
                    ",", "\"\<}\>\""}], "}"}], "]"}]}], "}"}], "]"}], ",", 
                   "\"\<}\>\""}], "}"}], "]"}], ",", "\"\<,\>\"", ",", 
                RowBox[{"RowBox", "[", 
                 RowBox[{"{", 
                  RowBox[{"\"\<{\>\"", ",", 
                   RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<{\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    "\"\<xmax\>\"", ",", "\"\<,\>\"", ",", "\"\<10\>\"", ",", 
                    "\"\<,\>\"", ",", "\"\<\\\"\\<range of plot\\>\\\"\>\""}],
                     "}"}], "]"}], ",", "\"\<}\>\""}], "}"}], "]"}], ",", 
                    "\"\<,\>\"", ",", "\"\<1\>\"", ",", "\"\<,\>\"", ",", 
                    "\"\<40\>\""}], "}"}], "]"}], ",", "\"\<}\>\""}], "}"}], 
                 "]"}], ",", "\"\<,\>\"", ",", 
                RowBox[{"RowBox", "[", 
                 RowBox[{"{", 
                  RowBox[{"\"\<{\>\"", ",", 
                   RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<{\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    "\"\<n\>\"", ",", "\"\<,\>\"", ",", "\"\<50\>\"", ",", 
                    "\"\<,\>\"", ",", 
                    "\"\<\\\"\\<initial number of points\\>\\\"\>\""}], "}"}],
                     "]"}], ",", "\"\<}\>\""}], "}"}], "]"}], ",", 
                    "\"\<,\>\"", ",", "\"\<2\>\"", ",", "\"\<,\>\"", ",", 
                    "\"\<100\>\"", ",", "\"\<,\>\"", ",", "\"\<1\>\""}], 
                    "}"}], "]"}], ",", "\"\<}\>\""}], "}"}], "]"}], ",", 
                "\"\<,\>\"", ",", 
                RowBox[{"RowBox", "[", 
                 RowBox[{"{", 
                  RowBox[{"\"\<{\>\"", ",", 
                   RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<{\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    "\"\<m\>\"", ",", "\"\<,\>\"", ",", "\"\<6\>\"", ",", 
                    "\"\<,\>\"", ",", 
                    "\"\<\\\"\\<maximum subdivision level\\>\\\"\>\""}], 
                    "}"}], "]"}], ",", "\"\<}\>\""}], "}"}], "]"}], ",", 
                    "\"\<,\>\"", ",", "\"\<0\>\"", ",", "\"\<,\>\"", ",", 
                    "\"\<8\>\"", ",", "\"\<,\>\"", ",", "\"\<1\>\""}], "}"}], 
                    "]"}], ",", "\"\<}\>\""}], "}"}], "]"}], ",", "\"\<,\>\"",
                 ",", "\"\< \>\"", ",", 
                RowBox[{"RowBox", "[", 
                 RowBox[{"{", 
                  RowBox[{"\"\<AutorunSequencing\>\"", ",", "\"\<->\>\"", ",", 
                   RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{"\"\<{\>\"", ",", 
                    RowBox[{"RowBox", "[", 
                    RowBox[{"{", 
                    RowBox[{
                    "\"\<2\>\"", ",", "\"\<,\>\"", ",", "\"\<3\>\"", ",", 
                    "\"\<,\>\"", ",", "\"\<4\>\""}], "}"}], "]"}], ",", 
                    "\"\<}\>\""}], "}"}], "]"}]}], "}"}], "]"}]}], "}"}], 
              "]"}], ",", "\"\<]\>\""}], "}"}], "]"}], "]"}], ",", 
         "\"\<Input\>\"", ",", 
         RowBox[{"CellChangeTimes", "\[Rule]", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{"3.35415280193427*^9", ",", "3.35415283120027*^9"}], 
             "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"3.35415286735699*^9", ",", "3.35415302670278*^9"}], 
             "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"3.35415315682944*^9", ",", "3.35415318028287*^9"}], 
             "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"3.35415321147077*^9", ",", "3.35415327573721*^9"}], 
             "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"3.35415330730012*^9", ",", "3.35415332578473*^9"}], 
             "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"3.35415349792756*^9", ",", "3.35415357163163*^9"}], 
             "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"3.35415369574259*^9", ",", "3.35415369830512*^9"}], 
             "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"3.35733197835938*^9", ",", "3.35733197851563*^9"}], 
             "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"3.35742855921875*^9", ",", "3.35742857132813*^9"}], 
             "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"3.35818313378514*^9", ",", "3.35818313436598*^9"}], 
             "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"3.36244773887781*^9", ",", "3.36244776869031*^9"}], 
             "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"3.36244817034656*^9", ",", "3.36244817062781*^9"}], 
             "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"3.36951297854688*^9", ",", "3.36951298003125*^9"}], 
             "}"}], ",", 
            RowBox[{"{", 
             RowBox[{
             "3.3839155679511156`*^9", ",", "3.3839155685761156`*^9"}], "}"}],
             ",", "3.7331802128999968`*^9"}], "}"}]}], ",", 
         RowBox[{"CellID", "\[Rule]", "1496021318"}]}], "]"}], ",", 
       RowBox[{"Cell", "[", 
        RowBox[{
         RowBox[{"BoxData", "[", 
          RowBox[{"TagBox", "[", 
           RowBox[{
            RowBox[{"StyleBox", "[", 
             RowBox[{
              RowBox[{"DynamicModuleBox", "[", 
               RowBox[{
                RowBox[{"{", 
                 RowBox[{
                  RowBox[{"$CellContext`fun$$", "=", 
                   RowBox[{
                    RowBox[{"Abs", "[", 
                    RowBox[{"Sin", "[", "$CellContext`x", "]"}], "]"}], "^", 
                    RowBox[{"Rational", "[", 
                    RowBox[{"1", ",", "2"}], "]"}]}]}], ",", 
                  RowBox[{"$CellContext`m$$", "=", "6"}], ",", 
                  RowBox[{"$CellContext`n$$", "=", "50"}], ",", 
                  RowBox[{"$CellContext`xmax$$", "=", "10"}], ",", 
                  RowBox[{"Typeset`show$$", "=", "True"}], ",", 
                  RowBox[{"Typeset`bookmarkList$$", "=", 
                   RowBox[{"{", "}"}]}], ",", 
                  RowBox[{"Typeset`bookmarkMode$$", "=", "\"\<Menu\>\""}], 
                  ",", "Typeset`animator$$", ",", 
                  RowBox[{"Typeset`animvar$$", "=", "1"}], ",", 
                  RowBox[{"Typeset`name$$", "=", "\"\<\\\"untitled\\\"\>\""}],
                   ",", 
                  RowBox[{"Typeset`specs$$", "=", 
                   RowBox[{"{", 
                    RowBox[{
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"Hold", "[", "$CellContext`fun$$", "]"}], ",", 
                    RowBox[{"Sin", "[", "$CellContext`x", "]"}], ",", 
                    "\"\<function to plot\>\""}], "}"}], ",", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"Sin", "[", "$CellContext`x", "]"}], ",", 
                    RowBox[{"Tan", "[", "$CellContext`x", "]"}], ",", 
                    RowBox[{"Sin", "[", 
                    RowBox[{"Tan", "[", "$CellContext`x", "]"}], "]"}], ",", 
                    RowBox[{
                    RowBox[{"Abs", "[", 
                    RowBox[{"Sin", "[", "$CellContext`x", "]"}], "]"}], "^", 
                    RowBox[{"Rational", "[", 
                    RowBox[{"1", ",", "2"}], "]"}]}]}], "}"}]}], "}"}], ",", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"Hold", "[", "$CellContext`xmax$$", "]"}], ",", 
                    "10", ",", "\"\<range of plot\>\""}], "}"}], ",", "1", 
                    ",", "40"}], "}"}], ",", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"Hold", "[", "$CellContext`n$$", "]"}], ",", "50",
                     ",", "\"\<initial number of points\>\""}], "}"}], ",", 
                    "2", ",", "100", ",", "1"}], "}"}], ",", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"Hold", "[", "$CellContext`m$$", "]"}], ",", "6", 
                    ",", "\"\<maximum subdivision level\>\""}], "}"}], ",", 
                    "0", ",", "8", ",", "1"}], "}"}]}], "}"}]}], ",", 
                  RowBox[{"Typeset`size$$", "=", 
                   RowBox[{"{", 
                    RowBox[{"360.", ",", 
                    RowBox[{"{", 
                    RowBox[{"112.", ",", "116."}], "}"}]}], "}"}]}], ",", 
                  RowBox[{"Typeset`update$$", "=", "0"}], ",", 
                  "Typeset`initDone$$", ",", 
                  RowBox[{"Typeset`skipInitDone$$", "=", "True"}], ",", 
                  RowBox[{"$CellContext`fun$34220$$", "=", "0"}], ",", 
                  RowBox[{"$CellContext`xmax$34221$$", "=", "0"}], ",", 
                  RowBox[{"$CellContext`n$34222$$", "=", "0"}], ",", 
                  RowBox[{"$CellContext`m$34223$$", "=", "0"}]}], "}"}], ",", 
                
                RowBox[{"DynamicBox", "[", 
                 RowBox[{
                  RowBox[{"Manipulate`ManipulateBoxes", "[", 
                   RowBox[{"1", ",", "StandardForm", ",", 
                    RowBox[{"\"\<Variables\>\"", "\[RuleDelayed]", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"$CellContext`fun$$", "=", 
                    RowBox[{"Sin", "[", "$CellContext`x", "]"}]}], ",", 
                    RowBox[{"$CellContext`m$$", "=", "6"}], ",", 
                    RowBox[{"$CellContext`n$$", "=", "50"}], ",", 
                    RowBox[{"$CellContext`xmax$$", "=", "10"}]}], "}"}]}], 
                    ",", 
                    RowBox[{"\"\<ControllerVariables\>\"", "\[RuleDelayed]", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"Hold", "[", 
                    RowBox[{
                    "$CellContext`fun$$", ",", "$CellContext`fun$34220$$", 
                    ",", "0"}], "]"}], ",", 
                    RowBox[{"Hold", "[", 
                    RowBox[{
                    "$CellContext`xmax$$", ",", "$CellContext`xmax$34221$$", 
                    ",", "0"}], "]"}], ",", 
                    RowBox[{"Hold", "[", 
                    RowBox[{
                    "$CellContext`n$$", ",", "$CellContext`n$34222$$", ",", 
                    "0"}], "]"}], ",", 
                    RowBox[{"Hold", "[", 
                    RowBox[{
                    "$CellContext`m$$", ",", "$CellContext`m$34223$$", ",", 
                    "0"}], "]"}]}], "}"}]}], ",", 
                    RowBox[{"\"\<OtherVariables\>\"", "\[RuleDelayed]", 
                    RowBox[{"{", 
                    RowBox[{
                    "Typeset`show$$", ",", "Typeset`bookmarkList$$", ",", 
                    "Typeset`bookmarkMode$$", ",", "Typeset`animator$$", ",", 
                    "Typeset`animvar$$", ",", "Typeset`name$$", ",", 
                    "Typeset`specs$$", ",", "Typeset`size$$", ",", 
                    "Typeset`update$$", ",", "Typeset`initDone$$", ",", 
                    "Typeset`skipInitDone$$"}], "}"}]}], ",", 
                    RowBox[{"\"\<Body\>\"", "\[RuleDelayed]", 
                    RowBox[{"Plot", "[", 
                    RowBox[{"$CellContext`fun$$", ",", 
                    RowBox[{"{", 
                    RowBox[{
                    "$CellContext`x", ",", "0", ",", "$CellContext`xmax$$"}], 
                    "}"}], ",", 
                    RowBox[{"Mesh", "\[Rule]", "All"}], ",", 
                    RowBox[{"MeshStyle", "\[Rule]", 
                    RowBox[{"Directive", "[", 
                    RowBox[{"Red", ",", 
                    RowBox[{"PointSize", "[", "0.012", "]"}]}], "]"}]}], ",", 
                    
                    RowBox[{"PlotPoints", "\[Rule]", "$CellContext`n$$"}], 
                    ",", 
                    RowBox[{"MaxRecursion", "\[Rule]", "$CellContext`m$$"}]}],
                     "]"}]}], ",", 
                    RowBox[{"\"\<Specifications\>\"", "\[RuleDelayed]", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"{", 
                    RowBox[{"$CellContext`fun$$", ",", 
                    RowBox[{"Sin", "[", "$CellContext`x", "]"}], ",", 
                    "\"\<function to plot\>\""}], "}"}], ",", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"Sin", "[", "$CellContext`x", "]"}], ",", 
                    RowBox[{"Tan", "[", "$CellContext`x", "]"}], ",", 
                    RowBox[{"Sin", "[", 
                    RowBox[{"Tan", "[", "$CellContext`x", "]"}], "]"}], ",", 
                    RowBox[{
                    RowBox[{"Abs", "[", 
                    RowBox[{"Sin", "[", "$CellContext`x", "]"}], "]"}], "^", 
                    RowBox[{"Rational", "[", 
                    RowBox[{"1", ",", "2"}], "]"}]}]}], "}"}]}], "}"}], ",", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"{", 
                    RowBox[{
                    "$CellContext`xmax$$", ",", "10", ",", 
                    "\"\<range of plot\>\""}], "}"}], ",", "1", ",", "40"}], 
                    "}"}], ",", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"{", 
                    RowBox[{
                    "$CellContext`n$$", ",", "50", ",", 
                    "\"\<initial number of points\>\""}], "}"}], ",", "2", 
                    ",", "100", ",", "1"}], "}"}], ",", 
                    RowBox[{"{", 
                    RowBox[{
                    RowBox[{"{", 
                    RowBox[{
                    "$CellContext`m$$", ",", "6", ",", 
                    "\"\<maximum subdivision level\>\""}], "}"}], ",", "0", 
                    ",", "8", ",", "1"}], "}"}]}], "}"}]}], ",", 
                    RowBox[{"\"\<Options\>\"", "\[RuleDelayed]", 
                    RowBox[{"{", 
                    RowBox[{"AutorunSequencing", "\[Rule]", 
                    RowBox[{"{", 
                    RowBox[{"2", ",", "3", ",", "4"}], "}"}]}], "}"}]}], ",", 
                    
                    RowBox[{"\"\<DefaultOptions\>\"", "\[RuleDelayed]", 
                    RowBox[{"{", 
                    RowBox[{"ControllerLinking", "\[Rule]", "True"}], 
                    "}"}]}]}], "]"}], ",", 
                  RowBox[{"ImageSizeCache", "\[Rule]", 
                   RowBox[{"{", 
                    RowBox[{"405.", ",", 
                    RowBox[{"{", 
                    RowBox[{"200.", ",", "206."}], "}"}]}], "}"}]}], ",", 
                  RowBox[{"SingleEvaluation", "\[Rule]", "True"}]}], "]"}], 
                ",", 
                RowBox[{"Deinitialization", "\[RuleDelayed]", "None"}], ",", 
                RowBox[{"DynamicModuleValues", "\[RuleDelayed]", 
                 RowBox[{"{", "}"}]}], ",", 
                RowBox[{"SynchronousInitialization", "\[Rule]", "True"}], ",", 
                RowBox[{"UnsavedVariables", "\[RuleDelayed]", 
                 RowBox[{"{", "Typeset`initDone$$", "}"}]}], ",", 
                RowBox[{"UntrackedVariables", "\[RuleDelayed]", 
                 RowBox[{"{", "Typeset`size$$", "}"}]}]}], "]"}], ",", 
              "\"\<Manipulate\>\"", ",", 
              RowBox[{"Deployed", "\[Rule]", "True"}], ",", 
              RowBox[{"StripOnInput", "\[Rule]", "False"}]}], "]"}], ",", 
            RowBox[{"Manipulate`InterpretManipulate", "[", "1", "]"}]}], 
           "]"}], "]"}], ",", "\"\<Output\>\"", ",", 
         RowBox[{"CellChangeTimes", "\[Rule]", 
          RowBox[{"{", "3.733180212900612*^9", "}"}]}], ",", 
         RowBox[{"CellID", "\[Rule]", "683697159"}]}], "]"}]}], "}"}], ",", 
     RowBox[{"{", "2", "}"}]}], "]"}], "]"}], "\n", 
  "\[IndentingNewLine]"}]], "Input",
 CellChangeTimes->{{3.778306057223578*^9, 
  3.778306057362853*^9}},ExpressionUUID->"d4d915dd-4060-4c51-9777-\
08da9b6e2b6e"]
},
WindowSize->{808, 755},
WindowMargins->{{Automatic, 270}, {Automatic, 34}},
FrontEndVersion->"11.1 for Mac OS X x86 (32-bit, 64-bit Kernel) (April 27, \
2017)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 2597, 47, 265, "Input", "ExpressionUUID" -> \
"e575e2a6-5485-462d-aef9-57b02a7de3fb",
 Evaluatable->False,
 CellID->1496021318],
Cell[CellGroupData[{
Cell[3180, 71, 2548, 60, 138, "Input", "ExpressionUUID" -> \
"4d900f12-0f4c-4554-86df-4df721d906b7"],
Cell[5731, 133, 3222, 65, 417, "Output", "ExpressionUUID" -> \
"9b4206e4-055c-403c-a31d-2983c1752314",
 CellID->683697159]
}, Open  ]],
Cell[8968, 201, 22402, 459, 2217, "Input", "ExpressionUUID" -> \
"d4d915dd-4060-4c51-9777-08da9b6e2b6e"]
}
]
*)