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Cell["\<\
This notebook is by Steven Amgott.  Please send any questions or comments to \
samgott1@swarthmore.edu.  Feel free to use and distribute this notebook, but \
keep this author information in any copy you use or distribute.\
\>", "SmallText"],

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This notebook produces Taylor polynomials for various functions, and plots \
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\>", "Text"],

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Did you notice a difference between this function and the ones in the earlier \
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    FontColor->RGBColor[1, 0, 1]],
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  StyleBox["f(x)",
    FontColor->RGBColor[1, 0, 1]],
  " is the function whose Taylor polynomials (plotted in ",
  StyleBox["red",
    FontColor->RGBColor[1, 0, 0]],
  ") you wish to animate, and ",
  StyleBox["a",
    FontColor->RGBColor[1, 0, 1]],
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remainder term (f(x) minus the Taylor polynomial) is in ",
  StyleBox["green",
    FontColor->RGBColor[0, 1, 0]],
  " on a second graph whose y bounds are given by ",
  StyleBox["rmin",
    FontColor->RGBColor[1, 0, 1]],
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  StyleBox["rmax",
    FontColor->RGBColor[1, 0, 1]],
  ".  You may have to change some (or all) of the values in ",
  StyleBox["magenta",
    FontColor->RGBColor[1, 0, 1]],
  " in order to produce nice graphs to animate.  You can change the size of \
the displayed graphs by adjusting the value following the option ",
  StyleBox["ImageSize",
    FontColor->RGBColor[1, 0, 0]],
  " at the end of the cell."
}], "Text"],

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output graphs, and choose ",
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    FontColor->RGBColor[0, 0, 1]],
  " from the ",
  StyleBox["Cell",
    FontColor->RGBColor[0, 0, 1]],
  " menu item.    VCR like controls will appear at the bottom of the notebook \
window so that you can slow (or speed) the animation, pause it, and do other \
operations."
}], "Text"],

Cell["The next cell creates the graphs to be animated.", "Text"],

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      RowBox[{"a", "=", 
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      RowBox[{"max", "=", 
        StyleBox["20",
          FontColor->RGBColor[1, 0, 1]]}], ";"}], "\n", 
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        StyleBox[\(\(-2\) \[Pi]\),
          FontColor->RGBColor[1, 0, 1]]}], ";"}], "\n", 
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        StyleBox[\(-2\),
          FontColor->RGBColor[1, 0, 1]]}], ";"}], "\[IndentingNewLine]", 
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        StyleBox["2",
          FontColor->RGBColor[1, 0, 1]]}], ";"}], "\n", 
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        StyleBox[\(- .1\),
          FontColor->RGBColor[1, 0, 1]]}], ";"}], "\[IndentingNewLine]", 
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        StyleBox[".1",
          FontColor->RGBColor[1, 0, 1]]}], ";"}], "\[IndentingNewLine]", 
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      StyleBox[\(Sin[x]\),
        FontColor->RGBColor[1, 0, 1]]}], "\n", \(fPlot = 
        Plot[f[x], {x, xmin, xmax}, PlotStyle \[Rule] {Thickness[0.005]}, 
          PlotRange \[Rule] {ymin, ymax}, 
          DisplayFunction \[Rule] Identity];\), "\n", \(p[n_, 
          x_] = \[Sum]\+\(k = 0\)\%n\(\((\((\[PartialD]\_{x, k}\ f[x])\) /. x \
\[Rule] a)\) \((x - a)\)\^k\)\/\(k!\);\), "\[IndentingNewLine]", \(pPlot[n_, 
          c_] := Plot[p[n, x], {x, xmin, xmax}, PlotStyle \[Rule] {Hue[c]}, 
          PlotRange \[Rule] {ymin, ymax}, 
          DisplayFunction \[Rule] Identity];\), "\n", \(rPlot[n_] := 
        Plot[f[x] - p[n, x], {x, xmin, xmax}, 
          PlotStyle \[Rule] RGBColor[0, 1, 0], PlotLabel -> "\<remainder\>", 
          PlotRange \[Rule] {rmin, rmax}, 
          DisplayFunction \[Rule] Identity];\), "\[IndentingNewLine]", 
    RowBox[{"Animate", "[", 
      RowBox[{
        RowBox[{"Show", "[", 
          
          RowBox[{\(Graphics[{Rectangle[{0, 0}, {1, 1}, 
                  Show[fPlot, pPlot[k, k\/max], 
                    PlotLabel \[Rule] "\<degree = \>" <> ToString[k]]], 
                Rectangle[{1.2, 0}, {2.2, 1}, rPlot[k]]}]\), 
            ",", \(DisplayFunction \[Rule] $DisplayFunction\), ",", 
            RowBox[{"ImageSize", "\[Rule]", 
              StyleBox["800",
                FontColor->RGBColor[1, 0, 1]]}]}], "]"}], 
        ",", \({k, 0, max, 1}\)}], "]"}]}], "Input",
  AnimationDisplayTime->19.005]
}, Closed]]
}, Open  ]]
},
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WindowToolbars->"EditBar",
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