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                    Mathematica-Compatible Notebook

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Cell[TextData[{
  "Instructions:  \nBegin by reading the Introduction.\nIn Part I, after \
executing and animating the command \n\t\
Do[compare[Sin[x],0,n,{-10,10},{-3,3}],{n,0,20,2}];\n\texplain what the \
graphs are telling you.\nIn the You Try It for Part I, first execute the \
commands as they are (with Log[x]),\n\tthen contrast what happens with the \
Do[compare... command here with the Sin[x] example.\n\tWhat is the major \
difference you notice?\n\tTry out another function of your own choosing.\nIn \
Part II, contrast the behavior of the sine function to the rational function \
given.\n\tDescribe the difference and explain why it occurs.\nIn the You Try \
It for Part II, try out some functions and values of \"a\" of your own.\n\tBe \
sure to adjust the xlimits, ylimits, and nrange as necessary.\n\tBy the way, \
not all functions will work here.\n\n",
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Cell["Taylor Polynomial Approximations of a Function", "Title",
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              AxesLabel \[Rule] {"\<x\>", None}, 
              ImageSize -> {72*size, 72*size/3*2}, AspectRatio \[Rule] 2/3, 
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OBJECTIVE: Observe an animated demonstration of the convergence of Taylor \
polynomials to a function that has derivatives of all orders over some \
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\>", "Text",
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  "Part II of this module contains a specially designed function that can be \
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  "command demonstrates the convergence of Taylor polynomials to a function \
over some interval of its domain, provided the function has derivatives of \
all orders. The command generates a series of plots showing the function and \
the Taylor polynomial, as the degree of the polynomial increases. The series \
of plots that is generated can be animated to demonstrate the convergence of \
the Taylor polynomials. Several functions are included in the module and \
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",
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Cell["Part I: Computing and Visualizing Taylor Polynomials", "Section",
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  " "
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  "The ",
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Cell["You Try It: Part I", "Section",
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To create a series of plots with the function you have chosen, execute the \
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\>", "Text",
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  "The Taylor polynomial seems to approximate the function well in the \
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Cell["\<\
Part II: Demonstrations of Convergence and Lack of Convergence\
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The sine function you just plotted is very well behaved. Consider the \
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\>", "Text",
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