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The \ Table command can be used to create a table of numerical values of a \ function. For example, if we wanted to know the values of the sine function \ at the first 11 nonnegative integers, we could use the command", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["T = Table[{n, Sin[n]}, {n, 0, 10}]"], "Input", AspectRatioFixed->True], Cell[TextData[ "to create the list of ordered pairs (0,0), (1, sin(1)), ... , (10, sin(10)). \ We can force the computer to actually evaluate the sine function at each of \ the values of n by following this command with"], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["N[T]"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox["(", Evaluatable->False, AspectRatioFixed->True], StyleBox["N[", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox["expr", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontSlant->"Italic"], StyleBox["]", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" returns the numerical value of ", Evaluatable->False, AspectRatioFixed->True], StyleBox["expr", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontSlant->"Italic"], StyleBox[".)", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["Part 1: A Familiar Function"], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["\tDefine the function ", Evaluatable->False, AspectRatioFixed->True], StyleBox["f[x_] := Sin[x]/x", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[ ". 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Based on the tables you \ have made, guess the limit as ", Evaluatable->False, AspectRatioFixed->True], StyleBox["x", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" approaches zero for ", Evaluatable->False, AspectRatioFixed->True], StyleBox["f", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["(", Evaluatable->False, AspectRatioFixed->True], StyleBox["x", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["):\n\n\n\n", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "(b)\tTo refresh your memory of this function\[CloseCurlyQuote]s graph, use"], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["Plot[f[x], {x, -2Pi, 2Pi}]"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox["to draw the graph of ", Evaluatable->False, AspectRatioFixed->True], StyleBox["f", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["(", Evaluatable->False, AspectRatioFixed->True], StyleBox["x", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ ") over the interval [\[Dash]2\[Pi],2\[Pi]]. 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Define a function that has (at least) one point, ", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Chicago"], StyleBox["a", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Chicago", FontSlant->"Italic"], StyleBox[ ", not in its domain.\n Evaluate the limit of your function as the input \ approaches ", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Chicago"], StyleBox["a", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Chicago", FontSlant->"Italic"], StyleBox[ ", using tables and plots.\n Be sure to give the definition of your \ function; there is extra credit for especially \n interesting functions!\n \ \n \n \n \n \n \n \n \n \n \n \n \n \n \ \n \n \n \n \n \n \n \n \:ffff\n \n \n \n \n\ ", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Chicago"] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["Part 4: An Unfamiliar Function"], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["\tThe error function, erf(", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Chicago"], StyleBox["x", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Chicago", FontSlant->"Italic"], StyleBox[ ")\[LongDash]a function which has no \[OpenCurlyDoubleQuote]elementary\ \[CloseCurlyDoubleQuote] transformation rule\[LongDash]arises frequently in \ the study of probability and statistics and in other areas as well; its \ domain is the entire real line. Mathematica knows this function as ", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Chicago"], StyleBox["Erf[x]", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[ ". 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