(* 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[ 1247913, 22004] NotebookOptionsPosition[ 1240472, 21782] NotebookOutlinePosition[ 1240889, 21800] CellTagsIndexPosition[ 1240846, 21797] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ "Visualizing your solutions with ", StyleBox["Mathematica", FontSlant->"Italic"] }], "Title", CellChangeTimes->{{3.392646569941063*^9, 3.3926465710026007`*^9}, { 3.3926482050485363`*^9, 3.3926482264395084`*^9}}, Magnification->1.5], Cell["\<\ Comp 160 Module 3 \ \>", "Subtitle", CellChangeTimes->{{3.392646573876762*^9, 3.392646574016965*^9}, 3.3926517535864663`*^9, {3.458656205328125*^9, 3.45865621*^9}}, Magnification->1.5], Cell[TextData[{ "The previous module introduced ", StyleBox["Mathematica'", FontSlant->"Italic"], "s visualization tools ", StyleBox["Plot", FontFamily->"Courier New"], " and ", StyleBox["ListPlot", FontFamily->"Courier New"], ". Today, we will explore these further, plus more visualization tools." }], "Text", CellChangeTimes->{{3.3926513562311354`*^9, 3.392651420714501*^9}, { 3.392651761177457*^9, 3.392651762539429*^9}, {3.45916574496875*^9, 3.45916579084375*^9}, {3.459165827453125*^9, 3.459165858125*^9}, 3.459166435703125*^9, {3.460995341015625*^9, 3.460995432078125*^9}}, Magnification->1.5], Cell["Consider the following function", "Text", CellChangeTimes->{{3.3926513562311354`*^9, 3.392651420714501*^9}, { 3.392651761177457*^9, 3.392651762539429*^9}, {3.45916574496875*^9, 3.45916579084375*^9}, 3.459166034234375*^9}, Magnification->1.5], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "x_", "]"}], ":=", RowBox[{"Sin", "[", FractionBox["1", "x"], "]"}]}]], "Input", CellChangeTimes->{{3.3926514229877925`*^9, 3.392651457507774*^9}}, Magnification->1.5], Cell[TextData[{ "How does the function ", Cell[BoxData[ RowBox[{"f", "[", "x", "]"}]]], " behave as ", Cell[BoxData["x"]], " approaches zero? 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A ", StyleBox["contour", FontSlant->"Italic"], " is the set of all points ", Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]]], " such that ", Cell[BoxData[ RowBox[{ RowBox[{"h", "[", RowBox[{"x", ",", "y"}], "]"}], "\[Equal]", "c"}]]], ", where ", Cell[BoxData[ FormBox[ StyleBox["c", FontFamily->"Courier New", FontSlant->"Plain"], TraditionalForm]]], " is a constant. 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