(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. The line below identifies what version of Mathematica created this file, but it can be opened using any other version as well."; FrontEndVersion = "X Window System Mathematica Notebook Front End Version 2.2"; X11StandardFontEncoding; fontset = title, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8, 24, fontName, "times"; fontset = subtitle, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6, 18, fontName, "times"; fontset = subsubtitle, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6, 14, fontName, "times"; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20, 18, fontName, "times"; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15, 14, fontName, "times"; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 12, fontName, "times"; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times"; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, fontName, "times"; fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, 12, fontName, "courier"; fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, fontName, "courier"; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, 12, fontName, "courier"; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, 12, fontName, "courier"; fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, 12, fontName, "courier"; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, 12, fontName, "courier"; fontset = name, inactive, noPageBreakInGroup, nohscroll, preserveAspect, M7, italic, B65535, 10, fontName, "times"; fontset = header, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, 12, fontName, "times"; fontset = leftheader, 12, fontName, "times"; fontset = footer, inactive, nohscroll, noKeepOnOnePage, preserveAspect, center, M7, italic, 12, fontName, "times"; fontset = leftfooter, 12, fontName, "times"; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times"; fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times"; fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "courier"; fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times"; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times"; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times"; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times"; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, fontName, "times";paletteColors = 128; automaticGrouping; currentKernel; ] :[font = title; inactive; preserveAspect; startGroup] Slope of Tangent Line Animation :[font = section; inactive; preserveAspect] The following is an animation which shows a secant line approaching the tangent line for the function f(x)=sin(x^2 - 2x -2) at the point x=1. :[font = section; inactive; preserveAspect; startGroup] To see the animation, do the following: If you are running Mathematica: double click on the picture below. The speed and other parameters in the animation are controlled by buttons which will appear at the bottom of the window. If you are running MathReader, select the cell bracket to the right of the picture below, and then select the "animate selected graphics" option under the Graphics menu. 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