(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 476529, 6995]*) (*NotebookOutlinePosition[ 477651, 7035]*) (* CellTagsIndexPosition[ 477577, 7029]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Lab 3.1 Tangent Planes", "Title"], Cell["\<\ Save your final work on your account and submit your solution to \ the Engineering Math 2 Digital Dropbox with a file name in the form\ \>", \ "Solution", Evaluatable->False, AspectRatioFixed->True, CellTags->"eExam1"], Cell["\<\ LastNameFirstInitialChapterLabNumber.nb (no spaces or other \ characters)\ \>", "Solution", Evaluatable->False, AspectRatioFixed->True, CellTags->"eExam1"], Cell["for example, StroyanK3Lab1.nb", "Solution", Evaluatable->False, AspectRatioFixed->True, CellTags->"eExam1"], Cell[CellGroupData[{ Cell["\<\ Your name:Seth Cohen & T.A.'s name: Lisa Powers here Section \ A05\ \>", "Section"], Cell[CellGroupData[{ Cell[TextData[{ "This Lab is focused on understanding the gradient with the help of ", StyleBox["Mathematica", FontSlant->"Italic"], ". Open eSection 3.6 from your CD or the on-line version of the text and \ work through it. Modify those examples to do the computations for the \ function in the next exercise." }], "Text"], Cell["", "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell["", "Exercise"], Cell[CellGroupData[{ Cell[TextData[{ "a) Use ", StyleBox["Mathematica", FontSlant->"Italic"], " to graph the function ", Cell[BoxData[ \(TraditionalForm\`f[x, y] = 3 Cos[\[Pi]\ x\ y\ ] \[ExponentialE]\^\(-\((x\^2 + y\^2)\)\)\)]], " and its tangent plane together at ", Cell[BoxData[ \(TraditionalForm\`\((x, y)\) = \((1/5, 1/7)\)\)]], ". Plot with changes in ", Cell[BoxData[ \(TraditionalForm\`x\)]], " and ", Cell[BoxData[ \(TraditionalForm\`y\)]], " of \[PlusMinus]1 away from this center. Your plot will look similar to:" }], "IndentedText"], Cell[GraphicsData["PostScript", ], "Graphics", ImageSize->{124.625, 199.625}, ImageMargins->{{46, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgkoDeAEo`00 0?l0003oUINHo`000?l@413on_go0_l00002oo[mo`;o0000C_ojoOl003oon_go00KoDeAEogAfMooj oOoojNc^oe=DEOl00002oo[mo`06onW/k_lQ8B7oQHJ7okNi^_l0003of=_M<_ojoOl3o`000003oa0@ 4?ojoOoon_go01Kon_go000ooo[mo`06o`000?ojoOoon_gooo[moooYk>ko00000oojoOl01?oHfmgo 0000oa0@4?o8b/`eoo[mo`03oa0@4?ng^K[on_go01Oon_go000ooo[mo`06o`000?ojoOoon_gooo[m oooYk>ko00000oojoOl01?oYk>ko8B4Qoa0@4?oYk>heoo[mo`03oiFGV?lakoDeAEo`000?l0003oUINHo`000?l@41000_ojoOl0 0ooHfmgo0000okNi^P0Goo[mo`00?oojoOl01_oYk>koDeAEo`000?l@413ob<[koDeAEo`000?ojoOoojNc^ o`000?oYk>h2oo[mo`03o`000?oHfmgon_go01Con_go001@oo[mo`05onW/k_lah01OojoOl2ob4Q8@Gon_go00Go@T=4o`000?l0003okoDeAEo`000?l@413ob<[oo[mo`Co000000?o n_goo`000?ojoOl00_ojoOl01Ol0003oekRkomNh^ooG^;_o000000;oe;Nm0ol000000oojoOoo0000 oo[mo`05oo[mo`;o00002_ojoOl01Ol@413on_gooo[mooojoOoo410@01[on_go000Zoo[mo`05o`00 0?ojoOoon_gooo[mool000003oojoOl00olf=cOo2@T9oo[mo`0@oo[mo`Co00000_ojoOl00ol0003o n_gooo[mo`04oo[mo`08o`000?oG^;_oekRkomNh^ooB/;So0000omBg_Ol00002oln^^0Wo000000?o n_goo`000?l000002?ojoOl01Ol0003on_gooo[mooojoOoo000001[on_go000Zoo[mo`05o`000?oj oOoon_gooo[mool000003?ojoOl01Ol0003o8B4Qo`000?l92@WoX:6S00kon_go0ol00002oo[mo`03 o`000?ojoOoon_go00Son_go00So0000omNh^ooG^;_o0000om:`^?l0003oe;Nmo`0000;ocjjh0_l0 0003olVY^@;o00000_o3Y;X4o`0000Oon_go00Go0000oo[mooojoOoon_goo`00000Joo[mo`008_oj oOl4o`000005oa0@4?ojoOoon_gooo[mool@41000oojoOl00ol@413on_gooo[mo`0:oo[mo`03o`00 0?ojoOoon_go00con_go1?l00002oo[mo`03o`000?ojoOoon_go00[on_go00Ko0000omNh^ooG^;_o ekRko`000?oB/;P2o`0000?ocjjh0_l00002olVY^@03o`000?o4X[Ko000000;o`jBj00?o0000okjM ]_l000000ol00005oo[mo`05oa0@4?ojoOoon_gooo[mool@41006_ojoOl002Con_go00?o0000oo[m ooojoOl00oojoOl01Olf=cOoFEYKoo[moomIFU_o=SLg00con_go00?o0000oo[mooojoOl02?ojoOl4 o`0000;on_go00?o0000oo[mooojoOl03_ojoOl01?l0003oekRkomNh^ooG^;/3om:`^006o`000?o? 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FontSlant->"Italic"], " to graph the function ", Cell[BoxData[ \(TraditionalForm\`f[x, y] = 3 Cos[\[Pi]\ x\ y\ ] \[ExponentialE]\^\(-\((x\^2 + y\^2)\)\)\)]], " and its tangent plane together at ", Cell[BoxData[ \(TraditionalForm\`\((x, y)\) = \((1/5, 1/7)\)\)]], ". Plot with changes in ", Cell[BoxData[ \(TraditionalForm\`x\)]], " and ", Cell[BoxData[ \(TraditionalForm\`y\)]], " of \[PlusMinus]0.1 away from this center. Your plot will look similar \ to:" }], "IndentedText"], Cell[GraphicsData["PostScript", "\<\ \ \>"], "Graphics", ImageSize->{211, 199.5}, ImageMargins->{{47.5625, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgkooo[mo`03o`000?ojoOoon_go04Son_go002Yoo[mo`05o`000?ojoOoon_gooo[m ool000003_ojoOl00ol0003on_gooo[mo`18oo[mo`00ZOojoOl01Ol0003on_gooo[mooojoOoo0000 00kon_go00?o0000oo[mooojoOl0B?ojoOl00:Won_go00Go410@oo[mooojoOoon_gooa0@400>oo[m o`03o`000?ojoOoon_go04Son_go001Too[mo`08onW/k_mCE5Go0000o`000?nEUiSo0000oa0@4?oj oOl2o`0000;on_go0_l0000goo[mo`05ogAfMonEUiSon_gooiFGV?mdMWL03_ojoOl00ol0003on_go oo[mo`18oo[mo`00I?ojoOl01_mCE5GoM7Igoo[moooYk>koDeAEo`0000;on_go00KojNc^ob4Q8On5 QXOo]kVjo`000?oHfmdgoo[mo`05onW/k_lah03?ojoOl00omCE5GoI6EVo`00 001:oo[mo`00I?ojoOl01_l0003on_gooo[mooojoOoojNc^o`0000?on_go00Cof=_Mo`000?l@413o 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