(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 28106, 688] NotebookOptionsPosition[ 26812, 646] NotebookOutlinePosition[ 27156, 661] CellTagsIndexPosition[ 27113, 658] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Etude de fonction 07", "Section", CellChangeTimes->{{3.485916422151963*^9, 3.4859164276242332`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"f(x) = \"\>", "\[InvisibleSpace]", FractionBox[ RowBox[{ RowBox[{"3", " ", "x"}], "-", "5"}], RowBox[{"4", "-", RowBox[{"2", " ", "x"}]}]]}], SequenceForm[ "f(x) = ", (4 - 2 $CellContext`x)^(-1) (-5 + 3 $CellContext`x)], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485916413385476*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"1. Domaine de d\[EAcute]finition\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.485916413386673*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\*TagBox[\\\"\ \[DoubleStruckCapitalR]\\\", Function[List[], Reals]]\\) \\\\ \ {\\!\\(TraditionalForm\\`2\\)}\"\>", StringForm["`1` \\ {`2`}", Reals, 2], Editable->False], TraditionalForm]}], SequenceForm["Dom f = ", analyse`Ens[ Or[$CellContext`x < 2, $CellContext`x > 2], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485916413388431*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ RowBox[{"3", " ", "x"}], "-", "5"}], RowBox[{"4", "-", RowBox[{"2", " ", "x"}]}]], "\[InvisibleSpace]", "\<\" n'est ni paire ni impaire\"\>"}], SequenceForm[(4 - 2 $CellContext`x)^(-1) (-5 + 3 $CellContext`x), " n'est ni paire ni impaire"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485916413390307*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"2. Signe de f\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.485916413391621*^9}], Cell[BoxData[ FormBox[ TagBox[GridBox[{ {"x", " ", FractionBox["5", "3"], " ", "2", " "}, { FractionBox[ RowBox[{ RowBox[{"3", " ", "x"}], "-", "5"}], RowBox[{"4", "-", RowBox[{"2", " ", "x"}]}]], "-", "0", "+", "|", "-"} }, GridBoxDividers->{ "Columns" -> {{True}}, "ColumnsIndexed" -> {}, "Rows" -> {{True}}, "RowsIndexed" -> {}}], DisplayForm], TraditionalForm]], "Print", CellChangeTimes->{3.485916413392912*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"3. Limites et asymptotes\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.485916413394886*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(\[Piecewise] \ \\*GridBox[{{\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 2\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"<\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(3\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \ x\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) - 5\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\ \\\\\\\\\\\\(4 - \ \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(2\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ x\\\\\\\\\ \\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\ \\\\\\)\\\\\\\\) = \ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"+\\\\\\\\\\\\\\\\!\\\ \\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\[Infinity]\\\\\ \\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\"\\\", \\\"\\\\\\\" \ \\\\\\\"\\\"}, \ {\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 2\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\">\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(3\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \ x\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) - 5\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\ \\\\\\\\\\\\(4 - \ \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(2\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ x\\\\\\\\\ \\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\ \\\\\\)\\\\\\\\) = \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(-\ \[Infinity]\\\\\\\\)\\\\\\\\)\\\\\\\"\\\", \\\"\\\\\\\" \\\\\\\"\\\"}}, \ ColumnAlignments -> {Left}, ColumnSpacings -> 1.2, ColumnWidths -> Automatic]\ \\)\\)\"\>", StringForm["`1`", Piecewise[{{ StringForm["`1` = `2`", analyse`Limite[(4 - 2 $CellContext`x)^(-1) (-5 + 3 $CellContext`x), $CellContext`x, 2, -1], StringForm["+`1`", DirectedInfinity[1]]], " "}, { StringForm["`1` = `2`", analyse`Limite[(4 - 2 $CellContext`x)^(-1) (-5 + 3 $CellContext`x), $CellContext`x, 2, 1], DirectedInfinity[-1]], " "}}, 0]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485916413396243*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"AV \[Congruent] \\!\\(TraditionalForm\\`x\\) = \ \\!\\(TraditionalForm\\`2\\)\"\>", StringForm["AV \[Congruent] `1` = `2`", $CellContext`x, 2], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485916413402625*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\(\\\\(3\\\\\\\\ x\\\\)\\\\) \ - 5\\\\)\\\\/\\\\(4 - \\\\(\\\\(2\\\\\\\\ x\\\\)\\\\)\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\(-\\(\\(3\\/2\\)\\)\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(4 - 2 $CellContext`x)^(-1) (-5 + 3 $CellContext`x), $CellContext`x, DirectedInfinity[1]], Rational[-3, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485916413404011*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\(\\\\(3\\\\\\\\ x\\\\)\\\\) - 5\\\\)\\\ \\/\\\\(4 - \\\\(\\\\(2\\\\\\\\ x\\\\)\\\\)\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\(-\\(\\(3\\/2\\)\\)\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(4 - 2 $CellContext`x)^(-1) (-5 + 3 $CellContext`x), $CellContext`x, DirectedInfinity[-1]], Rational[-3, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485916413406288*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", RowBox[{"-", FractionBox["3", "2"]}]}]}], SequenceForm["AH", " \[Congruent] ", $CellContext`y == Rational[-3, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485916413542327*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"4. Intersection avec les axes\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.4859164135438633`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\\"\\\\!\\\\(\ TraditionalForm\\\\`\\\\\\\"Gf \\\\\\\\[Intersection] X = { \ \\\\\\\"\\\\)\\\\!\\\\(TraditionalForm\\\\`\\\\\\\"(\\\\\\\\!\\\\\\\\(\ TraditionalForm\\\\\\\\`5\\\\\\\\/3\\\\\\\\),\\\\\\\\!\\\\\\\\(\ TraditionalForm\\\\\\\\`0\\\\\\\\))\\\\\\\"\\\\)\\\"\\) }\"\>", StringForm["`1` }", StringForm["`1``2`", StringForm["`1`{ ", "Gf \[Intersection] X = "], StringForm["(`1`,`2`)", Rational[5, 3], 0]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485916413545183*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"Gf \[Intersection] Y = { (0,\\!\\(TraditionalForm\\`\ \\(-\\(\\(5\\/4\\)\\)\\)\\)) }\"\>", StringForm["`1`{ (0,`2`) }", "Gf \[Intersection] Y = ", Rational[-5, 4]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.48591641355875*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"5. Etude de f'\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.485916413583214*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"f'(x) = \"\>", "\[InvisibleSpace]", FractionBox["1", RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "2"}], ")"}], "2"]}]]}], SequenceForm["f'(x) = ", Rational[1, 2] (-2 + $CellContext`x)^(-2)], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4859164136008787`*^9}], Cell[BoxData[ FormBox[ TagBox[GridBox[{ {"x", " ", "2", " "}, { FractionBox["1", RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "2"}], ")"}], "2"]}]], "+", "|", "+"}, { FractionBox[ RowBox[{ RowBox[{"3", " ", "x"}], "-", "5"}], RowBox[{"4", "-", RowBox[{"2", " ", "x"}]}]], "\[UpperRightArrow]", "|", "\[UpperRightArrow]"} }, GridBoxDividers->{ "Columns" -> {{True}}, "ColumnsIndexed" -> {}, "Rows" -> {{True}}, "RowsIndexed" -> {}}], DisplayForm], TraditionalForm]], "Print", CellChangeTimes->{3.485916413617056*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"6. Etude de f\\\"\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.485916413633575*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"f\\\"(x) = \"\>", "\[InvisibleSpace]", RowBox[{"-", FractionBox["1", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "2"}], ")"}], "3"]]}]}], SequenceForm["f\"(x) = ", (-1) (-2 + $CellContext`x)^(-3)], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485916413650429*^9}], Cell[BoxData[ FormBox[ TagBox[GridBox[{ {"x", " ", "2", " "}, { RowBox[{"-", FractionBox["1", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "2"}], ")"}], "3"]]}], "+", "|", "-"}, { FractionBox[ RowBox[{ RowBox[{"3", " ", "x"}], "-", "5"}], RowBox[{"4", "-", RowBox[{"2", " ", "x"}]}]], "\[UnderParenthesis]", "|", "\[OverParenthesis]"} }, GridBoxDividers->{ "Columns" -> {{True}}, "ColumnsIndexed" -> {}, "Rows" -> {{True}}, "RowsIndexed" -> {}}], DisplayForm], TraditionalForm]], "Print", CellChangeTimes->{3.4859164136668053`*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"7.Tableau r\[EAcute]capitulatif\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.4859164136829233`*^9}], Cell[BoxData[ FormBox[ TagBox[GridBox[{ {"x", RowBox[{"-", "\[Infinity]"}], " ", "0", " ", FractionBox["5", "3"], " ", "2", " ", RowBox[{"+", "\[Infinity]"}]}, { RowBox[{"f", RowBox[{"(", "x", ")"}]}], RowBox[{"-", FractionBox["3", "2"]}], "-", RowBox[{"-", FractionBox["5", "4"]}], "-", "0", "+", "|", "-", RowBox[{"-", FractionBox["3", "2"]}]}, {" ", RowBox[{"y", "\[LongEqual]", RowBox[{"-", FractionBox["3", "2"]}]}], " ", " ", " ", " ", " ", " ", " ", RowBox[{"y", "\[LongEqual]", RowBox[{"-", FractionBox["3", "2"]}]}]}, {"croissance", " ", "\[UpperRightArrow]", " ", "\[UpperRightArrow]", " ", "\[UpperRightArrow]", " ", "\[UpperRightArrow]", " "}, {"concavit\[EAcute]", " ", "\[UnderParenthesis]", " ", "\[UnderParenthesis]", " ", "\[UnderParenthesis]", " ", "\[OverParenthesis]", " "} }, GridBoxDividers->{ "Columns" -> {{True}}, "ColumnsIndexed" -> {}, "Rows" -> {{True}}, "RowsIndexed" -> {}}], DisplayForm], TraditionalForm]], "Print", CellChangeTimes->{3.485916413700239*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"8. Graphe de f\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.485916413716823*^9}] }, Open ]], Cell[BoxData[ FormBox[ GraphicsBox[{ {RGBColor[ NCache[ Rational[2, 3], 0.6666666666666666], 0, 0], Thickness[Medium], Dashing[{Small, Small}], TagBox[ TooltipBox[ LineBox[NCache[{{-20, Rational[-3, 2]}, { 20, Rational[-3, 2]}}, {{-20, -1.5}, {20, -1.5}}]], RowBox[{"y", "\[LongEqual]", RowBox[{"-", FractionBox["3", "2"]}]}]], Annotation[#, $CellContext`y == Rational[-3, 2], "Tooltip"]& ]}, {RGBColor[ NCache[ Rational[2, 3], 0.6666666666666666], 0, 0], Thickness[Medium], Dashing[{Small, Small}], TagBox[ TooltipBox[ LineBox[NCache[{{-20, Rational[-3, 2]}, { 20, Rational[-3, 2]}}, {{-20, -1.5}, {20, -1.5}}]], RowBox[{"y", "\[LongEqual]", RowBox[{"-", FractionBox["3", "2"]}]}]], Annotation[#, $CellContext`y == Rational[-3, 2], "Tooltip"]& ]}, {{}, {}, TagBox[ TooltipBox[ {RGBColor[0, 0, NCache[ Rational[2, 3], 0.6666666666666666]], Thickness[Medium], LineBox[CompressedData[" 1:eJwd1Hc819/3AHA7MzsrGpTMhIqSK0QkSYWoFPFJhKxkpchooxSyUopEklmc W7JKlBGSFb3t9R6vl+37/v3u43Ef9/H8457HOeeex93k5GXtwsbCwjLI3P93 hg4fpq6uauHJx/TykWckUILXMbqXtPCFQgHPbqYthfrI0nktrNZ7Uq6J6Y26 3steNC2sPR7pW8T051vx3P0ULcxPJadDmeZW75DD37Xw+IO+7SJMP/Q7eyg8 RQsvJczC7kwSXrP6PmfZrYXffMcQkE4Cp4upptRpTUxPcMCXUkgQ7azxeBa3 A6OOs2J2j0mwrk52Vvqqgb1cTvKxJpAQPL3P48HgdjzFbl7Ze5eEsivJFwuO qOMGYwmr9BhmvvEnNq4kqeKn/xaST90gwTS10vLghDJ2TK0qvRVMQnbd1V++ Dko4qcJUM8iPhDORD8WbXylifk2hslF3EsLOsufziW7FOevydEedSGBR2wBG NxWwQnNnH92OhN+3k6Jft2/GTe+aUtItSFjPeyGHbrgJJ1KWee0RCe47lTm7 12/Ajjev/bqrToIPZ/nLAMENWPgtWmPCdFC7qbkI2wYsd7aQa0WNhFv+LvfN huVw3rMe70tM5xZnSJUVyuGQqLIJM1USRndKqD8ykcPaojeOzyuR8N8uDtsj 3rK4gmbhorGFBOfdva+qq2VwtqNQFFWaBNdXu21MSmVwxQeBS8+YvigVx96Q K4PXPKPKWDPtvWh0pilOBme8jfrxVoqEEMgR7XKUwXV8R+65SzLfy9Q/bGpR Gv+4yqb4S5yEWlv+41La0rhFvVIwTIgE5cA9q57PJXGjpPMjHk4ScI+l8mCi JP6tGWGcyUGCjZHzCdtYSZxSXvtUh+kba++8Rp6SWPk1h6krOwldz3tshXQk sZKLRUAlKwkxP8PfFn6TwJvqFHrsVwigKNedo1PXYZ9SjTuWJAGZPce+XN0v jt1CLNOXhgnQHNJcaNMWx8KbR10jmP4yJqyhsU0cP+w8V8PDNIVsTqGsFce1 0fXG4hQClEUsfI/9EcMFWEtfcYiAdybGm9WuiOESpdS0Xf3M+wXa4f15opjV XHp+pYOAEyWiJXszRPG7um/XrjBN+UgdT0wQxQ5thremfxHA/fWt7eEgUWyT 3arY207A4SHV7RWmopidFuhT3ErAL8ktvQl/RbBXtGvOoWYChq+L65lKiuCY Qidf4VoCeEMLphN4RXB3o6u5Rw0B6oFmWf1LwnibhKlv7RcCAjxDeYMGhHEc h3lJYDUBXA7/OvNyhTHX6yd/2zABCtrF/iL7hHG51vVfFz8Q4EQ5XtBzTghX nFxTyvGWgKiBKSfl40JY+ffaCNMCAnL/xKy7YiKE+aSjrsbmE0Bt+RgqpCKE PUUl+nnfEMB2zexJ1Iggxg3H3NlzCUA7Rn8eFRDEYveKVb5mEVDxaNuBERsB rG8YtjkrkVm/w7Azq54AFpq+otv4iACbjdk3pDcJ4BNJulb0h8z4ufLYYpwf C94c9N+fQIASlttbeI0fS96N9Gy+T8CTMbEdQa/4cOwT7F4WQ4A/YpXlX+DB y9XfLd5eJeAzB967pY8Hz+cvRxcHEiD0Ncxe/wsPDtWUDy+/QkDe8aXH3vd4 8PnY66mV/gQMuZEi7Zt5sIR8lEnJZQKsH05ypx3ixrTqZL7/3AjQGO2ib0/l wva7NxW/syXAb0ZNSSKSC3P3Tu5NsyGgjLx+euUiF/N/u3Ey5gQB+7mUaxt1 uPDRmuHDdseY8eSDHru1cWJHObVGiiUz39PSe7L4OLHu7fHYDweY/flpf21d EDterd+Rr6ZJwEpnftHyWXYsPxUmStEgwLCfbWTIlB3HFJdmP91OwLepXKsi cXYc73bIlEONgD98i5usCtlwLpssa6UiAasHUr7EjrDiywLZhT/WE2Bc0c2z bMOCN1j2a5zjJCA/94Vu3V4W3C3WdrOYnQDJFC+3uI0sOH+9PdcaNub8kVzx h9pWQUBH6VLmCgO2BNsIpS6sgHrqW9YikgGfrzP4DUyXYWE029NwlAGJTrEe bULLMK2g/tdlmAFuRrKNF34vwSI+xRr1jwFCnAdux11agsLm93IfBxjgGPOQ ZzBhEVSzDFpWuhiwdE+LK6p/HvYfkYlvb2DAD686F+nceTj7Omo/1DEgy8qh Jt93Hsw7ipae1zDAXCQisoNrHj5087md/8SApEctbEpqc/C5Vb61sIwBu55e Xv3GnAMvi/gNIdkM8M4pmBMWpUFp3bLzpTAGaKz1jDDsp8KddsMXE8EMmPVR Xev7hmmf/AHXqwzw0cuRbzOlAvluvaCFHwP8m59ZJobMgo1FZmSHGwNoYypm OxunIUxtjeHQMQb4vX91JtF1Glwdem/zHWUAEbrFj2SZhqbe2ipVSwbMCW1I L985BUab5x+cOsisd5cIY1/6BLAf0s7z0mMAV8RchonPKDxYeVlmJc+AaAv/ kpf8o4CGuJP5NzKAex31G/fLEQgRv7eC1zOAN2ec+No9DA6kxKjIOgYINvda HDlAAbk7Q0ftuBkgKVMzZys5CJtaW7dbjdPBxlU+syWkC8IZom94c+lw67Jv THxxJ3zjlfF/+4IOlSHVXtZTHaCi/rzFPJMOCgnO+i2Ov+AhWfrk1BM6UCGr +6dhK2Ra3FaYvkkHOa2Dqs+Ev8LJTxzuWWfocNNsZGFTRD2E6ntsDT5JhwnH mIZMei2UxhVtMT5Oh4o79a6ZHdWQJuQ988qMDm8a4wz37/0ApVWT/5Vo0WHm SdL52aQb8KrngXQmBx1C2B7WmOi4oW921n/cV2ignuxcJ7brPnIcsVKQn6PB Ma3Oj1H7n6MTqgOtJ8ZpcNnVffTLwxJ0oFpmzacfNGBhKV51rqpDyY3xnVaP aZA0KrZjyKIBNZb6aRfdp4Fmq5/T+e6vaK5+o+hiNA3OZ2vXnJ/7jrTtPLbp BjK91b5GU6oFmes9u37GlgZ1jV23tI51oqWGz02VgjS4EPi7zkGlC1056IZO cdKAW6GbI5L9Nwq70JTftEAF8+A/YW1F3YgMr5NQ+UeFRqU+H3+xPkTqDdRn lFLBo72vIHWiD0U1K22uek2FKANvwsmpH1FrGVEv0qmgOOGtdXvPAMrcQktu jKLCBSOfN91jf5EH1zD1iDUVdJKo36ZtBlGGSxdbvDEVuKd9xtirB9FWcffJ B7uokJPsq6iaMoQG9R4FV0pRYWzWLzPkEAVl3AlSTvwzCx4ZVx7J5o0inYTO nvXWs6BHkEU7JMdQemRElDCaBX6LwJYDkWNoOs/41BOVWXhDBgp6nhpHmcXX HA+zz8KUZVBsFf8kypCy0ezPm4Gq5wsvWwInUUBFaiX10QzcWwiqpQxNopSP xvO+YTOwPTuYXbByCm3IzHPMOzwDZWFVVQW7ZpCY+UxzfP00ZOSsfC/3mEFU tYLdRx5MQ0ybfk/1sxlk/Frx1zWbabBThsWOtbMo6sKVtIWeKTA4scr713gW YYl7bRvTp2BbOJKeCJpFZpFiu3zPTMF8O+iwDM+i8fIJ94Mdk/CXheUgrywV iT8t4Ep7MAlfVQxsxY5R0fb1Joo1ppOQfB37bwMqCrovrydbMAF71D69Y84N 4kyobss6Mw47234lVjXQ0M0GCw8fnnHQCJ4IUl2iIeHlwF7/wjHY2iBhxH2O jg6LKP+OnRuFTd5qigEJdKQswOZ06PEorJcw4huqoaOcPwFWWZqjIOri2QrK DJSt745tz4zAWv7IUrXTDKROn5C1mBoG3qKklJT7DFTTFT7NGTQMLKw1zlfo DHTdw0j9WwQFJp7K0NWrCHSE1Wy/v90QDBvt6Hw6QyCrso9z0VWD8HfM5COv PImiLmGhatlB6NLxiaREk2g+Ij6ooWYA2vqiLxyvINHPWtV9EQID8CMq1eLz BIlKOn9fRBb9UNtWL5Z2dA557JO5zLDtgU/BvXN8kXNISmxRuSWxGz5upv+5 WjKHMo6dTXat7ILSBp5PwyNzKGG2Py2voQPeeW94cUJmHulFrOt1Km+HNxI7 Y6sPz6OnGT4CHLda4VWV+aUd4fMoJjk8+6POT0jnD9gp8G8eyZ1SU802qYfk ottSwRIL6PsQ512hgs+QaJ+5PGK2gFQUdEp93cohjrV0wCZkAW2RN+7X1M6B O68aa77kL6DHoiM3SiN8UPSRvzmaAwsoIWCNiyqtAN0gyLsZoouor295KmwB UKCxvE1I4CJq9+5tO8n7E/mO6+wZy11EhbPyY4rqv5BnvKWcXc8i+pvs5nO0 uRtd1D3PViu4hPqHBiatWQaQS/9VipbhEgpaopz29xhCZ6Pvf830W0KrF0Z/ LOiOoFPqL/IFXy6hToXgYrGgCWTbXhEf2rWE3o/czdmYOYOsQ34EjPMto/eU Ab8eGxo6LE+xP6m/jOIkzeQ+exHo4NdF/TrvZZQ4HPG6iG0BGV0Wlt+ZtYxi B26RuuorSF9ScU1W+zI6npZ8cekuq4Eu6I0Lca+gfgP56A0RHAbartbNYXtW 0PnTlq4vNnIbaAhcKJrwWEF2PU2+n17wG6i8D31sn76CmkQDqZQ9wgZbHRKC 63+uoMxDR5P2yIgbbGbLcdzFsYpKPPVMBGKlDWRzqoye71pFL+1cpCJsNxlI WrUpiritooPr5x9dld9mIEqO8oWnrCIf4rxmU7+mwdq01enJ76uoNlOHEVpk ZLBz65/skqZVxPL/ywz/D5Q/s2g= "]], LineBox[CompressedData[" 1:eJwd0gk01Ov7APCZMWPf98auMYQoI4XikSg3JFFCyZDuVVeXENnqKkpKEmXN rqJIspTr/UqhlGSpJCSyRLIM5jtj+c3//57znud8zvOc857neV4N5mnn4yQC gTDIu/8XM4uFr3msIwDh/48dRgqV++rLcwbZMf/KxC7M/diDzlpjAlA2+4Ya TRljlX9YvhZ1IkB5blTHv6n6mPCWbnTsJAFq73r/WShNx5hqf1VXxREg3cqR pWCsiT0TWi0TzCeADnn85MHdapg062aB538ESO1eMD+Zp4T5D2hnVHwmQD3R dJ/kmCL2orX+BplFAOuS4XH11/IY9cn+eDcJIkwkzru7K8phQdmjUWW6ROBr CsFfVctgb+Ijggm2ROhNztcOvyGNaQZJnnTxJsJrqaayyttS2DnPIu97kUQY SRmILHwhiXXamrkt3ybC2bJWSQ1hSUx383tHpydEiL1jnHnjgzgWq+RrU9hO hLECsXOrVWLYVwpuzp4gwi+n/EbdWlHMeOaakT2FBLdYA/FiH0WwxC+aG3LV SZBhJ8nMExbBRl7WqLHMSWBVnlxQ5CyMbS+3l99ziASsQIF/A0uFsFvpQ6JZ QSRg+GUtdkoLYVOxoXwz10ggzzL+tRAniO0KEOFY3yeBvmX+qf38gliWW+7M 7Zck+OQlrpSeJICxdm4ZmxwkQX/fueXHGgKY/cY3/ZZcEuR8ss26/5wfK1Tw 6k6R5wOtvHmRck9+bJnIejO2mQ8udZ6wEyPzYy5TlxvNHfhg0dflOf0xBSM3 Vj4ajuWDTovMpGAqBfMs3V209S4f5L2fJbzqIWNVqV8zrz7jgzKrJityKhnz 9ee/wpjlgwf7dYUEVclYvUtmTLwoGfjn669ajPFhspabQvu0yRAsdS3H5gkf 9krG3Sf2KBksuCSjOWc+THV1+vCncDIMxQ/cN6PzYaHjsU56qWQwxabO3OGS MPp/D3d0tZGhpsjsGqWMhEWX7DTWHiNDRFSRb08cCfuY/Ek3gkSByv0nF8x8 SFicH1FxvSkFesu7Gn3USdiAU5r4WRcKVO86sI1DIGEm5nqUttMUoK08C3/7 nYiNSrjOBRXzXPL85df7RMyCMzHe3EiBGIm6A5zrRCxtJHqQ2k+BI4qXz0mH EDHbuntvX8jwg2Ge3n8r1kQsp2BHk7whP+S89qip1Sdii9c66/z/4Id207CB HfJErJi5XCx9gR/Q4OxQ9CQBExB1usCc5oeWI7j7WDYBc9N2x0yEBIC7KJVt n0jAHuz0XROmCYBypqWOSQQBcwwPi3pyWAAe+tWcjXEnYGmjueHkVwKQnNtZ eESVgI0TS2s/DwrAr5G1Pa6SBMxM5elSGUcA5gzH/yglEbCBA69DXDcJQltF WVdLxxqiN84GFmcK8vqz5Hc7vYbCvnIrzlULgl1Bg8oZtzX0Zoky4/hBEEIN BuPW7VxDAQbUgCV+IRA3d/zBkl9D1Zk7/fcECUH+jx9k/+ZVJFhjf1/5mhCo L4pRmU9WkXvnwfGZEiGgePwx05S7ilYFT/ql9wuB5btvvjWRq8gmNIX5c48w TGovN/KbrqK05Oy8Bh9heLSlR2FBZxWNl5V8uxktDD/0JtK2rFtFicPPj5pX CQP+KPmvAs4K6nYacU9UE4FvYQGj89gKop+aTj9mJgJFDn37jZ+soLB49mdj VxF4InO352nRClJuED3UnyAClutjxEOuriBfvS0HDBZF4HLFC2r14RVUbWt5 kyQlCu8y9HI7HFaQINPuw0c9UcgaGLqttnMFld05si/GWxRsSk4kuOqtIBYl bm/HW1GgUs7nr64to9hvH62DCsSg8HrKouPjZTRQt/fvsHoxAL/Fsy/uLSOz FCwtukcM2ry6Rl1yl9GMzYOJBAFxGG4jLHUlLaOjpVFJBSfF4cjrtBcb/uHV h9L6uhkS4L6rYHftlmWUti+d3GcvAckOsnk9BstoVkfcYOi4BIQ0PvQQ0llG 9/qWzv+6LQHFl7xtKqnLSN6qjc6/LAFb7915ukpYRjjFtE6JKQlx0lyTTR+4 qDho/l1OgCS83+m6Ja6Ni1wGH37XiJAEZQv5n1OvuKiiVlNU55Yk7N5n7zz5 jIv8Top6GTdLgnHvrvDCIi7q7hgkO+hKQVWXxvD7KF59ZpxT9JwUPK7Rjb+6 lYvaZOLGJAjS0CLlpmzA4KLRq5ei88SkQbD1U/hXAy5SjrxY9lJHGkqElzo8 6Fx02fNfQREvaXh8s587KMdFx1Sisdtt0uCVcfVG7yIHRaRGHdrQKw1d24RO 0uY5KE0savrZqDQIB+w7H/abg96uRCgPEGVA1uVRp/k4B20bCA+jbZOBp1Ua MXpfOEjybsimx4UycME+edMtxEF6CiEtOytlIGfrT45PPQfZJgUf7UYyMNUb omlex0GRMWcSl77IQF0AkbZWyUHjXoHjO6RkofXie5u+Yg7C1P/OfRMlC2jS VqAjiYNO5/tKjhyUgynOrvuqfhx0PTw967qPHMxuv13R68NBj5zadUz/kYPF Sfm1O94cNL261er6FTlI00izoh3hoFMeIkHb6uXgraeQ/CkXDvKXrexK1JAH n9S8/TXWHOQXt5a2ZUoeSrqVTi3SOCjuiPH6b2x58Fb1ItHXc1Cx8V/lCRQF KLT8UOKmwUE/vne2DKoqwLGjF4gtKhzka1nMvrJfASw9PFVb5DmIybZ3H6hW ADqkIEchDjrqn6ESf0ER7NJydB1ncMTtFWqfvaYIcW4yE73TOLpjFx7tmaEI D/UPdJ/4haMPOm6Dm58ogofxW5WEnzjaNSaX93VEER5lTi6NjeBog28yzWjP OhB1/fCe/AVHrCOX9frFqaD+26en6BWObrxb6tutRIXizPD/Al7iaOOOE4mV 2lQQ26iwz7QJR37Ktr/igQo9um7eXRiOer/wlRsFUUHOgTVCrcdRw6EYo8s9 VBjNOpHNqsTRlf2hpowsJdDPO6jZkIejm291T5XdVwLPoenvd3NxlLV7MEer RgkOtLzUjb2Lo4ode8iKnUogrFBp7ZiNo88bqO+XBZTh3WGazeIdHOmQGnyb zyjDr3uuCwk3cNRcSblxeK8KRNeoCVadx1HHxmcvOt1U4Ij4rW2NMTj6ci9g Ya+fCrQrv854H42j6ZxP7hYXVMAm59zk70gcyV+9r7W+RgWSRg6dtwjH0XEf h+dTmqrAXgzNkgrCEVk2dTSGowrlmfEtF3xxJD0dLS4toAbDdLYO8sGRRuuf JoUyatD/MfDoChNHFpHb41r11SAmWBkivXEUPjKsJeWlBnw1jLrYo7z3q4yO 5zepQe/2ZmatG46mdMcDmbbqIFJ4Wr3CgbcPhf5LpfbqUDz6Op3CM5fcmc5y VodaB7lGD3scCQ8+b4zzUodfDA854b040k5JkioNUwef2XW1AXtwxOSaPJ5/ oA4fep4JHrLG0ae2SzMXJTSgXMjOIdsUR7cssm1c5TWAOmxI4WzDkfPjqgwt FQ1o9Xrpd4jn9rThXc26GjCS+llTditvvt5W6QK2GvDpqgsz1RhH1UvLVgmR GnBILk6z2hBHaeuDU5ImNKDCf5u+Px1HrhFMk4wmTbj9yIwWIMfLZ8vyL73W hBcl3a2Lsjj6iJp7DnRoQlPnQlcMzwfJeiFi/ZogJYuUUmRw5HZt/sn5RU2o T9/q0yCFI/e7Fzef2LAeHH8PMLXFcXSsqVjfOGk9jD0/99lSAEenRCY1291p EMW8mRvEYaPJ8GdkEW8avHKgWsrw7D9+ZXT3CRr8/VufXoWz0YlXOg8az9BA xe7e20U2GzFj/DY/TaSBHUM0KGaJjQ7PD1lmNdCgPrLhczaLjWz7Pnv6a2rB XPjeNdHfbKRW2pzG/1MLFsNZh4tG2Mjlbm3dmxkteCiSqLqP54SUB1+vL2nB I2t5Gj7MRqyI65oKFDrsIg3MOPD8xv7gI211OhzXcL7CGWKj0Okfr/YcpEOx 8+hZr0E2ereZspDwgg5iwmGBB7+wUUSt9QGJTG0QjZkzmexgo3+KT1WbGG6A xjtTkYcb2UiUtJVp8EMXEhuG+kcr2cjmb5dU3RR9WPienFdWzEaKdSqnbWgG 8Ffiv9blWWx0M+hy8qZPhiBokJWilsJGznH7NmZXbwK5fNG4zVfZSNfjomth 1GagJ+zQ2nKRjT6OCuWnuBrBUcPy495RbNTO/GElrcYAsU36n7PPstEQuYSd qsmAoLngfZd4ZhX/Wb6OzgBM8m3HKZ7XTU4qa2xkgGpF4qw5z75n5pYMzRnw vb70wZdQNuLErj10OMSAh2dlFtfxTC9aR72SxIDgM0qtd4PZyHR3X4doCgOi atNCLvNsP5EVfyONATRZX/1AngM3qi/czmZARcPA05081z+ldxSXMmCxsHbr 6Blef82MuJctDPAwY8wZ8Hz8z4Xte9oYIJdsbqTIc5hwzXxbOwN21FhEEHnO djTz7uphANFEXac7iI3GP8L278MMQNb1U+E8c8JI88fHGDBuIRDsw7OY0sv7 Ez8ZUL+iSXbg2chrt8LsLAPSxGst1Hm2IQq1By8w4Ku49oQQz24Fby6y2Qyw MHTOmg/k/U+bRPPIZQZMOxm79fMcNeYwt7bGAOrhVuUWnv8HMmrTsQ== "]]}, InterpretationBox[ "\"y = \\!\\(TraditionalForm\\`\\(\\(\\(3\\\\ x\\)\\) - 5\\)\\/\\(4 - \ \\(\\(2\\\\ x\\)\\)\\)\\)\"", StringForm[ "`1` = `2`", "y", (4 - 2 $CellContext`x)^(-1) (-5 + 3 $CellContext`x)], Editable -> False]], Annotation[#, StringForm[ "`1` = `2`", "y", (4 - 2 $CellContext`x)^(-1) (-5 + 3 $CellContext`x)], "Tooltip"]& ]}, {RGBColor[ NCache[ Rational[2, 3], 0.6666666666666666], 0, 0], Thickness[Medium], Dashing[{Small, Small}], LineBox[{{2, -100}, {2, 100}}]}}, AspectRatio->Automatic, Axes->True, Frame->False, GridLines->FrontEndValueCache[ analyse`grids, {{-5., -4., -3., -2., -1., 0., 1., 2., 3., 4., 5.}, {-5., -4., -3., -2., -1., 0., 1., 2., 3., 4., 5.}}], GridLinesStyle->Directive[ GrayLevel[0.85], Dashing[{0, Small}]], PlotLabel->None, PlotRange->{{-5, 5}, {-5, 5}}, Prolog->{{ GrayLevel[0.], AbsoluteThickness[0.25], ArrowBox[{{-5., 0.}, {5., 0.}}]}, { GrayLevel[0.], AbsoluteThickness[0.25], ArrowBox[{{0., -5.}, {0., 5.}}]}}, Ticks->FrontEndValueCache[analyse`ticks, {{{-5., FormBox[ RowBox[{"-", "5"}], TraditionalForm]}, {-4., FormBox[ RowBox[{"-", "4"}], TraditionalForm]}, {-3., FormBox[ RowBox[{"-", "3"}], TraditionalForm]}, {-2., FormBox[ RowBox[{"-", "2"}], TraditionalForm]}, {-1., FormBox[ RowBox[{"-", "1"}], TraditionalForm]}, {0., FormBox["0", TraditionalForm]}, {1., FormBox["1", TraditionalForm]}, {2., FormBox["2", TraditionalForm]}, {3., FormBox["3", TraditionalForm]}, {4., FormBox["4", TraditionalForm]}, {5., FormBox["5", TraditionalForm]}}, {{-5., FormBox[ RowBox[{"-", "5"}], TraditionalForm]}, {-4., FormBox[ RowBox[{"-", "4"}], TraditionalForm]}, {-3., FormBox[ RowBox[{"-", "3"}], TraditionalForm]}, {-2., FormBox[ RowBox[{"-", "2"}], TraditionalForm]}, {-1., FormBox[ RowBox[{"-", "1"}], TraditionalForm]}, {0., FormBox["0", TraditionalForm]}, {1., FormBox["1", TraditionalForm]}, {2., FormBox["2", TraditionalForm]}, {3., FormBox["3", TraditionalForm]}, {4., FormBox["4", TraditionalForm]}, {5., FormBox["5", TraditionalForm]}}}]], TraditionalForm]], "Output", CellChangeTimes->{3.4859164152765007`*^9}] }, Open ]] }, WindowSize->{640, 750}, WindowMargins->{{419, Automatic}, {Automatic, 136}}, FrontEndVersion->"7.0 for Mac OS X x86 (32-bit) (February 18, 2009)", StyleDefinitions->"stylemath.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 107, 1, 44, "Section"], Cell[CellGroupData[{ Cell[699, 27, 407, 12, 44, "Print"], Cell[1109, 41, 213, 5, 24, "Print"], Cell[1325, 48, 576, 15, 24, "Print"], Cell[1904, 65, 451, 13, 44, "Print"], Cell[2358, 80, 194, 5, 24, "Print"], Cell[2555, 87, 507, 16, 72, "Print"], Cell[3065, 105, 205, 5, 24, "Print"], Cell[3273, 112, 2883, 50, 90, "Print"], Cell[6159, 164, 286, 6, 24, "Print"], Cell[6448, 172, 742, 14, 44, "Print"], Cell[7193, 188, 692, 14, 44, "Print"], Cell[7888, 204, 398, 10, 43, "Print"], Cell[8289, 216, 212, 5, 24, "Print"], Cell[8504, 223, 604, 13, 44, "Print"], Cell[9111, 238, 311, 7, 43, "Print"], Cell[9425, 247, 195, 5, 24, "Print"], Cell[9623, 254, 402, 11, 48, "Print"], Cell[10028, 267, 671, 22, 98, "Print"], Cell[10702, 291, 198, 5, 24, "Print"], Cell[10903, 298, 389, 11, 48, "Print"], Cell[11295, 311, 669, 22, 98, "Print"], Cell[11967, 335, 214, 5, 24, "Print"], Cell[12184, 342, 1201, 33, 146, "Print"], Cell[13388, 377, 195, 5, 24, "Print"] }, Open ]], Cell[13598, 385, 13198, 258, 378, "Output"] }, Open ]] } ] *) (* End of internal cache information *)