(* 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[ 28361, 714] NotebookOptionsPosition[ 26956, 668] NotebookOutlinePosition[ 27300, 683] CellTagsIndexPosition[ 27257, 680] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Etude de fonction 12", "Section", CellChangeTimes->{{3.485918103624321*^9, 3.485918107365548*^9}}], Cell[CellGroupData[{ Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"f(x) = \"\>", "\[InvisibleSpace]", FractionBox[ RowBox[{ SuperscriptBox["x", "2"], "+", RowBox[{"4", " ", "x"}], "-", "1"}], RowBox[{"x", "-", "1"}]]}], SequenceForm[ "f(x) = ", (-1 + $CellContext`x)^(-1) (-1 + 4 $CellContext`x + $CellContext`x^2)], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485917906547469*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"1. Domaine de d\[EAcute]finition\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.4859179065485983`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\*TagBox[\\\"\ \[DoubleStruckCapitalR]\\\", Function[List[], Reals]]\\) \\\\ \ {\\!\\(TraditionalForm\\`1\\)}\"\>", StringForm["`1` \\ {`2`}", Reals, 1], Editable->False], TraditionalForm]}], SequenceForm["Dom f = ", analyse`Ens[ Or[$CellContext`x < 1, $CellContext`x > 1], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4859179065503387`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["x", "2"], "+", RowBox[{"4", " ", "x"}], "-", "1"}], RowBox[{"x", "-", "1"}]], "\[InvisibleSpace]", "\<\" n'est ni paire ni impaire\"\>"}], SequenceForm[(-1 + $CellContext`x)^(-1) (-1 + 4 $CellContext`x + $CellContext`x^2), " n'est ni paire ni impaire"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485917906552195*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"2. Signe de f\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.485917906553562*^9}], Cell[BoxData[ FormBox[ TagBox[GridBox[{ {"x", " ", RowBox[{ RowBox[{"-", "2"}], "-", SqrtBox["5"]}], " ", RowBox[{ RowBox[{"-", "2"}], "+", SqrtBox["5"]}], " ", "1", " "}, { FractionBox[ RowBox[{ SuperscriptBox["x", "2"], "+", RowBox[{"4", " ", "x"}], "-", "1"}], RowBox[{"x", "-", "1"}]], "-", "0", "+", "0", "-", "|", "+"} }, GridBoxDividers->{ "Columns" -> {{True}}, "ColumnsIndexed" -> {}, "Rows" -> {{True}}, "RowsIndexed" -> {}}], DisplayForm], TraditionalForm]], "Print", CellChangeTimes->{3.4859179066705847`*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"3. Limites et asymptotes\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.485917906673283*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(\[Piecewise] \ \\*GridBox[{{\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"<\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(x\\\\\\\\\\\\\\\\^2 + \ \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(4\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ x\\\\\\\\\ \\\\\\\\)\\\\\\\\\\\\\\\\) - \ 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\\\\\\\\(x - \ 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\\) = \ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(-\[Infinity]\\\\\\\\)\\\\\\\ \\)\\\\\\\"\\\", \\\"\\\\\\\" \\\\\\\"\\\"}, \ {\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\">\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(x\\\\\\\\\\\\\\\\^2 + \ \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(4\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ x\\\\\\\\\ \\\\\\\\)\\\\\\\\\\\\\\\\) - \ 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\\\\\\\\(x - \ 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\\) = \ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"+\\\\\\\\\\\\\\\\!\\\ \\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\[Infinity]\\\\\ \\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\"\\\", \\\"\\\\\\\" \ \\\\\\\"\\\"}}, ColumnAlignments -> {Left}, ColumnSpacings -> 1.2, \ ColumnWidths -> Automatic]\\)\\)\"\>", StringForm["`1`", Piecewise[{{ StringForm["`1` = `2`", analyse`Limite[(-1 + $CellContext`x)^(-1) (-1 + 4 $CellContext`x + $CellContext`x^2), $CellContext`x, 1, -1], DirectedInfinity[-1]], " "}, { StringForm["`1` = `2`", analyse`Limite[(-1 + $CellContext`x)^(-1) (-1 + 4 $CellContext`x + $CellContext`x^2), $CellContext`x, 1, 1], StringForm["+`1`", DirectedInfinity[1]]], " "}}, 0]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485917906674673*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"AV \[Congruent] \\!\\(TraditionalForm\\`x\\) = \ \\!\\(TraditionalForm\\`1\\)\"\>", StringForm["AV \[Congruent] `1` = `2`", $CellContext`x, 1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485917906680106*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(x\\\\^2 + \\\\(\\\\(4\\\\\\\\ x\ \\\\)\\\\) - 1\\\\)\\\\/\\\\(x - 1\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-1 + $CellContext`x)^(-1) (-1 + 4 $CellContext`x + $CellContext`x^2), $CellContext`x, DirectedInfinity[1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4859179066815042`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(x\\\\^2 + \\\\(\\\\(4\\\\\\\\ x\\\\)\\\\) \ - 1\\\\)\\\\/\\\\(x - 1\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`\\(-\ \[Infinity]\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-1 + $CellContext`x)^(-1) (-1 + 4 $CellContext`x + $CellContext`x^2), $CellContext`x, DirectedInfinity[-1]], DirectedInfinity[-1]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4859179066839457`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AO\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", RowBox[{"x", "+", "5"}]}]}], SequenceForm["AO", " \[Congruent] ", $CellContext`y == 5 + $CellContext`x], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485917906817819*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"4. Intersection avec les axes\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.485917906819336*^9}] }, Open ]], Cell[TextData[Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubscriptBox["G", "f"], "\[Intersection]", "X"}], "=", RowBox[{"{", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], "-", SqrtBox["5"]}], ",", "0"}], ")"}], ",", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], "+", SqrtBox["5"]}], ",", "0"}], ")"}]}], "}"}]}], TraditionalForm]], FormatType->"TraditionalForm"]], "Text", CellChangeTimes->{{3.485917988234684*^9, 3.485918019564349*^9}}], Cell[CellGroupData[{ Cell[BoxData[ FormBox[ InterpretationBox["\<\"Gf \[Intersection] Y = { \ (0,\\!\\(TraditionalForm\\`1\\)) }\"\>", StringForm["`1`{ (0,`2`) }", "Gf \[Intersection] Y = ", 1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.48591790683919*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"5. Etude de f'\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.4859179068619947`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"f'(x) = \"\>", "\[InvisibleSpace]", FractionBox[ RowBox[{ SuperscriptBox["x", "2"], "-", RowBox[{"2", " ", "x"}], "-", "3"}], SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "1"}], ")"}], "2"]]}], SequenceForm[ "f'(x) = ", (-1 + $CellContext`x)^(-2) (-3 - 2 $CellContext`x + $CellContext`x^2)], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485917906878954*^9}], Cell[BoxData[ FormBox[ TagBox[GridBox[{ {"x", " ", RowBox[{"-", "1"}], " ", "1", " ", "3", " "}, { FractionBox[ RowBox[{ SuperscriptBox["x", "2"], "-", RowBox[{"2", " ", "x"}], "-", "3"}], SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "1"}], ")"}], "2"]], "+", "0", "-", "|", "-", "0", "+"}, { FractionBox[ RowBox[{ SuperscriptBox["x", "2"], "+", RowBox[{"4", " ", "x"}], "-", "1"}], RowBox[{"x", "-", "1"}]], "\[UpperRightArrow]", "2", "\[LowerRightArrow]", "|", "\[LowerRightArrow]", "10", "\[UpperRightArrow]"} }, GridBoxDividers->{ "Columns" -> {{True}}, "ColumnsIndexed" -> {}, "Rows" -> {{True}}, "RowsIndexed" -> {}}], DisplayForm], TraditionalForm]], "Print", CellChangeTimes->{3.485917907018407*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\" Max : \ (\\!\\(TraditionalForm\\`\\(-1\\)\\),\\!\\(TraditionalForm\\`2\\))\"\>", StringForm[" Max : (`1`,`2`)", -1, 2], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485917907032949*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\" Min : \ (\\!\\(TraditionalForm\\`3\\),\\!\\(TraditionalForm\\`10\\))\"\>", StringForm[" Min : (`1`,`2`)", 3, 10], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.485917907049912*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"6. Etude de f\\\"\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.485917907066208*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"f\\\"(x) = \"\>", "\[InvisibleSpace]", FractionBox["8", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "1"}], ")"}], "3"]]}], SequenceForm["f\"(x) = ", 8 (-1 + $CellContext`x)^(-3)], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4859179070851192`*^9}], Cell[BoxData[ FormBox[ TagBox[GridBox[{ {"x", " ", "1", " "}, { FractionBox["8", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "1"}], ")"}], "3"]], "-", "|", "+"}, { FractionBox[ RowBox[{ SuperscriptBox["x", "2"], "+", RowBox[{"4", " ", "x"}], "-", "1"}], RowBox[{"x", "-", "1"}]], "\[OverParenthesis]", "|", "\[UnderParenthesis]"} }, GridBoxDividers->{ "Columns" -> {{True}}, "ColumnsIndexed" -> {}, "Rows" -> {{True}}, "RowsIndexed" -> {}}], DisplayForm], TraditionalForm]], "Print", CellChangeTimes->{3.48591790709934*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"7.Tableau r\[EAcute]capitulatif\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.4859179071163683`*^9}], Cell[BoxData[ FormBox[ TagBox[GridBox[{ {"x", RowBox[{"-", "\[Infinity]"}], " ", RowBox[{ RowBox[{"-", "2"}], "-", SqrtBox["5"]}], " ", RowBox[{"-", "1"}], " ", "0", " ", RowBox[{ RowBox[{"-", "2"}], "+", SqrtBox["5"]}], " ", "1", " ", "3", " ", RowBox[{"+", "\[Infinity]"}]}, { RowBox[{"f", RowBox[{"(", "x", ")"}]}], RowBox[{"-", "\[Infinity]"}], "-", "0", "+", "2", "+", "1", "+", "0", "-", "|", "+", "10", "+", "\[Infinity]"}, {" ", RowBox[{"y", "\[LongEqual]", RowBox[{"x", "+", "5"}]}], " ", " ", " ", "Max", " ", " ", " ", " ", " ", " ", " ", "Min", " ", RowBox[{"y", "\[LongEqual]", RowBox[{"x", "+", "5"}]}]}, {"croissance", " ", "\[UpperRightArrow]", " ", "\[UpperRightArrow]", " ", "\[LowerRightArrow]", " ", "\[LowerRightArrow]", " ", "\[LowerRightArrow]", " ", "\[LowerRightArrow]", " ", "\[UpperRightArrow]", " "}, {"concavit\[EAcute]", " ", "\[OverParenthesis]", " ", "\[OverParenthesis]", " ", "\[OverParenthesis]", " ", "\[OverParenthesis]", " ", "\[OverParenthesis]", " ", "\[UnderParenthesis]", " ", "\[UnderParenthesis]", " "} }, GridBoxDividers->{ "Columns" -> {{True}}, "ColumnsIndexed" -> {}, "Rows" -> {{True}}, "RowsIndexed" -> {}}], DisplayForm], TraditionalForm]], "Print", CellChangeTimes->{3.4859179078258*^9}], Cell[BoxData[ FormBox[ StyleBox["\<\"8. Graphe de f\"\>", StripOnInput->False, FontVariations->{"Underline"->True}], TraditionalForm]], "Print", CellChangeTimes->{3.485917907842039*^9}] }, Open ]], Cell[BoxData[ GraphicsBox[{ {RGBColor[ NCache[ Rational[2, 3], 0.6666666666666666], 0, 0], Thickness[Medium], Dashing[{Small, Small}], TagBox[ TooltipBox[LineBox[{{-20, -15}, {20, 25}}], RowBox[{"y", "\[LongEqual]", RowBox[{"x", "+", "5"}]}]], Annotation[#, $CellContext`y == 5 + $CellContext`x, "Tooltip"]& ]}, {RGBColor[ NCache[ Rational[2, 3], 0.6666666666666666], 0, 0], Thickness[Medium], Dashing[{Small, Small}], TagBox[ TooltipBox[LineBox[{{-20, -15}, {20, 25}}], RowBox[{"y", "\[LongEqual]", RowBox[{"x", "+", "5"}]}]], Annotation[#, $CellContext`y == 5 + $CellContext`x, "Tooltip"]& ]}, {{}, {}, TagBox[ TooltipBox[ {RGBColor[0, 0, NCache[ Rational[2, 3], 0.6666666666666666]], Thickness[Medium], LineBox[CompressedData[" 1:eJwVlnk01PsbxycipC5ZspVESEgGEd3Hki1yK6VFslak7CprSBIVWpSQrVTu lavFLdvnY0uWFkOyhhDGPsaMGTPz/fk95zznOa+/3q9/3uc8Sh7+h8/wkUik 1pX9/40aO0AjCDI+OWvCve6ujX9HSC/2csj4XdXbx/bO2thBbID5H4uMJa2S TSSOauMtRgFc/wUydnQ/dTvXRhvXJt0VGvxNxtkiHz0rdmpjIe0fm/FnMp49 Hjo6z9XC90Pc7GIyyThUPXS/x2Mt/Peq4Kek3WScJV4odqhdEwucsdaVddHF OUf4zRnKO7BEV8OF/LRdeJIimZWSth0frnvsub1ZB+8WszYKWqOOI2b3Xkgd 3olFO/PZF0+p4veXH58v+Usbr1LgQ8FfVLDD3aNbeBma2M5HOeOHojK2zq5y sJnSwD8PRHr+DlPChY1hncHO27FdkmLZiV+K+HT8famvL9Swntn+q4OpCjja jf/VWglVHKNf+OJ0uCwmaSkii+sq2NesbKvtJWnck5xx4+/vW7GgvhYpUU8C K4h4v6SbK+F5xzPLBjvFsK++hkCvgiI2kBDRmP0pjD13/3xRVyeP1bS6lDel 8GONK3sIv6cyeHiy2aAtdhnl9TvWh5lJYYaUrfHDQzNoLFbKxFpmA7b09BMe /vAVlT9Qtxx3Wod/bqPJ5Pr/BJ2JbvrObEHcHH2ftlOUBiFzWts3xgviUY6z T64ODd4zY1145wXxk8eftdhHaGAmqPGx1VAQb2LEVXln0+CwcvhDnw4BnObs lrNDawFCXeT2FKwVwPeaN0lK2NChvO3kVelwfqw3qHEg1YcBvK5Xb7hu/HiE LmhcnMQA80G+8RFrfizg/k9F0d8MaJkpOvhGih8nxv3aaDXNgL61y0oHS/lw IWPNWbofEwjLzPqb46vwzHNL3T7fJdhX3ivMdSLhujg8P2PDhldFz4wajUlY o9qWr/IcG2Qy/X3StpCwtbh/q2MCGzqZgnftOgh0iqlWNljLhm0RTmLZbB7y nNW3cDZahtrYRVFTay7SVXP8uFWeA+keNy90iHGRcOo67p8GHPCx2NTq3cNB L1XOzMgc4oCYgGVy2kUO4gV90eVL4IBr4n3h4XvLSLky98GdKQ5w7pAFEwZZ SC5vZ0zu31z45t94Rq6IhYwUcb18LRcKDjo3vApmoViFG5oWXVzYv+Fa/A9B Fnoh3qmdxs+DjAcUvu1aS8hltIrG78SDC5fOelQxmGgorjGo3IcHpsfYNYcw E8mGTlDFo3gwLrM1NtyRieIKPDOy83lgkBVItIQxUKrkhUH2OA9EogRc3SwY SCLszP5bLB70u2RU00UZaLHWwq9UmIB4xZqoTbmLqPaW360SdQKOk472l/os ogi6N47fTYDm0LiJFXkRSfWtUfptSUB7vhjH7yMdSed7uVq6E1B47akzfyod xdd8lwM/AsK9DCsenqAjyZ4nVZXhBGxVdQvHUwtIl/CY2HOXAIYgvftI2QLa pTg0bpBNQNPYDaOJqwuo9PpsRfFzAgJeliyJSyygm/16WnwVBOis97tmPkhD foHByzZ1BMwHaa4PLqYhdaF12yRaCHj9g/qoIJyGVPcw4k5TCAgyeancYU1D plluQ+rdBJDzzr1aLUVDxBNnwn+AALqAqpH+r3kkIR10Z9coAW/Pj9SdKZlH Ifv26fpSCQj9mu+QHjmPom02x8jNEmCg59790XYerapJ4pksrPg/UvRiSs+j 2bghlW8MAsq4/TNqI3OoXY9yso1FwGWPrLDjpXOopoDK3MshwLDx5Oqb0XMo L1/GQoJHwNIO2ZQPdnNo0VwtyIEg4EPqD1mqzBy6RN79cmqFF6g7bPVbZ1HA el02dYVD3r44nX52Fm10NfSyWmFG1LYQJmkWyW8VaV/mruRZ5988njmDvsX5 bBZayVsSU8z5oD+D+O9dFvZe8QnryXwr920aGbwXMZdZ8WUXyDRHnJ9GR67z XKVoBERcfDDQt3oa7XsbOeI8TQDHYMPi3pwpVDjzp9H4GAFRpBSRHKMp1C7W VFI2RACvae0WUsckenw7M6auh4CYe4n67n6TKOe+S7NIOwGrXATsaoUmEfGQ l5rYTECcapybcgEVXf/0pdKwhoDVc7zQ+L1UZCx3R3bjfwQIXlvKtQqaQLJT CqQDuQTcsA8tey46gbaG37+ZeY8AIWlai9DzcXTUS9FMMIEAkZeTjObeMTQc NdKq4E1AcpC3qOalMeQo5pxWfYwAUZNRpdtiY+heR6u7txUBf3z9af+X5W9U lqnjWb2FgNRHzh7/Doyi6fpPdq6iBGzw6LosHj6K3Byz/pln8EBysS2//dUI mnFZ5U75xIMH1Q7v9WxH0MLtaj7Jf3kgndjy+cHwMAqM8n2nlc4DGfmGpWMy w8g4tLrs8+mV/o6Yrf/w+heyE/1QYmnGA7lX1cpyB34hdbtZ4bCtPNhk9t6h L3YILWTJFdIGufBERN9rr8IQKuqJfaFezQXFjtKwJ2WDKIFSf4OVwQWLL062 NZ0DaEIv7JTNAS5YuR8MubZ2AAk6zbS/UeGCDd02x9L0J6pKH9r2gM0Be7m9 i00v+5Dbi4PtqXkccDqrnEeJ7EYHOysTTXqXISkwOPHuuy5UQ2ko2Vu4DFWR df6HZ36gJ6KnqRf8l0HlnuefFNdOxJFON1TmsOH4kzfb7j76jnQWdBgpiA3J L/nXHW7rQJSNd8QYMWygoYLeNvN2FIZ6tEK4LFBtWahNi6Ag50fp5Rffs+BE p0XRobdtiCq9v0g5kAV4avhK27ZvaHumnVps7xJsJtto5os3ozmScRr/XSZc tx1nK137hOaMx/eMGjJhyjWxKY/+Eak1prlN9DGg/Nans3k/6pCCrkgQR54B SgXe+kq2tSiSVp/SU7YIiR+EVueVYyRtoBkU5rAIxa1p5mbGFSjvrMdgcjAd IlhtA6ab36M53vLtBhIdbFU3RJmueofYpY1b7JMWoIVQ8b96pxjV9jXYVqXR YO5Rhtd8RhxyllSq2+c3B5F89xusDH2g/d0d3zVvZ0H7sWejpEEKVML6h5Wx M+BI7qpMMHsKx/WmNQ7yJqGs+1jcjYgi8KT/K+n1DxXW4Unl+pP/Qrbipmey f01A4Fnfifr7ZeCLXakPA35DvtEO+4bSD9D+JoB1bmYEOkQnXzV8qQTfix8S xk4PQ9YJ/T2e8TUgy9KkvJUaBBLpHeFZ3QjftQszP6W1QcaE5K4R+yY4mV41 OqnRArrtIR5evc2wdvCuse5YLXgV6jV4LX0Gr6MBxwz4bwA35T5jJOErFJVq E7o7SlCLCfve66RvYF5xbsjNrQZ5qZ5s0JWlQHVJ97PuTgrSkRf5GTRIAZEt juLlu7sQ949yxuvn7ZDQla4187UfpbNk1ckG30H0PCdVt3sEecw0mQZzv8Nh UldM7qpxpD0cduJNfSeca3r93sl+EjW2dieRHbsg0TOa75j6PPK+0tPovKMb yqTDNQidBSSk0rs6nr8HPnsz28mOi2h/RF90x5teCNO54+81yUJU1f4KTnIf GLA6llzOcFAypX9JxasfigtbP0+QCNS6fSAoVHIAdmv7fEpw5MMXvg+UZE8N wDPOhY2olx8nmAYwPDwGwdh+8Vl+uAB2Sp+TvPxlEKomv++W0l2D1aYCyMl7 hqDp6l8Du1YL4yWz+UM5hUOQepaq6Lgggj89DAx4s+EXROxVv6XAtw57WwQV 91J/QVpqsnxogxg2zKC1zDoNQ0tJaI6I4AYsNBtE5a8bhm6eyx/FLhK4a9+C kMzOERD39Zjp+CKJXz4OVtPMXGHbX9HHT0nj8LkFS9M1o8DL72uJEpbB+61C vI4Ej8LHrFVrxHtksVwWPc57YBSstxPRMRR5TJ0PyYu0+w01Feq/COYmXG69 iFL/+w1ngpRTT6pvwUnZoT+fKo/BsXVJYqxAJXxyYZHzPmUMJFf3/4b+rXiH 7SX5z8tjMMBU8Y7xV8GcJwyjoXPjIHX2ed6enaq4lX7p+GL7OATrLwdeUlHH WfuZl4RNJ0DHbFr8zxMa+ELu5Qeb/pmA7XbsItseTWzCYL7ZJUMFAeubN+j/ rfzd9lcolvFU6GWP1bVd24X78pbmTsxRIcc65upsEBkXM6/84XdqEm7Hdis1 Verj6AMsrbhPk+C3ptcrJ9IQOxSE2afrTcFrsbTx9m5jvJnFOl+UOwVjHtNH 8RpTPOMQfrNadBrCKGly+6vMcfVT9nPKlWng2BbfEXK2wlmplgb6pdMrvfn/ 2OL/AdS2y9E= "]], LineBox[CompressedData[" 1:eJwdlAs0VG0fxceYYTBqULmF6MyMu2FcZlw6u0RKF1QqlUr4SqhUKLdXilRS FG+ESlGoVKKLbpJCd1KpXpFIeosx7uE733fWOuus33qeZ63nv/c+W99vq1cA nUajPaPe/33Naqsete3qJWn/f+bD8C9S6+eeXtJnUVXr6iI3cIrjjAZKe8nU +v+snzvsguG390W0Tmp9rbnfnlZntNFoboo6ElIsO3v5JJs5qDPBiilLJaSR sp3tgybgmvdfgbrJElL52EYl7UASWfEPdhnel5A/0ebUEemEvSW0/Vb9ErJY x/xq2hsHBL3DcUeTPrLJeK/TgL89vOjx+a4b+sjiqJ2Z27hi2Js9vOaR2UdO 1xpXaVUSwaaxKeNebR85MzDy+2N9Owiifu4x/dNHqkT/StFbYgsTA/q6LHMp +c5RNiLnqA14terOrA1SUnND35Okr9bQ32bGD0+XkoJd3hG5LtaYru6s1P5Y Sl7ocDxOuyGEWkBow33jfvKeUYJC2g0rTGLvqzBb208WDj186TLXCorXT2Zn p/aTvBlVOeKPlmD6XIlTqOongx2aLx/fbQmazOONEdJ+UvUy/98sXUuMFjbP +8YbIHdK+1ZdqBVgYHGPydJVA2RprtTDbI8AP09pS83vDZAcQdeOwAYLdDpb vj/VM0DWReV6P1pigbYfrpWKMwdJrz5m9t0Gc3wQhe3rSBokUyOm+vN6zNDY krRp2e1BMuZakzQ5yQyvEnMWVv0cJAvrfutuJ8xQ0/h0Sq7nEBm9JmeGOMQU D6P+GVLaN0RuWbo8e5OGKSoNpJ92lw+Rnrp5n8qfmODaNr3zy7WHSc6eDd9z LE1wSd0m+dGiYTJDq9i9stsYF+4tCLH8a5icFbJrh+xFY+Sxw22Uvw2TwZes PiwwNUbW9UOaUeojZKS2S1dfrxEyfM6MfZ8/QqrpOVycdtsIhy88e1x9eYTs LGqYcPQ0QtKStotWrSPk3SMf39BmGGHvwGDKabVRsqV5xOdejyEi5870jo4c JYMX8pbeyzTEjm6R/Y+iUXK2cq7y6xBDhKYt1l35eZTs4zg8iXExRMCX3R3C OX/IwduOht7DfHhFvwrvVhojqxLsladv52PRzA6fVbPGyLfNkCp78eFWNzrr ybYx8vynOisNaz5mafDl89+OkRVfi166jPIgvu/YzWGNk36Ocl1eX3iwDvR6 GWs/TkrstG661/BgUhaT6ZM3Tppopq1pPs4Db3V61NPX4+TrGWWbfGN4MKBf XGfLmCDzolhJRYE8aHg08lU3T5Dk5bL50Q480MOnfvLXpGEo9dCw879c+Kwv enPTmoY3rpN1nn7g4toCspbtQYPrc995wzVc+OltLi9LpGG/86arbvlc3FYY L2GdpSHMaf19nzQuVKVp+Wvu0uDQlxYos5eLqqeVRxlSGmIc3jgN+nGhdd0z aeVkGZwKehLsuIyLsJyOmBJjGbQUe5jQXbkwCONsWbZBBtMk6U/HjLlI0PZ3 OfdCBh3m5Z4uIwQ+MYcdhrpk4HlqnZPObwLWPSlWC5l0GGgkuK5oJ9BeXaEn daCD6bBo87eXBByvLJzmtoKOwm36pcIaAsdPtrJPhdHxpGP3lveVBOaGKo04 X6Qj/uz6T1rFBE6tPN2TWU2H4wLTs9fPEpDOsensbqHj8Pb1I39nETinvq4x fZosJMXrk3GIAOPhtctfE2Tx5N34s9qtBNYUzztvlyeLNIaGccpmAmUnPmUf ui2L1ulfQ1I2EvAPkksW9lL7t1vpz1pJoHJZdlwSm4G3tPTt3V4EppCC8I98 BpbKqWx+uYjAYzWfjQm+DFx9HHzOZi4B3fFfq97tZuBW9zOrGySB8O8JHiYn GPDXnvMnwIEA7+4lp4Z6BtKqHnh5CwnEFs6x5ncyUGGvnJBuQaDp2DvjKDoT yXs0rcdMCCQGymjMFDNxPqv6qSeXwD8eGZMiljGRX3s+y96AgK2DCbN+KxNf stRr3fUIdExeLgkroNbbGWFfNQnMGun6XvOQiWPVUVqb1AlktMe2aH1mwr36 2x6VqQRcb114VqUmh0x7K/ZLDoHcfKdH0yzkkLQq+kzrJAIDKW9uBS2g+Lly xVRlAosj/1N6L0AOocsMjgQpESjw+1OgGi8HQWB6SIsCgfGFx3ICT8lh55X8 MztYBLzteMdvV8jB6u2zKJ48gcv6dw5OapCDvH+q1yCTgDzbI97vlxxWv5wb /41BYCXf54GtgjxWqoaflsoSKJrjP6FIyENkHdOsS/GftaGzWmbJoyti9umN dOo+uyNjrq+Sx3BSWmCVDIHTx/dWJu2UR+ghuQJ7iiVXDo+uTpXH/pMfmutp VJ7qM+wFRfL4HfVi3y6KMzpO72Y8lkf/FQ7fjuLvMsU337fIozJT3Y1Dsb3O jcGSEXm8eX5wO43iw6L7tvFTWchN4QvkKf5nae2u5QIW3IlCNYJiwdaGMiN3 FgS+BZe9Kd578HPfWAALW7+lZORS3Hi+0+rNXyxMSYraOEox72Hv9oJsFuKW mZYGU/eN/DRauqechfjMTk0JxXWDzJ7Fr1loSg3CIWre6Woci5k/WQjpbXxs R+kRaq4VOiinABXtjMWDFD+YT1yq11dA+phPfC2lp2qA+c88RwXQSv7IXab0 Ls+eE+QWpgAXk+s3Syg/WBULL05PUUDK0SrUUH75vPH+3lOogLWO+xt6/ucn a0vgyc/U+WGFjgg2AQ9i1/mQIQUcU771qoHKw1kyrn22miKqmpuzyckEXMLT /X64KeLzlB93XFQpfY/lnLm3URGSJnZyixqlb0nhl7RYRWS19PMOUPk7/PWO r0OZIiy3TWtiUHlt9Gj3OaynBKeX5d7nZ1D6BP86ud5eCXEN2dLLVN4jk4be Wy9XQt7ojgOPCUqPe+wVnw8q4eC5yEoNI+r/NbFZaj5AnT82cNfTiprXlUyj q7Cx4ob+lrvW1Lx+8183mbBh6BQTZ21HoOTvtUviNrChqnbOaK4j1SfMRPdX z9hIds6qbXclkPClyTksXxn9Zfd5LF/K71vuIZGVynD3yh1rXU/lI/1BRuxb ZZR755x9RPVHj0tR10H5SWg+l/kzh+oX3+KY1PwtkyB7v+xq8S5qfzjxsVE4 Gc9+X+qflkpgmCm+pe3HQf5S/Mmk+q8grO95bigHXacr75B1BJa1XGrTj+Lg QIXutZ/PCZTeNGAbHucgN9ib6f2WQOAW9jrrGg4WEOI8f6pfG1+1MBYZqyCI p2McIMtFaXaiR6xEBZH66/yy5nJRr5bYOZmmihuTvP41ms9Fx6H9sWeUVdGs uv/R3UVcTI/eV1JtqApB0oIZEm8uDqzZy1Jap4pLgy3uhzdzsV4n9kFmvSqY e1/FRadywcnbJbh6Tg2Srr85zH+42HrWn9PuPRWv+f063xJ48A3K0kmK10D8 jR+ts1/xkewZLhae0obIXrdKxcgIjCknOuJGdPHj+rhWR4kx3tXv79k3WR+3 dx7Ji9YzxfIoP9usRwYIfbTT7neFGYKVug1e+FC9Ytp3YkBsAb3imgy5H1w0 6iuWNq8WIOqm89LJ2Xxc57l+8DS1xLaC4HJbCyPw5xfxe39bgk238zP/ZgxC wBtorraCS8iyE8bppmDePCtTkCGExi2drS6EOeWPAaPLxxppYQeOCd5ZYG7e /S6xwAZeiUvMcsoF+PP+oNrTQRsYr963/FyMJXxLhbcq79iiqUPhbPpyK/Q5 SWILjtrhhd+32ap6QogsdFyOrxChlVE4dMJAiL6aIJbyahGkBZuuaPKEKCQG Xu73FUGzu3u6vpkQBT6VWyICRPDfIRm0cBDCWlT11meHCCMJE5cWrRCCr5mx 3SBVBN55Ta3kVCECT7yuKKsRQTzv4yt2uhD007bjZnUiLOw6lXSUmmvY+ohb 4XMRtpvN6M/MEeIAm911slGEyhu8VwXFQlyyZayKaxPBq0aYWP1ECC5nRLJg XISATf2ObvVCJP6IjaiWESNSsaKv/oUQwgUNE05MMXIW229oeCvEDJU2bUu2 GN+b4Nj2VQi7NWvi1bXEGImk9wV0CnFUqk8c0xFDWbv6YtcPIW4bF9Qp6oth tW6eem+vENFabQbjfDFcZBRe7Oyn9Ck50RhhIsbK/Lp9Q0MUH5lI7jUXI8jl sEP0HyHuluo4b7ESI6ZzkWRiQgg9xq+Jdhsx/gu08Gya "]], LineBox[{{0.9870940037500628, -50.}, {0.987145495941174, 50.}}]}, InterpretationBox[ "\"y = \\!\\(TraditionalForm\\`\\(x\\^2 + \\(\\(4\\\\ x\\)\\) - 1\\)\\/\ \\(x - 1\\)\\)\"", StringForm[ "`1` = `2`", "y", (-1 + $CellContext`x)^(-1) (-1 + 4 $CellContext`x + $CellContext`x^2)], Editable -> False]], Annotation[#, StringForm[ "`1` = `2`", "y", (-1 + $CellContext`x)^(-1) (-1 + 4 $CellContext`x + $CellContext`x^2)], "Tooltip"]& ]}, {RGBColor[ NCache[ Rational[2, 3], 0.6666666666666666], 0, 0], Thickness[Medium], Dashing[{Small, Small}], LineBox[{{1, -100}, {1, 100}}]}}, AspectRatio->Automatic, Axes->True, Frame->False, GridLines->FrontEndValueCache[ analyse`grids, {{-5., -4., -3., -2., -1., 0., 1., 2., 3., 4., 5.}, {-2., -1., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.}}], GridLinesStyle->Directive[ GrayLevel[0.85], Dashing[{0, Small}]], PlotLabel->None, PlotRange->{{-5, 5}, {-2, 12}}, Prolog->{{ GrayLevel[0.], AbsoluteThickness[0.25], ArrowBox[{{-5., 0.}, {5., 0.}}]}, { GrayLevel[0.], AbsoluteThickness[0.25], ArrowBox[{{0., -2.}, {0., 12.}}]}}, 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]}}, {{-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]}, {6., FormBox["6", TraditionalForm]}, {7., FormBox["7", TraditionalForm]}, {8., FormBox["8", TraditionalForm]}, {9., FormBox["9", TraditionalForm]}, {10., FormBox["10", TraditionalForm]}, {11., FormBox["11", TraditionalForm]}, {12., FormBox["12", TraditionalForm]}}}]]], "Input"] }, Open ]] }, WindowSize->{640, 750}, WindowMargins->{{Automatic, 587}, {171, Automatic}}, 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, 105, 1, 44, "Section"], Cell[CellGroupData[{ Cell[697, 27, 442, 13, 47, "Print"], Cell[1142, 42, 215, 5, 24, "Print"], Cell[1360, 49, 578, 15, 24, "Print"], Cell[1941, 66, 481, 13, 47, "Print"], Cell[2425, 81, 194, 5, 24, "Print"], Cell[2622, 88, 652, 21, 72, "Print"], Cell[3277, 111, 205, 5, 24, "Print"], Cell[3485, 118, 2755, 48, 98, "Print"], Cell[6243, 168, 286, 6, 24, "Print"], Cell[6532, 176, 808, 16, 47, "Print"], Cell[7343, 194, 691, 14, 47, "Print"], Cell[8037, 210, 385, 10, 24, "Print"], Cell[8425, 222, 210, 5, 24, "Print"] }, Open ]], Cell[8650, 230, 548, 18, 37, "Text"], Cell[CellGroupData[{ Cell[9223, 252, 269, 6, 24, "Print"], Cell[9495, 260, 197, 5, 24, "Print"], Cell[9695, 267, 500, 15, 51, "Print"], Cell[10198, 284, 885, 27, 104, "Print"], Cell[11086, 313, 263, 6, 24, "Print"], Cell[11352, 321, 257, 6, 24, "Print"], Cell[11612, 329, 198, 5, 24, "Print"], Cell[11813, 336, 364, 10, 48, "Print"], Cell[12180, 348, 651, 21, 102, "Print"], Cell[12834, 371, 214, 5, 24, "Print"], Cell[13051, 378, 1484, 37, 128, "Print"], Cell[14538, 417, 195, 5, 24, "Print"] }, Open ]], Cell[14748, 425, 12192, 240, 447, "Input"] }, Open ]] } ] *) (* End of internal cache information *)