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$CellContext`x + 2 $CellContext`x^2 + $CellContext`x^3), $CellContext`x, DirectedInfinity[-1]], DirectedInfinity[-1]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075817191938*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AO\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", RowBox[{ FractionBox["x", "2"], "+", FractionBox["3", "4"]}]}]}], SequenceForm[ "AO", " \[Congruent] ", $CellContext`y == Rational[3, 4] + Rational[1, 2] $CellContext`x], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075817210814*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "2", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"[\ \\\\!\\\\(TraditionalForm\\\\`1\\\\), \\\\!\\\\(TraditionalForm\\\\`5\\\\)[\\\ \"\\)\\) \[Union] \ \\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"]\\\\!\\\\(TraditionalForm\\\ \\`5\\\\), \\\\[LongRightArrow]\\\"\\)\\)\"\>", StringForm["`1` \[Union] `2`", analyse`Ens[ Inequality[1, LessEqual, $CellContext`x, Less, 5], $CellContext`x], analyse`Ens[$CellContext`x > 5, $CellContext`x]], Editable->False], TraditionalForm]}], SequenceForm[2, ". Dom f = ", analyse`Ens[ Or[ Inequality[1, LessEqual, $CellContext`x, Less, 5], $CellContext`x > 5], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075817242934*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 1\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x - 1\\\\) - \ 2\\\\)\\\\/\\\\(\\\\@\\\\(\\\\(\\\\(2\\\\\\\\ x\\\\)\\\\) - 1\\\\) - 3\\\\)\\\ \\)\\\"\\)\\) = \\!\\(TraditionalForm\\`1\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-2 + (-1 + $CellContext`x)^Rational[1, 2])/(-3 + (-1 + 2 $CellContext`x)^Rational[1, 2]), $CellContext`x, 1], 1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075817298191*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 5\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x - 1\\\\) - \ 2\\\\)\\\\/\\\\(\\\\@\\\\(\\\\(\\\\(2\\\\\\\\ x\\\\)\\\\) - 1\\\\) - 3\\\\)\\\ \\)\\\"\\)\\) = \\!\\(TraditionalForm\\`3\\/4\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-2 + (-1 + $CellContext`x)^Rational[1, 2])/(-3 + (-1 + 2 $CellContext`x)^Rational[1, 2]), $CellContext`x, 5], Rational[3, 4]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758174046507`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x - 1\\\\) - 2\\\\)\\\ \\/\\\\(\\\\@\\\\(\\\\(\\\\(2\\\\\\\\ x\\\\)\\\\) - 1\\\\) - \ 3\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`1\\/\\@2\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-2 + (-1 + $CellContext`x)^Rational[1, 2])/(-3 + (-1 + 2 $CellContext`x)^Rational[1, 2]), $CellContext`x, DirectedInfinity[1]], 2^Rational[-1, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758175165977`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x - 1\\\\) - \ 2\\\\)\\\\/\\\\(\\\\@\\\\(\\\\(\\\\(2\\\\\\\\ x\\\\)\\\\) - 1\\\\) - 3\\\\)\\\ \\)\\\"\\)\\) n'existe pas\"\>", StringForm["`1` `2`", analyse`Limite[(-2 + (-1 + $CellContext`x)^Rational[1, 2])/(-3 + (-1 + 2 $CellContext`x)^Rational[1, 2]), $CellContext`x, DirectedInfinity[-1]], " n'existe pas"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758175646067`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", FractionBox["1", SqrtBox["2"]]}], "\[InvisibleSpace]", "\<\" \[AGrave] droite\"\>"}], SequenceForm[ "AH", " \[Congruent] ", $CellContext`y == 2^Rational[-1, 2], " \[AGrave] droite"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075817619671*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "3", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\ \\\\[LongLeftArrow], \ \\\\!\\\\(TraditionalForm\\\\`\\\\(-1\\\\)\\\\)]\\\"\\)\\) \[Union] \ \\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"[\\\\!\\\\(TraditionalForm\\\ \\`3\\\\), \\\\[LongRightArrow]\\\"\\)\\)\"\>", StringForm["`1` \[Union] `2`", analyse`Ens[$CellContext`x <= -1, $CellContext`x], analyse`Ens[$CellContext`x >= 3, $CellContext`x]], Editable->False], TraditionalForm]}], SequenceForm[3, ". Dom f = ", analyse`Ens[ Or[$CellContext`x <= -1, $CellContext`x >= 3], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.43607581764115*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-1\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 - \\\\(\\\\(2\\\\\\\\ \ x\\\\)\\\\) - 3\\\\) - x\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`1\\)\"\ \>", StringForm["`1` = `2`", analyse`Limite[-$CellContext`x + (-3 - 2 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, -1], 1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758176771317`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 3\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 - \ \\\\(\\\\(2\\\\\\\\ x\\\\)\\\\) - 3\\\\) - x\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\(-3\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[-$CellContext`x + (-3 - 2 $CellContext`x + $CellContext`x^2)^Rational[1, 2], $CellContext`x, 3], -3], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075817714312*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 - \\\\(\\\\(2\ \\\\\\\\ x\\\\)\\\\) - 3\\\\) - x\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\ \\`\\(-1\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[-$CellContext`x + (-3 - 2 $CellContext`x + $CellContext`x^2)^Rational[1, 2], $CellContext`x, DirectedInfinity[1]], -1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075817768179*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 - \\\\(\\\\(2\\\\\\\\ \ x\\\\)\\\\) - 3\\\\) - x\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[-$CellContext`x + (-3 - 2 $CellContext`x + $CellContext`x^2)^Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075817793927*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", RowBox[{"-", "1"}]}], "\[InvisibleSpace]", "\<\" \[AGrave] droite\"\>"}], SequenceForm[ "AH", " \[Congruent] ", $CellContext`y == -1, " \[AGrave] droite"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075817837628*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "4", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\ \\\\[LongLeftArrow], \\\\!\\\\(TraditionalForm\\\\`1\\\\)]\\\"\\)\\) \[Union] \ \\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"[\\\\!\\\\(TraditionalForm\\\ \\`2\\\\), \\\\[LongRightArrow]\\\"\\)\\)\"\>", StringForm["`1` \[Union] `2`", analyse`Ens[$CellContext`x <= 1, $CellContext`x], analyse`Ens[$CellContext`x >= 2, $CellContext`x]], Editable->False], TraditionalForm]}], SequenceForm[4, ". Dom f = ", analyse`Ens[ Or[$CellContext`x <= 1, $CellContext`x >= 2], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075817861486*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 1\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\@\\\\(x\\\\^2 - \\\\(\\\\(3\\\\\ \\\\ x\\\\)\\\\) + 2\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`0\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(2 - 3 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, 1], 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075817894979*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 2\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\@\\\\(x\\\\^2 - \\\\(\\\\(3\\\\\ \\\\ x\\\\)\\\\) + 2\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`0\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(2 - 3 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, 2], 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758179279222`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\@\\\\(x\\\\^2 - \ \\\\(\\\\(3\\\\\\\\ x\\\\)\\\\) + 2\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(2 - 3 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758179609623`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\@\\\\(x\\\\^2 - \\\\(\\\\(3\\\\\\\\ \ x\\\\)\\\\) + 2\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(2 - 3 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075817994657*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AO\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", RowBox[{"x", "-", FractionBox["3", "2"]}]}], "\[InvisibleSpace]", "\<\" \[AGrave] droite\"\>"}], SequenceForm[ "AO", " \[Congruent] ", $CellContext`y == Rational[-3, 2] + $CellContext`x, " \[AGrave] droite"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818028461*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AO\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", RowBox[{ FractionBox["3", "2"], "-", "x"}]}], "\[InvisibleSpace]", "\<\" \[AGrave] gauche\"\>"}], SequenceForm[ "AO", " \[Congruent] ", $CellContext`y == Rational[3, 2] - $CellContext`x, " \[AGrave] gauche"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818062056*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "5", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\ \\\\[LongLeftArrow], \ \\\\!\\\\(TraditionalForm\\\\`\\\\(-1\\\\)\\\\)]\\\"\\)\\) \[Union] \ \\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\!\\\\(TraditionalForm\\\\\ `\\\\(TraditionalForm\\\\`\\\\\\\"[\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\ 1\\\\\\\\), \ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`3\\\\\\\\)[\\\\\\\"\\\\)\\\\) \ \\\\[Union] \ \\\\!\\\\(TraditionalForm\\\\`\\\\(TraditionalForm\\\\`\\\\\\\"]\\\\\\\\!\\\\\ \\\\(TraditionalForm\\\\\\\\`3\\\\\\\\), \ \\\\\\\\[LongRightArrow]\\\\\\\"\\\\)\\\\)\\\"\\)\\)\"\>", StringForm["`1` \[Union] `2`", analyse`Ens[$CellContext`x <= -1, $CellContext`x], analyse`Ens[ Or[ Inequality[1, LessEqual, $CellContext`x, Less, 3], $CellContext`x > 3], $CellContext`x]], Editable->False], TraditionalForm]}], SequenceForm[5, ". Dom f = ", analyse`Ens[ Or[$CellContext`x <= -1, Inequality[1, LessEqual, $CellContext`x, Less, 3], $CellContext`x > 3], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818095337*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-1\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\@\\\\(x\\\\^2 - 1\\\\)\\\\/\\\\(3 - \ x\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`0\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(3 - $CellContext`x)^(-1) (-1 + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, -1], 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758181284037`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 1\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\@\\\\(x\\\\^2 - \ 1\\\\)\\\\/\\\\(3 - x\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`0\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(3 - $CellContext`x)^(-1) (-1 + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, 1], 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818162448*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(\[Piecewise] \ \\*GridBox[{{\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 3\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"<\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\@\\\\\\\\\\\\\\\\(x\\\\\\\\\\\\\\\\^2 - \ 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\\\\\\\\(3 - \ x\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\\) = \ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"+\\\\\\\\\\\\\\\\!\\\ \\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\[Infinity]\\\\\ \\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\"\\\", \\\"\\\\\\\" \ \\\\\\\"\\\"}, \ {\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 3\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\">\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\@\\\\\\\\\\\\\\\\(x\\\\\\\\\\\\\\\\^2 - \ 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\\\\\\\\(3 - \ x\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\\) = \ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(-\[Infinity]\\\\\\\\)\\\\\\\ \\)\\\\\\\"\\\", \\\"\\\\\\\" \\\\\\\"\\\"}}, ColumnAlignments -> {Left}, \ ColumnSpacings -> 1.2, ColumnWidths -> Automatic]\\)\\)\"\>", StringForm["`1`", Piecewise[{{ StringForm["`1` = `2`", analyse`Limite[(3 - $CellContext`x)^(-1) (-1 + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, 3, -1], StringForm["+`1`", DirectedInfinity[1]]], " "}, { StringForm["`1` = `2`", analyse`Limite[(3 - $CellContext`x)^(-1) (-1 + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, 3, 1], DirectedInfinity[-1]], " "}}, 0]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818196065*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"AV \[Congruent] \\!\\(TraditionalForm\\`x\\) = \ \\!\\(TraditionalForm\\`3\\)\"\>", StringForm["AV \[Congruent] `1` = `2`", $CellContext`x, 3], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818229033*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\@\\\\(x\\\\^2 - \ 1\\\\)\\\\/\\\\(3 - x\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\(-1\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(3 - $CellContext`x)^(-1) (-1 + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[1]], -1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818262474*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\@\\\\(x\\\\^2 - 1\\\\)\\\\/\\\\(3 - \ x\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`1\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(3 - $CellContext`x)^(-1) (-1 + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], 1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.43607581830088*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", RowBox[{"-", "1"}]}], "\[InvisibleSpace]", "\<\" \[AGrave] droite\"\>"}], SequenceForm[ "AH", " \[Congruent] ", $CellContext`y == -1, " \[AGrave] droite"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818329835*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", "1"}], "\[InvisibleSpace]", "\<\" \[AGrave] gauche\"\>"}], SequenceForm[ "AH", " \[Congruent] ", $CellContext`y == 1, " \[AGrave] gauche"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818363413*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "6", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"[\\!\\(TraditionalForm\\`1\\), \ \[LongRightArrow]\"\>", StringForm["[`1`, \[LongRightArrow]", 1], Editable->False], TraditionalForm]}], SequenceForm[6, ". Dom f = ", analyse`Ens[$CellContext`x >= 1, $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818396296*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 1\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x - 1\\\\) - \ \\\\@x\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`\\(-1\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-1 + $CellContext`x)^Rational[1, 2] - $CellContext`x^ Rational[1, 2], $CellContext`x, 1], -1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818430173*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x - 1\\\\) - \\\\@x\\\ \\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`0\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-1 + $CellContext`x)^Rational[1, 2] - $CellContext`x^ Rational[1, 2], $CellContext`x, DirectedInfinity[1]], 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758184635077`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x - 1\\\\) - \ \\\\@x\\\\)\\\\)\\\"\\)\\) n'existe pas\"\>", StringForm["`1` `2`", analyse`Limite[(-1 + $CellContext`x)^Rational[1, 2] - $CellContext`x^ Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], " n'existe pas"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758184963408`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", "0"}], "\[InvisibleSpace]", "\<\" \[AGrave] droite\"\>"}], SequenceForm[ "AH", " \[Congruent] ", $CellContext`y == 0, " \[AGrave] droite"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818529866*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "7", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"]\\!\\(TraditionalForm\\`\\(-2\\)\\), \ \\!\\(TraditionalForm\\`2\\)[\"\>", StringForm["]`1`, `2`[", -2, 2], Editable->False], TraditionalForm]}], SequenceForm[7, ". Dom f = ", analyse`Ens[ Inequality[-2, Less, $CellContext`x, Less, 2], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818563271*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(\\\\(x \\\\[Rule] \ \\\\(\\\\(-2\\\\)\\\\)\\\\)\\\\+\\\\\\\">\\\\\\\"\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`1\\\\/\\\\@\\\\(4 - x\\\\^2\\\\)\\\\)\\\"\\)\\) \ = \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\ \\)\\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(4 - $CellContext`x^2)^Rational[-1, 2], $CellContext`x, -2, 1], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818597293*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"AV \[Congruent] \\!\\(TraditionalForm\\`x\\) = \ \\!\\(TraditionalForm\\`\\(-2\\)\\) a droite\"\>", StringForm["AV \[Congruent] `1` = `2` a droite", $CellContext`x, -2], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818629796*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(\\\\(x \\\\[Rule] \ 2\\\\)\\\\+\\\\\\\"<\\\\\\\"\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`1\\\\/\\\ \\@\\\\(4 - x\\\\^2\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(4 - $CellContext`x^2)^Rational[-1, 2], $CellContext`x, 2, -1], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758186645927`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"AV \[Congruent] \\!\\(TraditionalForm\\`x\\) = \ \\!\\(TraditionalForm\\`2\\) a gauche\"\>", StringForm["AV \[Congruent] `1` = `2` a gauche", $CellContext`x, 2], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818697291*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`1\\\\/\\\\@\\\\(4 - \ x\\\\^2\\\\)\\\\)\\\"\\)\\) n'existe pas\"\>", StringForm["`1` `2`", analyse`Limite[(4 - $CellContext`x^2)^Rational[-1, 2], $CellContext`x, DirectedInfinity[1]], " n'existe pas"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818731222*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`1\ \\\\/\\\\@\\\\(4 - x\\\\^2\\\\)\\\\)\\\"\\)\\) n'existe pas\"\>", StringForm["`1` `2`", analyse`Limite[(4 - $CellContext`x^2)^Rational[-1, 2], $CellContext`x, DirectedInfinity[-1]], " n'existe pas"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758187684793`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "8", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\ \\\\[LongLeftArrow], \ \\\\!\\\\(TraditionalForm\\\\`\\\\(-4\\\\)\\\\)]\\\"\\)\\) \[Union] \ \\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"[\\\\!\\\\(TraditionalForm\\\ \\`5\\\\), \\\\[LongRightArrow]\\\"\\)\\)\"\>", StringForm["`1` \[Union] `2`", analyse`Ens[$CellContext`x <= -4, $CellContext`x], analyse`Ens[$CellContext`x >= 5, $CellContext`x]], Editable->False], TraditionalForm]}], SequenceForm[8, ". Dom f = ", analyse`Ens[ Or[$CellContext`x <= -4, $CellContext`x >= 5], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818797784*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-4\\\\)\\\\)\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(x\\\\\\\\ \ \\\\@\\\\(x\\\\^2 - x - 20\\\\)\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`0\\)\"\>", StringForm["`1` = `2`", analyse`Limite[$CellContext`x (-20 - $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, -4], 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818830675*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 5\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(x\\\\\\\\ \\\\@\\\\(x\\\\^2 - \ x - 20\\\\)\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`0\\)\"\>", StringForm["`1` = `2`", analyse`Limite[$CellContext`x (-20 - $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, 5], 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818864769*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(x\\\\\\\\ \\\\@\\\\(x\\\\^2 - x \ - 20\\\\)\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[$CellContext`x (-20 - $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818898286*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(x\\\\\\\\ \\\\@\\\\(x\\\\^2 - x - \ 20\\\\)\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`\\(-\[Infinity]\\)\\)\"\ \>", StringForm["`1` = `2`", analyse`Limite[$CellContext`x (-20 - $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], DirectedInfinity[-1]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.43607581893193*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "9", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\ \\\\[LongLeftArrow], \\\\!\\\\(TraditionalForm\\\\`3\\\\)]\\\"\\)\\) \[Union] \ \\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"]\\\\!\\\\(TraditionalForm\\\ \\`4\\\\), \\\\[LongRightArrow]\\\"\\)\\)\"\>", StringForm["`1` \[Union] `2`", analyse`Ens[$CellContext`x <= 3, $CellContext`x], analyse`Ens[$CellContext`x > 4, $CellContext`x]], Editable->False], TraditionalForm]}], SequenceForm[9, ". Dom f = ", analyse`Ens[ Or[$CellContext`x <= 3, $CellContext`x > 4], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818965217*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 3\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\@\\\\(\\\\(x - \ 3\\\\)\\\\/\\\\(x - 4\\\\)\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`0\\)\ \"\>", StringForm["`1` = `2`", analyse`Limite[((-4 + $CellContext`x)^(-1) (-3 + $CellContext`x))^ Rational[1, 2], $CellContext`x, 3], 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075818998515*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(\\\\(x \\\\[Rule] \ 4\\\\)\\\\+\\\\\\\">\\\\\\\"\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\@\\\\(\\\\(x - 3\\\\)\\\\/\\\\(x - 4\\\\)\\\ \\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\ \\`\\\\[Infinity]\\\\)\\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[((-4 + $CellContext`x)^(-1) (-3 + $CellContext`x))^ Rational[1, 2], $CellContext`x, 4, 1], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758190321836`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"AV \[Congruent] \\!\\(TraditionalForm\\`x\\) = \ \\!\\(TraditionalForm\\`4\\) a droite\"\>", StringForm["AV \[Congruent] `1` = `2` a droite", $CellContext`x, 4], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819065243*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\@\\\\(\\\\(x - 3\\\\)\\\\/\\\\(x \ - 4\\\\)\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`1\\)\"\>", StringForm["`1` = `2`", analyse`Limite[((-4 + $CellContext`x)^(-1) (-3 + $CellContext`x))^ Rational[1, 2], $CellContext`x, DirectedInfinity[1]], 1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819099141*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\@\\\\(\\\\(x - 3\\\\)\\\\/\\\\(x - 4\\\\)\\\ \\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`1\\)\"\>", StringForm["`1` = `2`", analyse`Limite[((-4 + $CellContext`x)^(-1) (-3 + $CellContext`x))^ Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], 1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758191326036`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", "1"}]}], SequenceForm["AH", " \[Congruent] ", $CellContext`y == 1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819165948*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "10", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"[\ \\\\!\\\\(TraditionalForm\\\\`\\\\(-7\\\\)\\\\), \ \\\\!\\\\(TraditionalForm\\\\`2\\\\)[\\\"\\)\\) \[Union] \ \\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"]\\\\!\\\\(TraditionalForm\\\ \\`2\\\\), \\\\[LongRightArrow]\\\"\\)\\)\"\>", StringForm["`1` \[Union] `2`", analyse`Ens[ Inequality[-7, LessEqual, $CellContext`x, Less, 2], $CellContext`x], analyse`Ens[$CellContext`x > 2, $CellContext`x]], Editable->False], TraditionalForm]}], SequenceForm[10, ". Dom f = ", analyse`Ens[ Or[ Inequality[-7, LessEqual, $CellContext`x, Less, 2], $CellContext`x > 2], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819199082*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-7\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x + 7\\\\) - 3\\\\)\\\\/\\\\(x - \ 2\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`1\\/3\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-2 + $CellContext`x)^(-1) (-3 + (7 + $CellContext`x)^ Rational[1, 2]), $CellContext`x, -7], Rational[1, 3]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.43607581923691*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 2\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x + 7\\\\) - \ 3\\\\)\\\\/\\\\(x - 2\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`1\\/6\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-2 + $CellContext`x)^(-1) (-3 + (7 + $CellContext`x)^ Rational[1, 2]), $CellContext`x, 2], Rational[1, 6]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758192673807`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x + 7\\\\) - 3\\\\)\\\ \\/\\\\(x - 2\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`0\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-2 + $CellContext`x)^(-1) (-3 + (7 + $CellContext`x)^ Rational[1, 2]), $CellContext`x, DirectedInfinity[1]], 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819300156*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x + 7\\\\) - 3\\\\)\\\\/\\\\(x - \ 2\\\\)\\\\)\\\"\\)\\) n'existe pas\"\>", StringForm["`1` `2`", analyse`Limite[(-2 + $CellContext`x)^(-1) (-3 + (7 + $CellContext`x)^ Rational[1, 2]), $CellContext`x, DirectedInfinity[-1]], " n'existe pas"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819333343*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", "0"}], "\[InvisibleSpace]", "\<\" \[AGrave] droite\"\>"}], SequenceForm[ "AH", " \[Congruent] ", $CellContext`y == 0, " \[AGrave] droite"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819366602*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "11", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"[\\!\\(TraditionalForm\\`\\(-5\\)\\), \ \[LongRightArrow]\"\>", StringForm["[`1`, \[LongRightArrow]", -5], Editable->False], TraditionalForm]}], SequenceForm[11, ". Dom f = ", analyse`Ens[$CellContext`x >= -5, $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819399817*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-5\\\\)\\\\)\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(x + \\\\@\ \\\\(x + 5\\\\)\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\(-5\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[$CellContext`x + (5 + $CellContext`x)^ Rational[1, 2], $CellContext`x, -5], -5], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819433715*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(x + \\\\@\\\\(x + 5\\\\)\\\\)\\\ \\)\\\"\\)\\) = \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\ \\[Infinity]\\\\)\\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[$CellContext`x + (5 + $CellContext`x)^ Rational[1, 2], $CellContext`x, DirectedInfinity[1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758194666348`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(x + \\\\@\\\\(x + \ 5\\\\)\\\\)\\\\)\\\"\\)\\) n'existe pas\"\>", StringForm["`1` `2`", analyse`Limite[$CellContext`x + (5 + $CellContext`x)^ Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], " n'existe pas"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819500288*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "12", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ TagBox["\[DoubleStruckCapitalR]", Function[{}, Reals]], TraditionalForm]}], SequenceForm[12, ". Dom f = ", analyse`Ens[True, $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819534196*^9}], Cell[BoxData[ FormBox["\<\"pas d'asymptote verticale\"\>", TraditionalForm]], "Print", CellChangeTimes->{3.4360758195668507`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 + 1\\\\) - \ x\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`0\\)\"\>", StringForm["`1` = `2`", analyse`Limite[-$CellContext`x + (1 + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[1]], 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758196010447`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 + 1\\\\) - x\\\\)\\\\)\\\ \"\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[-$CellContext`x + (1 + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819633791*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", "0"}], "\[InvisibleSpace]", "\<\" \[AGrave] droite\"\>"}], SequenceForm[ "AH", " \[Congruent] ", $CellContext`y == 0, " \[AGrave] droite"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819667894*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "13", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"[\\!\\(TraditionalForm\\`1\\), \ \[LongRightArrow]\"\>", StringForm["[`1`, \[LongRightArrow]", 1], Editable->False], TraditionalForm]}], SequenceForm[13, ". Dom f = ", analyse`Ens[$CellContext`x >= 1, $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758197057133`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 1\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\((x - 1)\\\\)\\\\^\\\\(3/2\\\\)\ \\\\/\\\\@\\\\(x + 2\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`0\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-1 + $CellContext`x)^Rational[3, 2] (2 + $CellContext`x)^ Rational[-1, 2], $CellContext`x, 1], 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819734057*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\((x - \ 1)\\\\)\\\\^\\\\(3/2\\\\)\\\\/\\\\@\\\\(x + 2\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-1 + $CellContext`x)^Rational[3, 2] (2 + $CellContext`x)^ Rational[-1, 2], $CellContext`x, DirectedInfinity[1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819767494*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\((x - 1)\\\\)\\\\^\\\\(3/2\\\\)\\\\/\\\\@\\\ \\(x + 2\\\\)\\\\)\\\"\\)\\) n'existe pas\"\>", StringForm["`1` `2`", analyse`Limite[(-1 + $CellContext`x)^Rational[3, 2] (2 + $CellContext`x)^ Rational[-1, 2], $CellContext`x, DirectedInfinity[-1]], " n'existe pas"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819800911*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AO\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", RowBox[{"x", "-", FractionBox["5", "2"]}]}], "\[InvisibleSpace]", "\<\" \[AGrave] droite\"\>"}], SequenceForm[ "AO", " \[Congruent] ", $CellContext`y == Rational[-5, 2] + $CellContext`x, " \[AGrave] droite"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819834998*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "14", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\ \\\\[LongLeftArrow], \ \\\\!\\\\(TraditionalForm\\\\`\\\\(-1\\\\)\\\\)]\\\"\\)\\) \[Union] \ \\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"[\\\\!\\\\(TraditionalForm\\\ \\`3\\\\), \\\\[LongRightArrow]\\\"\\)\\)\"\>", StringForm["`1` \[Union] `2`", analyse`Ens[$CellContext`x <= -1, $CellContext`x], analyse`Ens[$CellContext`x >= 3, $CellContext`x]], Editable->False], TraditionalForm]}], SequenceForm[14, ". Dom f = ", analyse`Ens[ Or[$CellContext`x <= -1, $CellContext`x >= 3], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758198682013`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-1\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\(\\\\(-x\\\\)\\\\) + \\\\@\\\\(x\\\\^2 \ - \\\\(\\\\(2\\\\\\\\ x\\\\)\\\\) - 3\\\\) - 1\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`0\\)\"\>", StringForm["`1` = `2`", analyse`Limite[-1 - $CellContext`x + (-3 - 2 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, -1], 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819901478*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 3\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\(\\\\(-x\\\\)\\\\) + \\\\@\ \\\\(x\\\\^2 - \\\\(\\\\(2\\\\\\\\ x\\\\)\\\\) - 3\\\\) - \ 1\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`\\(-4\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[-1 - $CellContext`x + (-3 - 2 $CellContext`x + $CellContext`x^2)^Rational[1, 2], $CellContext`x, 3], -4], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819934963*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\(\\\\(-x\\\\)\\\\) + \ \\\\@\\\\(x\\\\^2 - \\\\(\\\\(2\\\\\\\\ x\\\\)\\\\) - 3\\\\) - \ 1\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`\\(-2\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[-1 - $CellContext`x + (-3 - 2 $CellContext`x + $CellContext`x^2)^Rational[1, 2], $CellContext`x, DirectedInfinity[1]], -2], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075819968598*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\(\\\\(-x\\\\)\\\\) + \\\\@\\\\(x\\\\^2 \ - \\\\(\\\\(2\\\\\\\\ x\\\\)\\\\) - 3\\\\) - 1\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[-1 - $CellContext`x + (-3 - 2 $CellContext`x + $CellContext`x^2)^Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820001563*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", RowBox[{"-", "2"}]}], "\[InvisibleSpace]", "\<\" \[AGrave] droite\"\>"}], SequenceForm[ "AH", " \[Congruent] ", $CellContext`y == -2, " \[AGrave] droite"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820035452*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "15", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"[\ \\\\!\\\\(TraditionalForm\\\\`2\\\\/3\\\\), \\\\!\\\\(TraditionalForm\\\\`2\\\ \\)[\\\"\\)\\) \[Union] \ \\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"]\\\\!\\\\(TraditionalForm\\\ \\`2\\\\), \\\\[LongRightArrow]\\\"\\)\\)\"\>", StringForm["`1` \[Union] `2`", analyse`Ens[ Inequality[ Rational[2, 3], LessEqual, $CellContext`x, Less, 2], $CellContext`x], analyse`Ens[$CellContext`x > 2, $CellContext`x]], Editable->False], TraditionalForm]}], SequenceForm[15, ". Dom f = ", analyse`Ens[ Or[ Inequality[ Rational[2, 3], LessEqual, $CellContext`x, Less, 2], $CellContext`x > 2], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820069751*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] 2\\\\/3\\\ \\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(\\\\(\\\\(3\\\\\\\\ x\\\ \\)\\\\) - 2\\\\) - \\\\@\\\\(x + 2\\\\)\\\\)\\\\/\\\\(x - 2\\\\)\\\\)\\\"\\)\ \\) = \\!\\(TraditionalForm\\`\\@\\(3\\/2\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-2 + $CellContext`x)^(-1) (-(2 + $CellContext`x)^ Rational[1, 2] + (-2 + 3 $CellContext`x)^ Rational[1, 2]), $CellContext`x, Rational[2, 3]], Rational[3, 2]^Rational[1, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820102355*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 2\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(\\\\(\\\\(3\\\\\\\\ \ x\\\\)\\\\) - 2\\\\) - \\\\@\\\\(x + 2\\\\)\\\\)\\\\/\\\\(x - 2\\\\)\\\\)\\\"\ \\)\\) = \\!\\(TraditionalForm\\`1\\/2\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-2 + $CellContext`x)^(-1) (-(2 + $CellContext`x)^ Rational[1, 2] + (-2 + 3 $CellContext`x)^ Rational[1, 2]), $CellContext`x, 2], Rational[1, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820136397*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(\\\\(\\\\(3\\\\\\\\ x\ \\\\)\\\\) - 2\\\\) - \\\\@\\\\(x + 2\\\\)\\\\)\\\\/\\\\(x - \ 2\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`0\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-2 + $CellContext`x)^(-1) (-(2 + $CellContext`x)^ Rational[1, 2] + (-2 + 3 $CellContext`x)^ Rational[1, 2]), $CellContext`x, DirectedInfinity[1]], 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820172986*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(\\\\(\\\\(3\\\\\\\\ x\\\\)\\\\) \ - 2\\\\) - \\\\@\\\\(x + 2\\\\)\\\\)\\\\/\\\\(x - 2\\\\)\\\\)\\\"\\)\\) \ n'existe pas\"\>", StringForm["`1` `2`", analyse`Limite[(-2 + $CellContext`x)^(-1) (-(2 + $CellContext`x)^ Rational[1, 2] + (-2 + 3 $CellContext`x)^ Rational[1, 2]), $CellContext`x, DirectedInfinity[-1]], " n'existe pas"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758202028503`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", "0"}], "\[InvisibleSpace]", "\<\" \[AGrave] droite\"\>"}], SequenceForm[ "AH", " \[Congruent] ", $CellContext`y == 0, " \[AGrave] droite"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820235924*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "16", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\ \\\\[LongLeftArrow], \ \\\\!\\\\(TraditionalForm\\\\`\\\\(-2\\\\)\\\\)]\\\"\\)\\) \[Union] \ \\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"[\\\\!\\\\(TraditionalForm\\\ \\`5\\\\), \\\\[LongRightArrow]\\\"\\)\\)\"\>", StringForm["`1` \[Union] `2`", analyse`Ens[$CellContext`x <= -2, $CellContext`x], analyse`Ens[$CellContext`x >= 5, $CellContext`x]], Editable->False], TraditionalForm]}], SequenceForm[16, ". Dom f = ", analyse`Ens[ Or[$CellContext`x <= -2, $CellContext`x >= 5], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820269907*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-2\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\(\\\\(-x\\\\)\\\\) + \\\\@\\\\(x\\\\^2 \ - \\\\(\\\\(3\\\\\\\\ x\\\\)\\\\) - 10\\\\) + 2\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`4\\)\"\>", StringForm["`1` = `2`", analyse`Limite[ 2 - $CellContext`x + (-10 - 3 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, -2], 4], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820303096*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 5\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\(\\\\(-x\\\\)\\\\) + \\\\@\ \\\\(x\\\\^2 - \\\\(\\\\(3\\\\\\\\ x\\\\)\\\\) - 10\\\\) + 2\\\\)\\\\)\\\"\\)\ \\) = \\!\\(TraditionalForm\\`\\(-3\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[ 2 - $CellContext`x + (-10 - 3 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, 5], -3], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758203368797`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\(\\\\(-x\\\\)\\\\) + \ \\\\@\\\\(x\\\\^2 - \\\\(\\\\(3\\\\\\\\ x\\\\)\\\\) - 10\\\\) + 2\\\\)\\\\)\\\ \"\\)\\) = \\!\\(TraditionalForm\\`1\\/2\\)\"\>", StringForm["`1` = `2`", analyse`Limite[ 2 - $CellContext`x + (-10 - 3 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[1]], Rational[1, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820370574*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\(\\\\(-x\\\\)\\\\) + \\\\@\\\\(x\\\\^2 \ - \\\\(\\\\(3\\\\\\\\ x\\\\)\\\\) - 10\\\\) + 2\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[ 2 - $CellContext`x + (-10 - 3 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820404085*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", FractionBox["1", "2"]}], "\[InvisibleSpace]", "\<\" \[AGrave] droite\"\>"}], SequenceForm[ "AH", " \[Congruent] ", $CellContext`y == Rational[1, 2], " \[AGrave] droite"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820436987*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "17", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\ \\\\[LongLeftArrow], \ \\\\!\\\\(TraditionalForm\\\\`\\\\(-3\\\\)\\\\)]\\\"\\)\\) \[Union] \ \\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"[\\\\!\\\\(TraditionalForm\\\ \\`7\\\\), \\\\[LongRightArrow]\\\"\\)\\)\"\>", StringForm["`1` \[Union] `2`", analyse`Ens[$CellContext`x <= -3, $CellContext`x], analyse`Ens[$CellContext`x >= 7, $CellContext`x]], Editable->False], TraditionalForm]}], SequenceForm[17, ". Dom f = ", analyse`Ens[ Or[$CellContext`x <= -3, $CellContext`x >= 7], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758204704857`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-3\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 - \\\\(\\\\(5\\\\\\\\ \ x\\\\)\\\\) - 14\\\\) - \\\\@\\\\(x\\\\^2 - \\\\(\\\\(2\\\\\\\\ x\\\\)\\\\) - \ 15\\\\)\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`\\@10\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-14 - 5 $CellContext`x + $CellContext`x^2)^ Rational[1, 2] - (-15 - 2 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, -3], 10^Rational[1, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820504243*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 7\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 - \ \\\\(\\\\(5\\\\\\\\ x\\\\)\\\\) - 14\\\\) - \\\\@\\\\(x\\\\^2 - \\\\(\\\\(2\\\ \\\\\\ x\\\\)\\\\) - 15\\\\)\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\(\\(\\(-2\\)\\)\\\\ \\@5\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-14 - 5 $CellContext`x + $CellContext`x^2)^ Rational[1, 2] - (-15 - 2 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, 7], (-2) 5^Rational[1, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820537033*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 - \\\\(\\\\(5\ \\\\\\\\ x\\\\)\\\\) - 14\\\\) - \\\\@\\\\(x\\\\^2 - \\\\(\\\\(2\\\\\\\\ \ x\\\\)\\\\) - 15\\\\)\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\(-\\(\\(3\\/2\\)\\)\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-14 - 5 $CellContext`x + $CellContext`x^2)^ Rational[1, 2] - (-15 - 2 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[1]], Rational[-3, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820570486*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 - \\\\(\\\\(5\\\\\\\\ \ x\\\\)\\\\) - 14\\\\) - \\\\@\\\\(x\\\\^2 - \\\\(\\\\(2\\\\\\\\ x\\\\)\\\\) - \ 15\\\\)\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`3\\/2\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-14 - 5 $CellContext`x + $CellContext`x^2)^ Rational[1, 2] - (-15 - 2 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], Rational[3, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.43607582060429*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", RowBox[{"-", FractionBox["3", "2"]}]}], "\[InvisibleSpace]", "\<\" \[AGrave] droite\"\>"}], SequenceForm[ "AH", " \[Congruent] ", $CellContext`y == Rational[-3, 2], " \[AGrave] droite"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820641596*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", FractionBox["3", "2"]}], "\[InvisibleSpace]", "\<\" \[AGrave] gauche\"\>"}], SequenceForm[ "AH", " \[Congruent] ", $CellContext`y == Rational[3, 2], " \[AGrave] gauche"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758206715527`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "18", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\ \\\\[LongLeftArrow], \ \\\\!\\\\(TraditionalForm\\\\`\\\\(-5\\\\)\\\\)]\\\"\\)\\) \[Union] \ \\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"[\\\\!\\\\(TraditionalForm\\\ \\`7\\\\), \\\\[LongRightArrow]\\\"\\)\\)\"\>", StringForm["`1` \[Union] `2`", analyse`Ens[$CellContext`x <= -5, $CellContext`x], analyse`Ens[$CellContext`x >= 7, $CellContext`x]], Editable->False], TraditionalForm]}], SequenceForm[18, ". Dom f = ", analyse`Ens[ Or[$CellContext`x <= -5, $CellContext`x >= 7], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758207046957`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-5\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 - \\\\(\\\\(5\\\\\\\\ \ x\\\\)\\\\) - 14\\\\) + \\\\@\\\\(x\\\\^2 + \\\\(\\\\(4\\\\\\\\ x\\\\)\\\\) - \ 5\\\\)\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`6\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-14 - 5 $CellContext`x + $CellContext`x^2)^ Rational[1, 2] + (-5 + 4 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, -5], 6], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820737938*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 7\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 - \ \\\\(\\\\(5\\\\\\\\ x\\\\)\\\\) - 14\\\\) + \\\\@\\\\(x\\\\^2 + \\\\(\\\\(4\\\ \\\\\\ x\\\\)\\\\) - 5\\\\)\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\(6\\\\ \\@2\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-14 - 5 $CellContext`x + $CellContext`x^2)^ Rational[1, 2] + (-5 + 4 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, 7], 6 2^Rational[1, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820771495*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 - \\\\(\\\\(5\ \\\\\\\\ x\\\\)\\\\) - 14\\\\) + \\\\@\\\\(x\\\\^2 + \\\\(\\\\(4\\\\\\\\ \ x\\\\)\\\\) - 5\\\\)\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`\\\"+\\\\!\ \\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-14 - 5 $CellContext`x + $CellContext`x^2)^ Rational[1, 2] + (-5 + 4 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820805544*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 - \\\\(\\\\(5\\\\\\\\ \ x\\\\)\\\\) - 14\\\\) + \\\\@\\\\(x\\\\^2 + \\\\(\\\\(4\\\\\\\\ x\\\\)\\\\) - \ 5\\\\)\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-14 - 5 $CellContext`x + $CellContext`x^2)^ Rational[1, 2] + (-5 + 4 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758208386517`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AO\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", RowBox[{ RowBox[{"2", " ", "x"}], "-", FractionBox["1", "2"]}]}], "\[InvisibleSpace]", "\<\" \[AGrave] droite\"\>"}], SequenceForm[ "AO", " \[Congruent] ", $CellContext`y == Rational[-1, 2] + 2 $CellContext`x, " \[AGrave] droite"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820872356*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AO\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", RowBox[{ FractionBox["1", "2"], "-", RowBox[{"2", " ", "x"}]}]}], "\[InvisibleSpace]", "\<\" \[AGrave] gauche\"\>"}], SequenceForm[ "AO", " \[Congruent] ", $CellContext`y == Rational[1, 2] - 2 $CellContext`x, " \[AGrave] gauche"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360758209049807`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "19", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\*TagBox[\\\"\ \[DoubleStruckCapitalR]\\\", Function[List[], Reals]]\\) \\\\ \ {\\!\\(TraditionalForm\\`\\(-2\\)\\),\\!\\(TraditionalForm\\`1\\/3\\)}\"\>", StringForm["`1` \\ {`2`,`3`}", Reals, -2, Rational[1, 3]], Editable->False], TraditionalForm]}], SequenceForm[19, ". Dom f = ", analyse`Ens[ Or[$CellContext`x < -2, Inequality[-2, Less, $CellContext`x, Less, Rational[1, 3]], $CellContext`x > Rational[1, 3]], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075820938881*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-2\\\\)\\\\)\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(x\\\\^2 - \ 4\\\\)\\\\/\\\\(\\\\(\\\\(3\\\\\\\\ x\\\\^2\\\\)\\\\) + \\\\(\\\\(5\\\\\\\\ x\ \\\\)\\\\) - 2\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`4\\/7\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-4 + $CellContext`x^2)/(-2 + 5 $CellContext`x + 3 $CellContext`x^2), $CellContext`x, -2], Rational[4, 7]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.43607582097276*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(\[Piecewise] \ \\*GridBox[{{\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 1\\\\\\\\\\\\\\\\/3\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\"<\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(x\\\\\\\\\\\\\\\\^2 - \ 4\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(\\\\\\\\\ \\\\\\\\(3\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \ x\\\\\\\\\\\\\\\\^2\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) + \\\\\\\\\\\\\\\\(\\\\\ \\\\\\\\\\\\(5\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ x\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\ \\\\) - 2\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\\) \ = \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"+\\\\\\\\\\\\\\\\!\ \\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\[Infinity]\\\ \\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\"\\\", \\\"\\\\\\\" \\\\\\\"\\\ \"}, {\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 1\\\\\\\\\\\\\\\\/3\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\">\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(x\\\\\\\\\\\\\\\\^2 - \ 4\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(\\\\\\\\\ \\\\\\\\(3\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \ x\\\\\\\\\\\\\\\\^2\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) + \\\\\\\\\\\\\\\\(\\\\\ \\\\\\\\\\\\(5\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ x\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\ \\\\) - 2\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\\) \ = \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(-\[Infinity]\\\\\\\\)\\\\\ \\\\)\\\\\\\"\\\", \\\"\\\\\\\" \\\\\\\"\\\"}}, ColumnAlignments -> {Left}, \ ColumnSpacings -> 1.2, ColumnWidths -> Automatic]\\)\\)\"\>", StringForm["`1`", Piecewise[{{ StringForm["`1` = `2`", analyse`Limite[(-4 + $CellContext`x^2)/(-2 + 5 $CellContext`x + 3 $CellContext`x^2), $CellContext`x, Rational[1, 3], -1], StringForm["+`1`", DirectedInfinity[1]]], " "}, { StringForm["`1` = `2`", analyse`Limite[(-4 + $CellContext`x^2)/(-2 + 5 $CellContext`x + 3 $CellContext`x^2), $CellContext`x, Rational[1, 3], 1], DirectedInfinity[-1]], " "}}, 0]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075821006009*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"AV \[Congruent] \\!\\(TraditionalForm\\`x\\) = \ \\!\\(TraditionalForm\\`1\\/3\\)\"\>", StringForm["AV \[Congruent] `1` = `2`", $CellContext`x, Rational[1, 3]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075821039249*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(x\\\\^2 - 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