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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->{3.43607531073363*^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->{3.436075310763198*^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->{3.436075310796479*^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->{3.436075310829784*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "3", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"[\\!\\(TraditionalForm\\`1\\), \ \[LongRightArrow]\"\>", StringForm["[`1`, \[LongRightArrow]", 1], Editable->False], TraditionalForm]}], SequenceForm[3, ". Dom f = ", analyse`Ens[$CellContext`x >= 1, $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075310863577*^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->{3.43607531089742*^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->{3.4360753109299707`*^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->{3.436075310963605*^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->{3.436075310996917*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "4", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"]\\!\\(TraditionalForm\\`\\(-2\\)\\), \ \\!\\(TraditionalForm\\`2\\)[\"\>", StringForm["]`1`, `2`[", -2, 2], Editable->False], TraditionalForm]}], SequenceForm[4, ". Dom f = ", analyse`Ens[ Inequality[-2, Less, $CellContext`x, Less, 2], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075311031287*^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->{3.436075311064438*^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->{3.436075311097616*^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->{3.436075311131255*^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->{3.436075311164418*^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->{3.436075311201908*^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->{3.4360753112314796`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "5", "\[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, $CellContext`x]], Editable->False], TraditionalForm]}], SequenceForm[5, ". Dom f = ", analyse`Ens[ Or[$CellContext`x <= 3, $CellContext`x > 4], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075311265265*^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->{3.436075311298521*^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->{3.43607531133249*^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->{3.4360753113650417`*^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->{3.436075311399044*^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->{3.436075311432632*^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->{3.43607531146596*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "6", "\[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[6, ". Dom f = ", analyse`Ens[ Or[ Inequality[-7, LessEqual, $CellContext`x, Less, 2], $CellContext`x > 2], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075311499501*^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->{3.436075311532765*^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->{3.4360753115665417`*^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->{3.436075311599187*^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->{3.43607531163253*^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->{3.4360753116708508`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "7", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"[\\!\\(TraditionalForm\\`\\(-5\\)\\), \ \[LongRightArrow]\"\>", StringForm["[`1`, \[LongRightArrow]", -5], Editable->False], TraditionalForm]}], SequenceForm[7, ". Dom f = ", analyse`Ens[$CellContext`x >= -5, $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.43607531169993*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-5\\\\)\\\\)\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(x + \\\\@\ \\\\(x + 5\\\\)\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\(-5\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[$CellContext`x + (5 + $CellContext`x)^ Rational[1, 2], $CellContext`x, -5], -5], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360753117330313`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(x + \\\\@\\\\(x + 5\\\\)\\\\)\\\ \\)\\\"\\)\\) = \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\ \\[Infinity]\\\\)\\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[$CellContext`x + (5 + $CellContext`x)^ Rational[1, 2], $CellContext`x, DirectedInfinity[1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075311766612*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(x + \\\\@\\\\(x + \ 5\\\\)\\\\)\\\\)\\\"\\)\\) n'existe pas\"\>", StringForm["`1` `2`", analyse`Limite[$CellContext`x + (5 + $CellContext`x)^ Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], " n'existe pas"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.43607531180063*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "8", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ TagBox["\[DoubleStruckCapitalR]", Function[{}, Reals]], TraditionalForm]}], SequenceForm[8, ". Dom f = ", analyse`Ens[True, $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075311834262*^9}], Cell[BoxData[ FormBox["\<\"pas d'asymptote verticale\"\>", TraditionalForm]], "Print", CellChangeTimes->{3.436075311867284*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 + 1\\\\) - \ x\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`0\\)\"\>", StringForm["`1` = `2`", analyse`Limite[-$CellContext`x + (1 + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[1]], 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360753119011297`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(x\\\\^2 + 1\\\\) - x\\\\)\\\\)\\\ \"\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[-$CellContext`x + (1 + $CellContext`x^2)^ Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075311934043*^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->{3.4360753119677477`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "9", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\*TagBox[\\\"\ \[DoubleStruckCapitalR]\\\", Function[List[], Reals]]\\) \\\\ \ {\\!\\(TraditionalForm\\`\\(-1\\)\\),\\!\\(TraditionalForm\\`1\\)}\"\>", StringForm["`1` \\ {`2`,`3`}", Reals, -1, 1], Editable->False], TraditionalForm]}], SequenceForm[9, ". Dom f = ", analyse`Ens[ Or[$CellContext`x < -1, Inequality[-1, Less, $CellContext`x, Less, 1], $CellContext`x > 1], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075312001258*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(\[Piecewise] \ \\*GridBox[{{\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(-1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\ \\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"<\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(x\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(\\\\\ \\\\\\\\\\\\[LeftBracketingBar] \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x - 1\\\\\\\ \\\\\\\\\\)\\\\\\\\\\\\\\\\) \\\\\\\\\\\\\\\\[RightBracketingBar]\\\\\\\\\\\\\ \\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\\\\\\\\(x\\\\\ \\\\\\\\\\\\^2 - 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\ \\\\\\\\) = \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(-\[Infinity]\\\ \\\\\\)\\\\\\\\)\\\\\\\"\\\", \\\"\\\\\\\" \\\\\\\"\\\"}, {\\\"\\\\\\\"\\\\\\\ \\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\\ \\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\ \\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\\\\\\\\\\\\\\[Rule] \ \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(-1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\ \\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\">\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(x\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(\\\\\ \\\\\\\\\\\\[LeftBracketingBar] \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x - 1\\\\\\\ \\\\\\\\\\)\\\\\\\\\\\\\\\\) \\\\\\\\\\\\\\\\[RightBracketingBar]\\\\\\\\\\\\\ \\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\\\\\\\\(x\\\\\ \\\\\\\\\\\\^2 - 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\ \\\\\\\\) = \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"+\\\\\\\ \\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\[\ Infinity]\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\"\\\", \\\"\\\\\\\" \ \\\\\\\"\\\"}}, ColumnAlignments -> {Left}, ColumnSpacings -> 1.2, \ ColumnWidths -> Automatic]\\)\\)\"\>", StringForm["`1`", Piecewise[{{ StringForm["`1` = `2`", analyse`Limite[$CellContext`x (-1 + $CellContext`x^2)^(-1) Abs[-1 + $CellContext`x], $CellContext`x, -1, -1], DirectedInfinity[-1]], " "}, { StringForm["`1` = `2`", analyse`Limite[$CellContext`x (-1 + $CellContext`x^2)^(-1) Abs[-1 + $CellContext`x], $CellContext`x, -1, 1], StringForm["+`1`", DirectedInfinity[1]]], " "}}, 0]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075312034005*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"AV \[Congruent] \\!\\(TraditionalForm\\`x\\) = \ \\!\\(TraditionalForm\\`\\(-1\\)\\)\"\>", StringForm["AV \[Congruent] `1` = `2`", $CellContext`x, -1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360753120682783`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(\[Piecewise] \ \\*GridBox[{{\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"<\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(x\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(\\\\\ \\\\\\\\\\\\[LeftBracketingBar] \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x - 1\\\\\\\ \\\\\\\\\\)\\\\\\\\\\\\\\\\) \\\\\\\\\\\\\\\\[RightBracketingBar]\\\\\\\\\\\\\ \\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\\\\\\\\(x\\\\\ \\\\\\\\\\\\^2 - 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\ \\\\\\\\) = \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(-\\\\\\\\(\\\\\ \\\\(1\\\\\\\\/2\\\\\\\\)\\\\\\\\)\\\\\\\\)\\\\\\\\)\\\\\\\"\\\", \ \\\"\\\\\\\" \\\\\\\"\\\"}, \ {\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\">\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(x\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(\\\\\ \\\\\\\\\\\\[LeftBracketingBar] \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x - 1\\\\\\\ \\\\\\\\\\)\\\\\\\\\\\\\\\\) \\\\\\\\\\\\\\\\[RightBracketingBar]\\\\\\\\\\\\\ \\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\\\\\\\\(x\\\\\ \\\\\\\\\\\\^2 - 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\ \\\\\\\\) = \ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`1\\\\\\\\/2\\\\\\\\)\\\\\\\"\\\", \ \\\"\\\\\\\" \\\\\\\"\\\"}}, ColumnAlignments -> {Left}, ColumnSpacings -> \ 1.2, ColumnWidths -> Automatic]\\)\\)\"\>", StringForm["`1`", Piecewise[{{ StringForm["`1` = `2`", analyse`Limite[$CellContext`x (-1 + $CellContext`x^2)^(-1) Abs[-1 + $CellContext`x], $CellContext`x, 1, -1], Rational[-1, 2]], " "}, { StringForm["`1` = `2`", analyse`Limite[$CellContext`x (-1 + $CellContext`x^2)^(-1) Abs[-1 + $CellContext`x], $CellContext`x, 1, 1], Rational[1, 2]], " "}}, 0]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360753121014967`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(x\\\\\\\\ \ \\\\(\\\\(\\\\[LeftBracketingBar] \\\\(\\\\(x - 1\\\\)\\\\) \ \\\\[RightBracketingBar]\\\\)\\\\)\\\\)\\\\/\\\\(x\\\\^2 - 1\\\\)\\\\)\\\"\\)\ \\) = \\!\\(TraditionalForm\\`1\\)\"\>", StringForm["`1` = `2`", analyse`Limite[$CellContext`x (-1 + $CellContext`x^2)^(-1) Abs[-1 + $CellContext`x], $CellContext`x, DirectedInfinity[1]], 1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075312138877*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(x\\\\\\\\ \ \\\\(\\\\(\\\\[LeftBracketingBar] \\\\(\\\\(x - 1\\\\)\\\\) \ \\\\[RightBracketingBar]\\\\)\\\\)\\\\)\\\\/\\\\(x\\\\^2 - 1\\\\)\\\\)\\\"\\)\ \\) = \\!\\(TraditionalForm\\`\\(-1\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[$CellContext`x (-1 + $CellContext`x^2)^(-1) Abs[-1 + $CellContext`x], $CellContext`x, DirectedInfinity[-1]], -1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360753121685343`*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", "1"}], "\[InvisibleSpace]", "\<\" \[AGrave] droite\"\>"}], SequenceForm[ "AH", " \[Congruent] ", $CellContext`y == 1, " \[AGrave] droite"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075312201838*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"AH\"\>", "\[InvisibleSpace]", "\<\" \[Congruent] \"\>", "\[InvisibleSpace]", RowBox[{"y", "\[LongEqual]", RowBox[{"-", "1"}]}], "\[InvisibleSpace]", "\<\" \[AGrave] gauche\"\>"}], SequenceForm[ "AH", " \[Congruent] ", $CellContext`y == -1, " \[AGrave] gauche"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075312235013*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "10", "\[InvisibleSpace]", "\<\". Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\*TagBox[\\\"\ \[DoubleStruckCapitalR]\\\", Function[List[], Reals]]\\) \\\\ \ {\\!\\(TraditionalForm\\`\\(-\\(\\(1\\/2\\)\\)\\)\\)}\"\>", StringForm["`1` \\ {`2`}", Reals, Rational[-1, 2]], Editable->False], TraditionalForm]}], SequenceForm[10, ". Dom f = ", analyse`Ens[ Or[$CellContext`x < Rational[-1, 2], $CellContext`x > Rational[-1, 2]], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360753122690163`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(\[Piecewise] \ \\*GridBox[{{\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(-\\\\\\\\\\\\\\\\(\\\\\ \\\\\\\\\\\\(1\\\\\\\\\\\\\\\\/2\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\ \\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\"<\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(\\\\\\\\\\\\\\\\[LeftBracketingBar] \ \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x\\\\\\\\\\\\\\\\^2 - x - \ 2\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\[RightBracketingBar]\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\ \\\\\\\\(\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(2\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \ x\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) + 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\ \\\\\\\\\\\"\\\\\\\\)\\\\\\\\) = \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\ \\\\\\(-\[Infinity]\\\\\\\\)\\\\\\\\)\\\\\\\"\\\", \\\"\\\\\\\" \ \\\\\\\"\\\"}, \ {\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(-\\\\\\\\\\\\\\\\(\\\\\ \\\\\\\\\\\\(1\\\\\\\\\\\\\\\\/2\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\ \\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\">\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(\\\\\\\\\\\\\\\\[LeftBracketingBar] \ \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x\\\\\\\\\\\\\\\\^2 - x - \ 2\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\[RightBracketingBar]\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\ \\\\\\\\(\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(2\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \ x\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) + 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\ \\\\\\\\\\\"\\\\\\\\)\\\\\\\\) = \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\ \\\\\\\\\\\\\"+\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\ \\`\\\\\\\\\\\\\\\\[Infinity]\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\ \"\\\", \\\"\\\\\\\" \\\\\\\"\\\"}}, ColumnAlignments -> {Left}, \ ColumnSpacings -> 1.2, ColumnWidths -> Automatic]\\)\\)\"\>", StringForm["`1`", Piecewise[{{ StringForm["`1` = `2`", analyse`Limite[(1 + 2 $CellContext`x)^(-1) Abs[-2 - $CellContext`x + $CellContext`x^2], $CellContext`x, Rational[-1, 2], -1], DirectedInfinity[-1]], " "}, { StringForm["`1` = `2`", analyse`Limite[(1 + 2 $CellContext`x)^(-1) Abs[-2 - $CellContext`x + $CellContext`x^2], $CellContext`x, Rational[-1, 2], 1], StringForm["+`1`", DirectedInfinity[1]]], " "}}, 0]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360753123016033`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"AV \[Congruent] \\!\\(TraditionalForm\\`x\\) = \ \\!\\(TraditionalForm\\`\\(-\\(\\(1\\/2\\)\\)\\)\\)\"\>", StringForm["AV \[Congruent] `1` = `2`", $CellContext`x, Rational[-1, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360753123352757`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\[LeftBracketingBar] \\\\(\\\ \\(x\\\\^2 - x - 2\\\\)\\\\) \ \\\\[RightBracketingBar]\\\\)\\\\/\\\\(\\\\(\\\\(2\\\\\\\\ x\\\\)\\\\) + \ 1\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(1 + 2 $CellContext`x)^(-1) Abs[-2 - $CellContext`x + $CellContext`x^2], $CellContext`x, DirectedInfinity[1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.436075312369051*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\[LeftBracketingBar] \\\\(\\\\(x\\\\^2 \ - x - 2\\\\)\\\\) \\\\[RightBracketingBar]\\\\)\\\\/\\\\(\\\\(\\\\(2\\\\\\\\ \ x\\\\)\\\\) + 1\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`\\(-\[Infinity]\ \\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(1 + 2 $CellContext`x)^(-1) Abs[-2 - $CellContext`x + $CellContext`x^2], $CellContext`x, DirectedInfinity[-1]], DirectedInfinity[-1]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4360753124023333`*^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->{3.43607531243616*^9}] }, Open ]] }, Open ]] }, Closed]] }, Open ]] }, WindowSize->{520, 740}, WindowMargins->{{235, Automatic}, {Automatic, 22}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, CellLabelAutoDelete->True, FrontEndVersion->"6.0 for Mac OS X x86 (32-bit) (May 21, 2008)", StyleDefinitions->"stylemath.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[590, 23, 153, 4, 39, "Subsection"], Cell[CellGroupData[{ Cell[768, 31, 5752, 189, 20, "Input", CellOpen->False], Cell[CellGroupData[{ Cell[6545, 224, 433, 13, 35, "Print"], Cell[6981, 239, 455, 14, 53, "Print"], Cell[7439, 255, 421, 13, 35, "Print"], Cell[7863, 270, 394, 11, 55, "Print"], Cell[8260, 283, 428, 13, 52, "Print"], Cell[8691, 298, 461, 14, 48, "Print"], Cell[9155, 314, 385, 11, 35, "Print"], Cell[9543, 327, 417, 12, 35, "Print"], Cell[9963, 341, 536, 15, 45, "Print"], Cell[10502, 358, 558, 16, 47, "Print"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[11109, 380, 34, 0, 28, "Subsubsection"], Cell[CellGroupData[{ Cell[11168, 384, 819, 25, 20, "Input", CellOpen->False], Cell[CellGroupData[{ Cell[12012, 413, 844, 19, 24, "Print"], Cell[12859, 434, 556, 10, 42, "Print"], Cell[13418, 446, 556, 10, 42, "Print"], Cell[13977, 458, 777, 16, 42, "Print"], Cell[14757, 476, 729, 16, 42, "Print"], Cell[15489, 494, 507, 13, 42, "Print"], Cell[15999, 509, 504, 13, 42, "Print"], Cell[16506, 524, 1321, 31, 24, "Print"], Cell[17830, 557, 575, 11, 53, "Print"], Cell[18408, 570, 555, 11, 53, "Print"], Cell[18966, 583, 2561, 44, 105, "Print"], Cell[21530, 629, 286, 6, 24, "Print"], Cell[21819, 637, 671, 13, 53, "Print"], Cell[22493, 652, 612, 12, 53, "Print"], Cell[23108, 666, 439, 11, 24, "Print"], Cell[23550, 679, 418, 10, 24, "Print"], Cell[23971, 691, 506, 14, 24, "Print"], Cell[24480, 707, 554, 10, 41, "Print"], Cell[25037, 719, 660, 12, 41, "Print"], Cell[25700, 733, 605, 12, 41, "Print"], Cell[26308, 747, 418, 10, 24, "Print"], Cell[26729, 759, 548, 15, 24, "Print"], Cell[27280, 776, 677, 14, 55, "Print"], Cell[27960, 792, 312, 6, 24, "Print"], Cell[28275, 800, 656, 14, 55, "Print"], Cell[28934, 816, 304, 6, 24, "Print"], Cell[29241, 824, 612, 11, 55, "Print"], Cell[29856, 837, 562, 10, 55, "Print"], Cell[30421, 849, 842, 19, 24, "Print"], Cell[31266, 870, 557, 11, 52, "Print"], Cell[31826, 883, 699, 14, 59, "Print"], Cell[32528, 899, 306, 6, 24, "Print"], Cell[32837, 907, 666, 12, 52, "Print"], Cell[33506, 921, 616, 12, 52, "Print"], Cell[34125, 935, 337, 8, 24, "Print"], Cell[34465, 945, 958, 23, 24, "Print"], Cell[35426, 970, 611, 12, 48, "Print"], Cell[36040, 984, 591, 12, 48, "Print"], Cell[36634, 998, 676, 12, 48, "Print"], Cell[37313, 1012, 622, 12, 48, "Print"], Cell[37938, 1026, 420, 10, 24, "Print"], Cell[38361, 1038, 514, 14, 24, "Print"], Cell[38878, 1054, 561, 11, 41, "Print"], Cell[39442, 1067, 746, 15, 41, "Print"], Cell[40191, 1084, 584, 12, 41, "Print"], Cell[40778, 1098, 401, 12, 24, "Print"], Cell[41182, 1112, 129, 2, 24, "Print"], Cell[41314, 1116, 649, 12, 42, "Print"], Cell[41966, 1130, 707, 16, 42, "Print"], Cell[42676, 1148, 420, 10, 24, "Print"], Cell[43099, 1160, 721, 18, 24, "Print"], Cell[43823, 1180, 3167, 49, 87, "Print"], Cell[46993, 1231, 296, 6, 24, "Print"], Cell[47292, 1239, 2892, 47, 87, "Print"], Cell[50187, 1288, 763, 14, 45, "Print"], Cell[50953, 1304, 723, 14, 45, "Print"], Cell[51679, 1320, 418, 10, 24, "Print"], Cell[52100, 1332, 439, 11, 24, "Print"], Cell[52542, 1345, 699, 18, 42, "Print"], Cell[53244, 1365, 3409, 55, 123, "Print"], Cell[56656, 1422, 330, 7, 42, "Print"], Cell[56989, 1431, 880, 18, 47, "Print"], Cell[57872, 1451, 763, 15, 47, "Print"], Cell[58638, 1468, 468, 13, 42, "Print"] }, Open ]] }, Open ]] }, Closed]] }, Open ]] } ] *) (* End of internal cache information *)