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\\(\\(4\\\\ x\\)\\) + \ 1\\)\\/\\(\\(\\(2\\\\ x\\)\\) - 3\\)\\) = \\!\\(TraditionalForm\\`\\\"lim\\\"\ \\+\\(x \[Rule] \\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\\\"\\)\ \\) \\!\\(\\!\\(TraditionalForm\\`\\(3\\\\ \ x\\^2\\)\\)\\/\\!\\(TraditionalForm\\`\\(2\\\\ x\\)\\)\\) = \ \\!\\(TraditionalForm\\`\\\"lim\\\"\\+\\(x \[Rule] \ \\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\\\"\\)\\) \ \\!\\(TraditionalForm\\`\\(3\\\\ x\\)\\/2\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` `2` = `1` \!\(`3`\/`4`\) = `1` `5` = `6`", Underscript["lim", $CellContext`x -> StringForm["+`1`", DirectedInfinity[1]]], (-3 + 2 $CellContext`x)^(-1) (1 - 4 $CellContext`x + 3 $CellContext`x^2), 3 $CellContext`x^2, 2 $CellContext`x, Rational[3, 2] $CellContext`x, StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.466135837931407*^9, 3.466135842592593*^9}}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\\"lim\\\"\\+\\(x \[Rule] \ \\(\\(-\[Infinity]\\)\\)\\)\\) \\!\\(TraditionalForm\\`\\(\\(\\(3\\\\ \ x\\^2\\)\\) - \\(\\(4\\\\ x\\)\\) + 1\\)\\/\\(\\(\\(2\\\\ x\\)\\) - 3\\)\\) = \ \\!\\(TraditionalForm\\`\\\"lim\\\"\\+\\(x \[Rule] \ \\(\\(-\[Infinity]\\)\\)\\)\\) \\!\\(\\!\\(TraditionalForm\\`\\(3\\\\ \ x\\^2\\)\\)\\/\\!\\(TraditionalForm\\`\\(2\\\\ x\\)\\)\\) = \ \\!\\(TraditionalForm\\`\\\"lim\\\"\\+\\(x \[Rule] \ \\(\\(-\[Infinity]\\)\\)\\)\\) \\!\\(TraditionalForm\\`\\(3\\\\ x\\)\\/2\\) = \ \\!\\(TraditionalForm\\`\\(-\[Infinity]\\)\\)\"\>", StringForm["`1` `2` = `1` \!\(`3`\/`4`\) = `1` `5` = `6`", Underscript[ "lim", $CellContext`x -> DirectedInfinity[-1]], (-3 + 2 $CellContext`x)^(-1) (1 - 4 $CellContext`x + 3 $CellContext`x^2), 3 $CellContext`x^2, 2 $CellContext`x, Rational[3, 2] $CellContext`x, DirectedInfinity[-1]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.466135837931407*^9, 3.466135842596496*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Limites", "[", RowBox[{ SqrtBox[ RowBox[{ RowBox[{"x", "^", "2"}], "-", RowBox[{"4", "x"}], "+", "7"}]], ",", "x"}], "]"}]], "Input", CellOpen->False, CellChangeTimes->{{3.466132577309978*^9, 3.466132619477727*^9}}], Cell[CellGroupData[{ Cell[BoxData[ FormBox[ FrameBox[ InterpretationBox["\<\"f(x) = \\!\\(TraditionalForm\\`\\@\\(x\\^2 - 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4 $CellContext`x + $CellContext`x^2)^ Rational[1, 2], ($CellContext`x^2)^Rational[1, 2], $CellContext`x, StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.466132595156287*^9, 3.466132624173523*^9}, 3.466133466774416*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\\"lim\\\"\\+\\(x \[Rule] \ \\(\\(-\[Infinity]\\)\\)\\)\\) \\!\\(TraditionalForm\\`\\@\\(x\\^2 - \ \\(\\(4\\\\ x\\)\\) + 7\\)\\) = \\!\\(TraditionalForm\\`\\\"lim\\\"\\+\\(x \ \[Rule] \\(\\(-\[Infinity]\\)\\)\\)\\) \\!\\(TraditionalForm\\`\\@\\(x\\^2\\)\ \\) = \\!\\(TraditionalForm\\`\\\"lim\\\"\\+\\(x \[Rule] \ \\(\\(-\[Infinity]\\)\\)\\)\\) \\!\\(TraditionalForm\\`\\(-x\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` `2` = `1` `3` = `1` `4` = `5`", Underscript[ "lim", $CellContext`x -> DirectedInfinity[-1]], (7 - 4 $CellContext`x + $CellContext`x^2)^Rational[1, 2], ($CellContext`x^2)^ Rational[1, 2], -$CellContext`x, StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.466132595156287*^9, 3.466132624173523*^9}, 3.466133466778866*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Limites", "[", RowBox[{ RowBox[{ SqrtBox[ RowBox[{ RowBox[{"2", "x"}], "-", "3"}]], "+", "x"}], ",", "x"}], "]"}]], "Input",\ CellOpen->False, CellChangeTimes->{{3.466132577309978*^9, 3.466132644854363*^9}, { 3.4661335377080584`*^9, 3.46613354581252*^9}, {3.466133744504917*^9, 3.466133751241008*^9}}], Cell[CellGroupData[{ Cell[BoxData[ FormBox[ FrameBox[ InterpretationBox["\<\"f(x) = \\!\\(TraditionalForm\\`\\(x + \\@\\(\\(\\(2\ \\\\ x\\)\\) - 3\\)\\)\\)\"\>", StringForm[ "f(x) = `1`", $CellContext`x + (-3 + 2 $CellContext`x)^Rational[1, 2]], Editable->False], StripOnInput->False], TraditionalForm]], "Print", CellChangeTimes->{ 3.466132647309057*^9, 3.4661329410583677`*^9, 3.46613312698067*^9, 3.466133261356593*^9, {3.4661333805805283`*^9, 3.466133405754774*^9}, 3.466133468381315*^9, 3.466133506069376*^9, {3.466133538366641*^9, 3.4661335460594997`*^9}, {3.4661336411849737`*^9, 3.466133663381022*^9}, { 3.466133708688218*^9, 3.4661337543405113`*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"[\\!\\(TraditionalForm\\`3\\/2\\), \ \[LongRightArrow]\"\>", StringForm["[`1`, \[LongRightArrow]", Rational[3, 2]], Editable->False], TraditionalForm]}], SequenceForm["Dom f = ", analyse`Ens[$CellContext`x >= Rational[3, 2], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{ 3.466132647309057*^9, 3.4661329410583677`*^9, 3.46613312698067*^9, 3.466133261356593*^9, {3.4661333805805283`*^9, 3.466133405754774*^9}, 3.466133468381315*^9, 3.466133506069376*^9, {3.466133538366641*^9, 3.4661335460594997`*^9}, {3.4661336411849737`*^9, 3.466133663381022*^9}, { 3.466133708688218*^9, 3.466133754370013*^9}}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] 3\\\\/2\\\ \\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(x + \\\\@\\\\(\\\\(\\\\(2\\\\\\\\ \ x\\\\)\\\\) - 3\\\\)\\\\)\\\\)\\\"\\)\\) = \\!\\(TraditionalForm\\`3\\/2\\)\"\ \>", StringForm["`1` = `2`", analyse`Limite[$CellContext`x + (-3 + 2 $CellContext`x)^ Rational[1, 2], $CellContext`x, Rational[3, 2]], Rational[3, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{ 3.466132647309057*^9, 3.4661329410583677`*^9, 3.46613312698067*^9, 3.466133261356593*^9, {3.4661333805805283`*^9, 3.466133405754774*^9}, 3.466133468381315*^9, 3.466133506069376*^9, {3.466133538366641*^9, 3.4661335460594997`*^9}, {3.4661336411849737`*^9, 3.466133663381022*^9}, { 3.466133708688218*^9, 3.46613375437357*^9}}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \\\\\\\"+\ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\\\\\\\"\ \\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(x + \\\\@\\\\(\\\\(\\\\(2\\\\\\\ \\ x\\\\)\\\\) - 3\\\\)\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\!\\\\(TraditionalForm\\\\\ `\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\\\\"+\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\[Infinity]\\\\\\\\)\ \\\\\\\"\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`x\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\\"+\\\\!\\\\(TraditionalForm\\\\`\\\\[Infinity]\\\\)\ \\\"\\)\"\>", StringForm["`1` = `2` = `3`", analyse`Limite[$CellContext`x + (-3 + 2 $CellContext`x)^ Rational[1, 2], $CellContext`x, DirectedInfinity[1]], analyse`Limite[$CellContext`x, $CellContext`x, DirectedInfinity[1]], StringForm["+`1`", DirectedInfinity[1]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{ 3.466132647309057*^9, 3.4661329410583677`*^9, 3.46613312698067*^9, 3.466133261356593*^9, {3.4661333805805283`*^9, 3.466133405754774*^9}, 3.466133468381315*^9, 3.466133506069376*^9, {3.466133538366641*^9, 3.4661335460594997`*^9}, {3.4661336411849737`*^9, 3.466133663381022*^9}, { 3.466133708688218*^9, 3.4661337543787317`*^9}}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\[Infinity]\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(x + \\\\@\\\\(\\\\(\\\\(2\\\\\\\\ x\\\\)\\\ \\) - 3\\\\)\\\\)\\\\)\\\"\\)\\) \[NotExists]\"\>", StringForm["`1` `2`", analyse`Limite[$CellContext`x + (-3 + 2 $CellContext`x)^ Rational[1, 2], $CellContext`x, DirectedInfinity[-1]], "\[NotExists]"], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{ 3.466132647309057*^9, 3.4661329410583677`*^9, 3.46613312698067*^9, 3.466133261356593*^9, {3.4661333805805283`*^9, 3.466133405754774*^9}, 3.466133468381315*^9, 3.466133506069376*^9, {3.466133538366641*^9, 3.4661335460594997`*^9}, {3.4661336411849737`*^9, 3.466133663381022*^9}, { 3.466133708688218*^9, 3.46613375440554*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Limites", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ SqrtBox[ RowBox[{ RowBox[{"2", "x"}], "+", "3"}]], "-", "2"}], ")"}], "/", RowBox[{"(", RowBox[{"1", "-", RowBox[{"2", "x"}]}], ")"}]}], ",", "x"}], "]"}]], "Input", CellOpen->False, CellChangeTimes->{{3.4661357377584867`*^9, 3.466135773813313*^9}}], Cell[CellGroupData[{ Cell[BoxData[ FormBox[ FrameBox[ InterpretationBox["\<\"f(x) = \\!\\(TraditionalForm\\`\\(\\@\\(\\(\\(2\\\\ \ x\\)\\) + 3\\) - 2\\)\\/\\(1 - \\(\\(2\\\\ x\\)\\)\\)\\)\"\>", StringForm[ "f(x) = `1`", (1 - 2 $CellContext`x)^(-1) (-2 + (3 + 2 $CellContext`x)^ Rational[1, 2])], Editable->False], StripOnInput->False], TraditionalForm]], "Print", CellChangeTimes->{3.466135774540715*^9}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"\<\"Dom f = \"\>", "\[InvisibleSpace]", FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"[\ \\\\!\\\\(TraditionalForm\\\\`\\\\(-\\\\(\\\\(3\\\\/2\\\\)\\\\)\\\\)\\\\), \\\ \\!\\\\(TraditionalForm\\\\`1\\\\/2\\\\)[\\\"\\)\\) \[Union] \ \\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"]\\\\!\\\\(TraditionalForm\\\ \\`1\\\\/2\\\\), \\\\[LongRightArrow]\\\"\\)\\)\"\>", StringForm["`1` \[Union] `2`", analyse`Ens[ Inequality[ Rational[-3, 2], LessEqual, $CellContext`x, Less, Rational[1, 2]], $CellContext`x], analyse`Ens[$CellContext`x > Rational[1, 2], $CellContext`x]], Editable->False], TraditionalForm]}], SequenceForm["Dom f = ", analyse`Ens[ Or[ Inequality[ Rational[-3, 2], LessEqual, $CellContext`x, Less, Rational[1, 2]], $CellContext`x > Rational[1, 2]], $CellContext`x]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.466135774566841*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ \\\\(\\\\(-\\\\(\\\\(3\\\\/2\\\\)\\\\)\\\\)\\\\)\\\\)\\\\) \ \\\\!\\\\(TraditionalForm\\\\`\\\\(\\\\@\\\\(\\\\(\\\\(2\\\\\\\\ x\\\\)\\\\) \ + 3\\\\) - 2\\\\)\\\\/\\\\(1 - \\\\(\\\\(2\\\\\\\\ \ x\\\\)\\\\)\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`\\(-\\(\\(1\\/2\\)\\)\\)\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(1 - 2 $CellContext`x)^(-1) (-2 + (3 + 2 $CellContext`x)^ Rational[1, 2]), $CellContext`x, Rational[-3, 2]], Rational[-1, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.4661357746319427`*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\\"lim\\\"\\+\\(x \[Rule] 1\ \\/2\\)\\) \\!\\(TraditionalForm\\`\\(\\@\\(\\(\\(2\\\\ x\\)\\) + 3\\) - 2\\)\ \\/\\(1 - \\(\\(2\\\\ x\\)\\)\\)\\) = \ [\\!\\(\\!\\(TraditionalForm\\`0\\)\\/\\!\\(TraditionalForm\\`0\\)\\)]\"\>", StringForm["`1` `2` = [\!\(`3`\/`4`\)]", Underscript[ "lim", $CellContext`x -> Rational[1, 2]], (1 - 2 $CellContext`x)^(-1) (-2 + (3 + 2 $CellContext`x)^Rational[1, 2]), 0, 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.466135774657576*^9}], Cell[BoxData[ FormBox[ InterpretationBox["\<\" = \\!\\(TraditionalForm\\`\\\"lim\\\"\\+\\(x \ \[Rule] 1\\/2\\)\\) \\!\\(\\!\\(TraditionalForm\\`\\(\\(\\((\\@\\(\\(\\(2\\\\ \ x\\)\\) + 3\\) - 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