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[\!\(`3`\/`4`\)]", Underscript[ "lim", $CellContext`x -> 4], (-16 + $CellContext`x^2)^(-1) (-4 - 3 $CellContext`x + $CellContext`x^2), 0, 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{ 3.434080786551343*^9, {3.434080901468561*^9, 3.434080935679633*^9}, { 3.434081397713005*^9, 3.434081413383654*^9}}], Cell[BoxData[ FormBox[ InterpretationBox["\<\" = \\!\\(TraditionalForm\\`\\\"lim\\\"\\+\\(x \ \[Rule] 4\\)\\) \\!\\(\\!\\(TraditionalForm\\`\\(\\(\\((x - 4)\\)\\)\\\\ \ \\(\\((x + 1)\\)\\)\\)\\)\\/\\!\\(TraditionalForm\\`\\(\\(\\((x - \ 4)\\)\\)\\\\ \\(\\((x + 4)\\)\\)\\)\\)\\) \"\>", StringForm[" = `1` \!\(`2`\/`3`\) ", Underscript[ "lim", $CellContext`x -> 4], (-4 + $CellContext`x) ( 1 + $CellContext`x), (-4 + $CellContext`x) (4 + $CellContext`x)], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{ 3.434080786551343*^9, {3.434080901468561*^9, 3.434080935679633*^9}, { 3.434081397713005*^9, 3.4340814134397297`*^9}}], Cell[BoxData[ FormBox[ InterpretationBox["\<\" = \\!\\(TraditionalForm\\`\\\"lim\\\"\\+\\(x \ \[Rule] 4\\)\\) \\!\\(TraditionalForm\\`\\(x + 1\\)\\/\\(x + 4\\)\\) \"\>", StringForm[" = `1` `2` ", Underscript["lim", $CellContext`x -> 4], (1 + $CellContext`x)/( 4 + $CellContext`x)], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{ 3.434080786551343*^9, {3.434080901468561*^9, 3.434080935679633*^9}, { 3.434081397713005*^9, 3.434081413476115*^9}}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(TraditionalForm\\`\\\"\\\\\ !\\\\(TraditionalForm\\\\`\\\\\\\"lim\\\\\\\"\\\\+\\\\(x \\\\[Rule] \ 4\\\\)\\\\) \\\\!\\\\(TraditionalForm\\\\`\\\\(x\\\\^2 - \\\\(\\\\(3\\\\\\\\ \ x\\\\)\\\\) - 4\\\\)\\\\/\\\\(x\\\\^2 - 16\\\\)\\\\)\\\"\\)\\) = \ \\!\\(TraditionalForm\\`5\\/8\\)\"\>", StringForm["`1` = `2`", analyse`Limite[(-16 + $CellContext`x^2)^(-1) (-4 - 3 $CellContext`x + $CellContext`x^2), $CellContext`x, 4], Rational[5, 8]], Editable->False], TraditionalForm]], "Print", 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StringForm["`1` = `2`", analyse`Limite[(2 + 3 $CellContext`x - 2 $CellContext`x^2)/(1 + 3 $CellContext`x + 2 $CellContext`x^2), $CellContext`x, Rational[-1, 2]], 5], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{ 3.434080786551343*^9, {3.434080901468561*^9, 3.434080935679633*^9}, { 3.434081397713005*^9, 3.4340814136760387`*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"4", "\[InvisibleSpace]", "\<\") \"\>"}], SequenceForm[4, ") "], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{ 3.434080786551343*^9, {3.434080901468561*^9, 3.434080935679633*^9}, { 3.434081397713005*^9, 3.434081413707522*^9}}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\\"lim\\\"\\+\\(x \[Rule] 2\ \\)\\) \\!\\(TraditionalForm\\`\\(5 - \\(\\(3\\\\ \ x\\)\\)\\)\\/\\(\\(\\(-x\\^2\\)\\) - x + 6\\)\\) = \ [\\!\\(\\!\\(TraditionalForm\\`\\(-1\\)\\)\\/\\!\\(TraditionalForm\\`0\\)\\)]\ \"\>", StringForm["`1` `2` = [\!\(`3`\/`4`\)]", Underscript["lim", $CellContext`x -> 2], (5 - 3 $CellContext`x)/( 6 - $CellContext`x - $CellContext`x^2), -1, 0], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{ 3.434080786551343*^9, {3.434080901468561*^9, 3.434080935679633*^9}, { 3.434081397713005*^9, 3.4340814137362947`*^9}}], Cell[BoxData[ FormBox[ TagBox[GridBox[{ {"x", " ", RowBox[{"-", "3"}], " ", FractionBox["5", "3"], " ", "2", " "}, { FractionBox[ RowBox[{"5", "-", RowBox[{"3", " ", "x"}]}], RowBox[{ RowBox[{"-", SuperscriptBox["x", "2"]}], "-", "x", "+", "6"}]], "-", "|", "+", "0", "-", "|", "+"} }, GridBoxDividers->{ "Columns" -> {{True}}, "ColumnsIndexed" -> {}, "Rows" -> {{True}}, "RowsIndexed" -> {}}], DisplayForm], TraditionalForm]], "Print", CellChangeTimes->{ 3.434080786551343*^9, {3.434080901468561*^9, 3.434080935679633*^9}, { 3.434081397713005*^9, 3.434081413769825*^9}}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(\[Piecewise] \ \\*GridBox[{{\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 2\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"<\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(5 - \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(3\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \ x\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\ \\\\\\\\(\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(-x\\\\\\\\\\\\\\\\^2\\\\\\\\\\\\\\\ \\)\\\\\\\\\\\\\\\\) - x + \ 6\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\\) = \ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(-\[Infinity]\\\\\\\\)\\\\\\\ \\)\\\\\\\"\\\", \\\"\\\\\\\" \\\\\\\"\\\"}, \ {\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 2\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\">\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(5 - \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(3\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \ x\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\ \\\\\\\\(\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(-x\\\\\\\\\\\\\\\\^2\\\\\\\\\\\\\\\ \\)\\\\\\\\\\\\\\\\) - x + \ 6\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\\) = \ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"+\\\\\\\\\\\\\\\\!\\\ \\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\[Infinity]\\\\\ \\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\"\\\", \\\"\\\\\\\" \ \\\\\\\"\\\"}}, ColumnAlignments -> {Left}, ColumnSpacings -> 1.2, \ ColumnWidths -> Automatic]\\)\\)\"\>", StringForm["`1`", Piecewise[{{ StringForm["`1` = `2`", analyse`Limite[(5 - 3 $CellContext`x)/( 6 - $CellContext`x - $CellContext`x^2), $CellContext`x, 2, -1], DirectedInfinity[-1]], " "}, { StringForm["`1` = `2`", analyse`Limite[(5 - 3 $CellContext`x)/( 6 - $CellContext`x - $CellContext`x^2), $CellContext`x, 2, 1], StringForm["+`1`", DirectedInfinity[1]]], " "}}, 0]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{ 3.434080786551343*^9, {3.434080901468561*^9, 3.434080935679633*^9}, { 3.434081397713005*^9, 3.434081413807773*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"5", "\[InvisibleSpace]", "\<\") \"\>"}], SequenceForm[5, ") "], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{ 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2)\\)\\)\\)\\)\\/\\!\\(TraditionalForm\\`\\(\\(\\((x \ + 2)\\)\\)\\\\ \\(\\((\\(\\(3\\\\ x\\)\\) - 4)\\)\\)\\)\\)\\) \"\>", StringForm[" = `1` \!\(`2`\/`3`\) ", Underscript[ "lim", $CellContext`x -> -2], (-4 + $CellContext`x) ( 2 + $CellContext`x), (2 + $CellContext`x) (-4 + 3 $CellContext`x)], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{ 3.434080786551343*^9, {3.434080901468561*^9, 3.434080935679633*^9}, { 3.434081397713005*^9, 3.434081413909131*^9}}], Cell[BoxData[ FormBox[ InterpretationBox["\<\" = \\!\\(TraditionalForm\\`\\\"lim\\\"\\+\\(x \ \[Rule] \\(\\(-2\\)\\)\\)\\) \\!\\(TraditionalForm\\`\\(x - 4\\)\\/\\(\\(\\(3\ \\\\ x\\)\\) - 4\\)\\) \"\>", StringForm[" = `1` `2` ", Underscript["lim", $CellContext`x -> -2], (-4 + $CellContext`x)/(-4 + 3 $CellContext`x)], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{ 3.434080786551343*^9, {3.434080901468561*^9, 3.434080935679633*^9}, { 3.434081397713005*^9, 3.4340814139372272`*^9}}], Cell[BoxData[ 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GridBoxDividers->{ "Columns" -> {{True}}, "ColumnsIndexed" -> {}, "Rows" -> {{True}}, "RowsIndexed" -> {}}], DisplayForm], TraditionalForm]], "Print", CellChangeTimes->{ 3.434080786551343*^9, {3.434080901468561*^9, 3.434080935679633*^9}, { 3.434081397713005*^9, 3.43408141407158*^9}}], Cell[BoxData[ FormBox[ InterpretationBox["\<\"\\!\\(TraditionalForm\\`\\(\[Piecewise] \ \\*GridBox[{{\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 0\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"<\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(x\\\\\\\\\\\\\\\\^2 - \ 3\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\\\\\\\\(x\\\\\\\\\\\\\\\\^2 - \ \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(3\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ x\\\\\\\\\ \\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\ \\\\\\)\\\\\\\\) = \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(-\ \[Infinity]\\\\\\\\)\\\\\\\\)\\\\\\\"\\\", \\\"\\\\\\\" \\\\\\\"\\\"}, \ {\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 0\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\">\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ \\\\(x\\\\\\\\\\\\\\\\^2 - \ 3\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\\\\\\\\(x\\\\\\\\\\\\\\\\^2 - \ \\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(3\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ x\\\\\\\\\ \\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\ \\\\\\)\\\\\\\\) = \ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"+\\\\\\\\\\\\\\\\!\\\ \\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\[Infinity]\\\\\ \\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\"\\\", \\\"\\\\\\\" \ \\\\\\\"\\\"}}, ColumnAlignments -> {Left}, ColumnSpacings -> 1.2, \ ColumnWidths -> Automatic]\\)\\)\"\>", StringForm["`1`", Piecewise[{{ StringForm["`1` = `2`", analyse`Limite[(-3 + $CellContext`x^2)/((-3) $CellContext`x + \ $CellContext`x^2), $CellContext`x, 0, -1], DirectedInfinity[-1]], " "}, { StringForm["`1` = `2`", analyse`Limite[(-3 + $CellContext`x^2)/((-3) $CellContext`x + \ $CellContext`x^2), $CellContext`x, 0, 1], StringForm["+`1`", DirectedInfinity[1]]], " "}}, 0]], Editable->False], 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6\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\/\\\\\\\\\\\\\\\\((1 - \ x)\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\^2\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\\ )\\\\\\\\) = \ \\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"+\\\\\\\\\\\\\\\\!\\\ \\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\[Infinity]\\\\\ \\\\\\\\\\\\)\\\\\\\\\\\\\\\"\\\\\\\\)\\\\\\\"\\\", \\\"\\\\\\\" \ \\\\\\\"\\\"}, \ {\\\"\\\\\\\"\\\\\\\\!\\\\\\\\(TraditionalForm\\\\\\\\`\\\\\\\\(\ TraditionalForm\\\\\\\\`\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(\ TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\"lim\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\(\\\\\\\\\\\\\\\\(x \\\ \\\\\\\\\\\\\\[Rule] \ 1\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\+\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\">\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\"\\\\\\\\\\\\\\\\)\\\\\\\\\\\\\\\\) \ \\\\\\\\\\\\\\\\!\\\\\\\\\\\\\\\\(TraditionalForm\\\\\\\\\\\\\\\\`\\\\\\\\\\\\\ 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