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Déterminer la limite en un réel a d'une fonction homographique    ressource 2131

Soit f la fonction définie pour tout x ] - ; - 7 2 [ SequenceForm ] DirectedInfinity -1 ; -72 [ ] - 7 2 ; + [ SequenceForm ] -72 ; + DirectedInfinity 1 [ TagBox[RowBox[List[InterpretationBox[RowBox[List["\"]\"", "\[InvisibleSpace]", RowBox[List["-", "\[Infinity]"]], "\[InvisibleSpace]", "\";\"", "\[InvisibleSpace]", RowBox[List["-", FractionBox["7", "2"]]], "\[InvisibleSpace]", "\"[\""]], SequenceForm["]", DirectedInfinity[-1], ";", Rational[-7, 2], "["], Rule[Editable, False]], "\[Union]", InterpretationBox[RowBox[List["\"]\"", "\[InvisibleSpace]", RowBox[List["-", FractionBox["7", "2"]]], "\[InvisibleSpace]", "\";\"", "\[InvisibleSpace]", "\"+\"", "\[InvisibleSpace]", "\[Infinity]", "\[InvisibleSpace]", "\"[\""]], SequenceForm["]", Rational[-7, 2], ";", "+", DirectedInfinity[1], "["], Rule[Editable, False]]]], HoldForm] SequenceForm x HoldForm SequenceForm ] DirectedInfinity -1 ; -72 [ SequenceForm ] -72 ; + DirectedInfinity 1 [ par f ( x ) = 2 x - 1 2 x + 7 .

Déterminez lim x "\[Rule]" - 7 2 x < - 7 2 f ( x ) SequenceForm Underscript lim Underscript Rule x -72 x -72 f x et lim x "\[Rule]" - 7 2 x > - 7 2 f ( x ) SequenceForm Underscript lim Underscript Rule x -72 x -72 f x .

lim x "\[Rule]" - 7 2 x < - 7 2 f ( x ) SequenceForm Underscript lim Underscript Rule x -72 x -72 f x =
lim x "\[Rule]" - 7 2 x > - 7 2 f ( x ) SequenceForm Underscript lim Underscript Rule x -72 x -72 f x =