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Déterminer la limite en un réel a de l'inverse d'une fonction affine    ressource 2130

Soit f la fonction définie pour tout x ] - ; 1 6 [ SequenceForm ] DirectedInfinity -1 ; 16 [ ] 1 6 ; + [ SequenceForm ] 16 ; + DirectedInfinity 1 [ TagBox[RowBox[List[InterpretationBox[RowBox[List["\"]\"", "\[InvisibleSpace]", RowBox[List["-", "\[Infinity]"]], "\[InvisibleSpace]", "\";\"", "\[InvisibleSpace]", FractionBox["1", "6"], "\[InvisibleSpace]", "\"[\""]], SequenceForm["]", DirectedInfinity[-1], ";", Rational[1, 6], "["], Rule[Editable, False]], "\[Union]", InterpretationBox[RowBox[List["\"]\"", "\[InvisibleSpace]", FractionBox["1", "6"], "\[InvisibleSpace]", "\";\"", "\[InvisibleSpace]", "\"+\"", "\[InvisibleSpace]", "\[Infinity]", "\[InvisibleSpace]", "\"[\""]], SequenceForm["]", Rational[1, 6], ";", "+", DirectedInfinity[1], "["], Rule[Editable, False]]]], HoldForm] SequenceForm x HoldForm SequenceForm ] DirectedInfinity -1 ; 16 [ SequenceForm ] 16 ; + DirectedInfinity 1 [ par f ( x ) = 10 6 x - 1 .

Déterminez lim x "\[Rule]" 1 6 x < 1 6 f ( x ) SequenceForm Underscript lim Underscript Rule x 16 x 16 f x et lim x "\[Rule]" 1 6 x > 1 6 f ( x ) SequenceForm Underscript lim Underscript Rule x 16 x 16 f x .

lim x "\[Rule]" 1 6 x < 1 6 f ( x ) SequenceForm Underscript lim Underscript Rule x 16 x 16 f x =
lim x "\[Rule]" 1 6 x > 1 6 f ( x ) SequenceForm Underscript lim Underscript Rule x 16 x 16 f x =