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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow a} \frac{x^{-1}-a^{-1}}{x-a}=$
  • A
    $\frac{1}{a}$
  • B
    $\frac{-1}{ a }$
  • C
    $\frac{1}{ a ^2}$
  • ✓
    $\frac{-1}{ a ^2}$
✓

Answer

Correct option: D.
$\frac{-1}{ a ^2}$
(D)
$\lim _{x \rightarrow a } \frac{x^{-1}- a ^{-1}}{x- a }=-1( a )^{-1-1} \quad \ldots\left[\because \lim _{x \rightarrow a } \frac{x^{ n }- a ^{ n }}{x- a }= na ^{ n -1}\right]$
$=\frac{-1}{ a ^2}$

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