MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {1 + x} - \sqrt {1 - x} }}{{{{\sin }^{ - 1}}x}} = $
  • A
    $2$
  • $1$
  • C
    $-1$
  • D
    None of these

Answer

Correct option: B.
$1$
b
(b) Let ${\sin ^{ - 1}}x = y\,\, \Rightarrow x = \sin y$

So $\mathop {\lim }\limits_{y \to 0} \frac{{\sqrt {1 + \sin y} - \sqrt {1 - \sin y} }}{y}$

$(\because \,\,\,x \to 0 \Rightarrow y \to 0)$

$( $ Now multiply it by $\frac{\sqrt{1+\sin y}+\sqrt{1-\sin y}}{\sqrt{1+\sin y}+\sqrt{1-\sin y}}$ and solve $) $

$= 1$

Aliter : Apply  $ L-$ Hospital’s rule.

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