_ x 0 1 - x^2 - 1 + x^2 x^2 is equal to - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {1 - {x^2}} - \sqrt {1 + {x^2}} }}{{{x^2}}}$ is equal to

A
$1$
✓
$-1$
C
$-2$
D
$0$

✓

Answer

Correct option: B.

$-1$

b
(b) On rationalising, the given limit

$ = \mathop {\lim }\limits_{x \to 0} \,\frac{{(1 - {x^2} - 1 - {x^2})}}{{{x^2}\,(\sqrt {1 - {x^2}} + \sqrt {1 + {x^2})} }}$

$ = \mathop {\lim }\limits_{x \to 0} \,\frac{{ - 2}}{{\,(\sqrt {1 - {x^2}} + \sqrt {1 + {x^2})} }} = \frac{{ - 2}}{{1 + 1}} = - 1$

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