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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