_ x 0 ( x) - 1 x^2 = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 0} \frac{{\cos (\sin x) - 1}}{{{x^2}}} = $

A
$1$
B
$-1$
C
$1/2$
✓
$-1/2$

✓

Answer

Correct option: D.

$-1/2$

d
(d) $\mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{\cos (\sin x) - 1}}{{{x^2}}}$

$= \mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{ - 2{{\sin }^2}\left( {\frac{{\sin x}}{2}} \right)}}{{{x^2}}} = - 2.\frac{1}{4} = \frac{{ - 1}}{2}$.

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