lim x 0 sin ( cos 2 x ) x 2 equals [2001]

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Solution

Q.
$\lim_{x \to 0} \frac{\sin (π \cos^{2} x)}{x^{2}}$ equals [2001]

1 $- π$

2 $π$

3 $\frac{π}{2}$

4 $1$

Ans.
(2)

$\lim_{x \to 0} \frac{\sin (π \cos^{2} x)}{x^{2}} = \lim_{x \to 0} \frac{\sin (π - π \sin^{2} x)}{x^{2}}$

$= \lim_{x \to 0} \frac{\sin (π \sin^{2} x)}{π \sin^{2} x} \times \frac{π \sin^{2} x}{x^{2}} = π$

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