The correct option is C 0Given, lim _ x→π #160; / 2 #160; 1 sin x #160; / x #160; Substituting x = π #160; / 2 , we get lim _ x→π ...

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Algebra of Limits

limx→π/21-sin...

Question

$lim x \to \frac{π}{2} \frac{1 - sin x}{x}$ = ______

\infty

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Solution

The correct option is C 0
Given, $lim x \to \frac{π}{2} \frac{1 - sin x}{x}$
Substituting $x = \frac{π}{2}$ , we get
$lim x \to \frac{π}{2} \frac{1 - sin x}{x} = \frac{1 - sin \frac{π}{2}}{\frac{π}{2}} = \frac{1 - 1}{\frac{π}{2}} = 0$ Since ( $sin \frac{π}{2} = s i n 90 = 1$ )

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