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MCQ

$\mathop {\lim }\limits_{x \to \infty } \sqrt {\frac{{x + \sin x}}{{x - \cos x}}} = $

A
$0$
✓
$1$
C
$-1$
D
None of these

✓

Answer

Correct option: B.

$1$

b
(b) $\mathop {\lim }\limits_{x \to \infty } \,\,\sqrt {\left( {\frac{{x + \sin x}}{{x - \cos x}}} \right)} $

$= \mathop {\lim }\limits_{x \to \infty } \,\sqrt {\left( {\frac{{1 + \frac{{\sin x}}{x}}}{{1 - \frac{{\cos x}}{x}}}} \right)} = \mathop {\lim }\limits_{x \to \infty } \sqrt 1 = 1$

$[\,\because \,\,\mathop {\lim }\limits_{x \to \infty } \,\frac{{\sin x}}{x}$ and $\mathop {\lim }\limits_{x \to \infty } \,\frac{{\cos x}}{x}$ both are equal to $0$ ]

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