MCQ
$\mathop {\lim }\limits_{x \to \infty } \sqrt {\frac{{x + \sin x}}{{x - \cos x}}} = $
- A$0$
- ✓$1$
- C$-1$
- Dએકપણ નહી.
$= \mathop {\lim }\limits_{x \to \infty } \,\sqrt {\left( {\frac{{1 + \frac{{\sin x}}{x}}}{{1 - \frac{{\cos x}}{x}}}} \right)} = \mathop {\lim }\limits_{x \to \infty } \sqrt 1 = 1$
$[\,\because \,\,\mathop {\lim }\limits_{x \to \infty } \,\frac{{\sin x}}{x}$ and $\mathop {\lim }\limits_{x \to \infty } \,\frac{{\cos x}}{x}$ both are equal to $0$ ]
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