mathop {lim }limits_{x to infty } sqrt {frac{ | vedclass

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(B) We evaluate the limit: $\mathop {\lim }\limits_{x 	o \infty } \sqrt {\frac{{x + \sin x}}{{x - \cos x}}}$Divide the numerator and denominator insi

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(B) We evaluate the limit: $\mathop {\lim }\limits_{x 	o \infty } \sqrt {\frac{{x + \sin x}}{{x - \cos x}}}$Divide the numerator and denominator inside the square root by $x$:$= \mathop {\lim }\limits_{x 	o \infty } \sqrt {\frac{{1 + \frac{{\sin x}}{x}}}{{1 - \frac{{\cos x}}{x}}}}$Since $\mathop {\lim }\limits_{x 	o \infty } \frac{{\sin x}}{x} = 0$ and $\mathop {\lim }\limits_{x 	o \infty } \frac{{\cos x}}{x} = 0$,we have:$= \sqrt {\frac{{1 + 0}}{{1 - 0}}} = \sqrt {1} = 1$

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

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