If f(x) = sqrt{frac{x - sin x}{x + cos^{2} x} | vedclass

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(C) We need to evaluate $\lim_{x \rightarrow \infty} \sqrt{\frac{x - \sin x}{x + \cos^{2} x}}$.Divide the numerator and denominator by $x$ inside the

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$1$

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(C) We need to evaluate $\lim_{x \rightarrow \infty} \sqrt{\frac{x - \sin x}{x + \cos^{2} x}}$.Divide the numerator and denominator by $x$ inside the square root:$= \lim_{x \rightarrow \infty} \sqrt{\frac{1 - \frac{\sin x}{x}}{1 + \frac{\cos^{2} x}{x}}}$Since $\lim_{x \rightarrow \infty} \frac{\sin x}{x} = 0$ and $\lim_{x \rightarrow \infty} \frac{\cos^{2} x}{x} = 0$ (because $\sin x$ and $\cos^{2} x$ are bounded functions):$= \sqrt{\frac{1 - 0}{1 + 0}}$$= \sqrt{1} = 1$

If $f(x) = \sqrt{\frac{x - \sin x}{x + \cos^{2} x}}$,then $\lim_{x \rightarrow \infty} f(x)$ is

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