Explanation

(c)
$\lim_{x \rightarrow \infty}f(x) = \lim_{x \rightarrow \infty}\sqrt{\frac{x - \sin x}{x + \cos^{2}x}}$
$= \lim_{x \rightarrow \infty}\sqrt{\frac{x - \frac{\sin x}{x}}{1 + \frac{\cos^{2}x}{x}}}$
$= \sqrt{\frac{1 - 0}{1 + 0}}$
$\left\lbrack \because\ \frac{\sin x}{x} \rightarrow 0,\ \frac{\cos^{2}x}{x} \rightarrow 0\ as\ x \rightarrow \infty\ \right\rbrack$
$= 1$