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

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(C) We are given $f(x) = \sqrt{\frac{x - \sin x}{x + \cos^2 x}}$.To find $\lim_{x 	o \infty} f(x)$,we divide the numerator and denominator inside the

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$1$

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(C) We are given $f(x) = \sqrt{\frac{x - \sin x}{x + \cos^2 x}}$.To find $\lim_{x 	o \infty} f(x)$,we divide the numerator and denominator inside the square root by $x$:$\lim_{x 	o \infty} \sqrt{\frac{x - \sin x}{x + \cos^2 x}} = \lim_{x 	o \infty} \sqrt{\frac{1 - \frac{\sin x}{x}}{1 + \frac{\cos^2 x}{x}}}$As $x 	o \infty$,we know that $\frac{\sin x}{x} 	o 0$ and $\frac{\cos^2 x}{x} 	o 0$ because $-1 \le \sin x \le 1$ and $0 \le \cos^2 x \le 1$.Therefore,the limit becomes $\sqrt{\frac{1 - 0}{1 + 0}} = \sqrt{1} = 1$.

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

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