If f(x)=x−sin⁡xx+cos2⁡x then limx→∞ f(x) is

A
0
B
$\infty$
C
1
D
none of these

Solution:

We have,

$\begin{array}{l} lim_{x \to \infty} f (x) = lim_{x \to \infty} \sqrt{\frac{x - \sin x}{x + \cos^{2} x}} = lim_{x \to \infty} \sqrt{\frac{1 - \frac{\sin x}{x}}{1 + \frac{\cos^{2} x}{x}}} \\ \Rightarrow lim_{x \to \infty} f (x) = \sqrt{\frac{1 - 0}{1 + 0}} = 1 [∵ \frac{\sin x}{x} \to 0, \frac{\cos^{2} x}{x} \to 0 as x \to \infty] \end{array}$

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

Solution:

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