A) 0
B) \[\infty \]
C) 1
D) None of these
Correct Answer: C
Solution :
\[\underset{x\to \infty }{\mathop{\lim }}\,\,\,f(x)=\,\underset{x\to \infty }{\mathop{\lim }}\,\,\sqrt{\frac{x-\sin x}{x+{{\cos }^{2}}x}}=\underset{x\to \infty }{\mathop{\lim }}\,\,\,\sqrt{\frac{1-\frac{\sin x}{x}}{1+\frac{{{\cos }^{2}}x}{x}}}\] \[=\sqrt{\frac{1-0}{1+0}}=1\], \[\left( \because \,\,\,\frac{\sin x}{x}\to 0,\frac{{{\cos }^{2}}x}{x}\,\to 0\,\,\text{as }x\to \infty \right)\].
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