Functions Question 171
Question: If $ f(x)=\sqrt{\frac{x-\sin x}{x+{{\cos }^{2}}x}} $ , then $ \underset{x\to \infty }{\mathop{\lim }},f(x) $ is
[DCE 2000]
Options:
A) 0
B) $ \infty $
C) 1
D) None of these
Show Answer
Answer:
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 $ , $ ( \because ,\frac{\sin x}{x}\to 0,\frac{{{\cos }^{2}}x}{x},\to 0\text{as }x\to \infty ) $ .
BETA
