Functions Question 122
Question: $ \underset{x\to 0}{\mathop{\lim }},
[ \frac{x}{{{\tan }^{-1}}2x} ]= $ [IIT 1992; RPET 2001]
Options:
A) 0
B) $ \frac{1}{2} $
C) 1
D) $ \infty $
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ {{\tan }^{-1}}2x=\theta ,\Rightarrow x=\frac{1}{2}\tan \theta $ and as $ x\to 0,\theta \to 0 $
$ \Rightarrow \underset{x\to 0}{\mathop{\lim }}\frac{x}{{{\tan }^{-1}}2x}=\underset{\theta \to 0}{\mathop{\lim }}\frac{\frac{1}{2}\tan \theta }{\theta }=\frac{1}{2} $ .
BETA
