Functions Question 159
Question: $ \underset{x\to 0}{\mathop{\lim }},{{( \frac{1+\tan x}{1+\sin x} )}^{\text{cosec }x}} $ is equal to
[Kerala (Engg.) 2005]
Options:
A) $ e $
B) $ \frac{1}{e} $
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Given limit $ =\underset{x\to 0}{\mathop{\lim }},[{{(1+\tan x)}^{\cos ec,x}}\times 1/{{(1+\sin x)}^{\cos ec,x}}] $ $ =\underset{x\to 0}{\mathop{\lim }}{{[{{{1+\tan x)}^{\cot ,x}}}}^{sec,x}}\times {1/{{(1+\sin x)}^{\cos ec,x}}}] $ $ ={e^{\sec 0}}.\frac{1}{e}=e,.,\frac{1}{e}=1. $
BETA
