Functions Question 165
Question: $ \underset{x\to 0}{\mathop{\lim }},{{{ \tan ( \frac{\pi }{4}+x ) }}^{1/x}}= $
[IIT 1993; RPET 2001]
Options:
A) 1
B) ?1
C) $ e^{2} $
D) $ e $
Show Answer
Answer:
Correct Answer: C
Solution:
Given limit $ =\underset{x\to 0}{\mathop{\lim }},{{( \frac{1+\tan x}{1-\tan x} )}^{1/x}} $ $ =\underset{x\to 0}{\mathop{\lim }},\frac{{{{{{(1+\tan x)}^{1/\tan x}}}}^{(\tan x)/x}}}{{{{{{(1-\tan x)}^{1/\tan x}}}}^{(\tan x)/x}}}=\frac{e}{{e^{-1}}}=e^{2} $ .
BETA
