Functions Question 170
Question: $ \underset{x\to 0}{\mathop{\lim }},\frac{{e^{\tan x}}-e^{x}}{\tan x-x}= $
[EAMCET 1994; RPET 2001]
Options:
A) 1
B) $ e $
C) $ {e^{-1}} $
D) $ \frac{1}{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{x\to 0}{\mathop{\lim }},\frac{{e^{\tan x}}-e^{x}}{\tan x-x}=\underset{x\to 0}{\mathop{\lim }},\frac{e^{x}[{e^{\tan x-x}}-1]}{\tan x-x} $ $ =\underset{x\to 0}{\mathop{\lim }}e^{x},.\underset{x\to 0}{\mathop{\lim }}\frac{{e^{\tan x-x}}-1}{\tan x-x}=e^{0}\times 1=1 $ .
BETA
