Functions Question 216
Question: $ \underset{x\to 0}{\mathop{\lim }},\frac{{e^{\frac{1}{x}}}}{{e^{( \frac{1}{x}+1 )}}}= $
[DCE 1999]
Options:
A) 0
B) 1
C) Does not exist
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
$ \underset{x\to 0}{\mathop{lim}},\frac{{e^{1/x}}}{{e^{( \frac{1}{x}+1 )}}}=\underset{x\to 0}{\mathop{lim}},\frac{{e^{1/x}}}{{e^{\frac{1}{x}}}.e} $ $ =\underset{x\to 0}{\mathop{lim}},\frac{1}{e}={e^{-1}} $ .
BETA
