Functions Question 679
Question: $ \underset{x\to 0}{\mathop{\lim }},\frac{x(e^{x}-1)}{1-\cos x}= $
Options:
A) 0
B) $ \infty $
C) ?2
D) 2
Show Answer
Answer:
Correct Answer: D
Solution:
$ \underset{x\to 0}{\mathop{\lim }}\frac{x,(e^{x}-1)}{1-\cos x}=\underset{x\to 0}{\mathop{\lim }}\frac{2x,(e^{x}-1)}{4.{{\sin }^{2}}\frac{x}{2}} $ $ =2\underset{x\to 0}{\mathop{\lim }}[ \frac{{{(x/2)}^{2}}}{{{\sin }^{2}}\frac{x}{2}} ],( \frac{e^{x}-1}{x} )=2. $
BETA
