Functions Question 59
Question: $ \underset{x\to 0}{\mathop{\lim }},x\log (\sin x)= $
Options:
A) ?1
B) $ {\log_{e}}1 $
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to 0}{\mathop{\lim }},x\log \sin x=\underset{x\to 0}{\mathop{\lim }}\log ,{{(\sin x)}^{x}}=\log ,[\underset{x\to 0}{\mathop{\lim }},{{(\sin x)}^{x}}] $ $ =\log ,[ \underset{x\to 0}{\mathop{\lim }}{{(1+\sin x-1)}^{\frac{x(\sin x-1)}{\sin x-1}}} ] $ $ ={\log_{e}}[{e^{\underset{x\to 0}{\mathop{\lim }}x(\sin x-1)}}]={\log_{e}}1. $
BETA
