Differentiation Question 489
Question: The value of $ \underset{x\to 0}{\mathop{\lim }},{\log_{e}}{{(sinx)}^{\tan x}} $ is
Options:
A) 1
B) -1
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ \underset{x\to 0}{\mathop{\lim }},{\log_{e}}{{(sinx)}^{\tan x}}=\underset{x\to 0}{\mathop{\lim }},\tan x.{\log_{e}}\sin x $ $ (0\cdot \infty form) $ $ \underset{x\to 0}{\mathop{\lim }},\frac{{\log_{e}}\sin x}{\cot x}( \frac{\infty }{\infty }form ) $ $ =\underset{x\to 0}{\mathop{\lim }},\frac{\cot x}{-\cos ec^{2}x} $ [Using L?Hospital?s rule] $ =\underset{x\to 0}{\mathop{\lim }},(-cosx.sinx)=0. $
BETA
