Functions Question 279
Question: The $ \underset{x\to 0}{\mathop{\lim }},{{(\cos x)}^{\cot x}} $ is
[RPET 1999]
Options:
A) -1
B) 0
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ y=\underset{x\to 0}{\mathop{\lim }},{{(\cos x)}^{\cot x}} $
Taking log on both sides,
Þ $ \log y=\underset{x\to 0}{\mathop{\lim }},\cot x\log \cos x $
Þ $ \log y=\underset{x\to 0}{\mathop{\lim }},\frac{\log \cos x}{\tan x} $ , $ ( \frac{0}{0}form ) $
Applying L-Hospital?s rule,
Þ $ \log y=\underset{x\to 0}{\mathop{\lim }},\frac{-\tan x}{{{\sec }^{2}}x} $ = 0
Þ $ y=e^{0} $
Þ $ y=1 $ .
BETA
