Functions Question 205
Question: If the function $ f(x)= \begin{cases} & {{(\cos x)}^{1/x}},\ x\ne 0 \\ & ,k,,x=0 \\ \end{cases} . $ is continuous at $ x=0 $ , then the value of k is
[Kurukshetra CEE 1996]
Options:
A) 1
B) ?1
C) 0
D) e
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{x\to 0}{\mathop{\lim }},{{(\cos x)}^{1/x}}=k\Rightarrow \underset{x\to 0}{\mathop{\lim }},\frac{1}{x}\log ,(\cos x)=\log k $
$ \Rightarrow \underset{x\to 0}{\mathop{\lim }},\frac{1}{x}\underset{x\to 0}{\mathop{\lim }},\log ,\cos x=\log k $
$ \Rightarrow ,\underset{x\to 0}{\mathop{\lim }},\frac{1}{x}\times 0={\log_{e}}k\Rightarrow ,k=1 $ .
BETA
