Functions Question 225
Question: If $ f(x)= \begin{cases} & \sin x,x\ne n\pi ,n\in Z \\ & 0,otherwise \\ \end{cases} . $ and $ g(x)= \begin{cases} & x^{2}+1,x\ne 0,,2 \\ & 4,x=0 \\ & ,5,x=2 \\ \end{cases} . $ then $ \underset{x\to 0}{\mathop{\lim }},g{f(x)}= $
[Karnataka CET 2000]
Options:
A) 1
B) 0
C) $ \frac{1}{2} $
D) $ \frac{1}{4} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{x\to 0}{\mathop{lim}}g(f(x))=\underset{x\to 0}{\mathop{lim}}{{[f(x)]}^{2}}+1=\underset{x\to 0}{\mathop{lim}}({{\sin }^{2}}x+1)=1 $ .
BETA
