Functions Question 145
Question: If $ f(x)= \begin{cases} & \sin x,\ x\ne n\pi ,\ \ n\in Z \\ & 2,,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)} $ is
[Kurukshetra CEE 1996]
Options:
A) 5
B) 6
C) 7
D) 1
Show Answer
Answer:
Correct Answer: D
Solution:
As we are given $ f(x)=\sin x $ , if $ x\ne n\pi $ i.e., $ x\ne 0,,\pi ,2\pi ,…. $ = 2 otherwise
$ \therefore ,\underset{x\to {0^{+}}}{\mathop{\lim }},g,{f(x)}=,\underset{x\to {0^{+}}}{\mathop{\lim }},g,{\sin x}=,\underset{x\to {0^{+}}}{\mathop{\lim }},({{\sin }^{2}}x+1) $ = 1 Similarly, $ ,\underset{x\to {0^{-}}}{\mathop{\lim }},g,{ f(x) }=1. $
BETA
