Functions Question 609
Question: If $ f(x)= \begin{cases} & \frac{1}{x}\sin x^{2},,x\ne 0 \\ & 0,,x=0 \\ \end{cases} . $ , then
Options:
A) $ \underset{x\to 0+}{\mathop{\lim }},f(x)\ne 0 $
B) $ \underset{x\to 0-}{\mathop{\lim }},f(x)\ne 0 $
C) f(x) is continuous at $ x=0 $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(0)=0,,\underset{x\to 0+}{\mathop{\lim }},f(x)=\underset{x\to 0-}{\mathop{\lim }},f(x)=\underset{x\to 0}{\mathop{\lim }}x,[ \frac{\sin x^{2}}{x^{2}} ]=0 $ .
BETA
