Functions Question 324
Question: For the function $ f(x)= \begin{cases} & \frac{{{\sin }^{2}}ax}{x^{2}},,when,x\ne 0 \\ & 1,when,x=0 \\ \end{cases} . $ which one is a true statement
Options:
A) $ f(x) $ is continuous at $ x=0 $
B) $ f(x) $ is discontinuous at $ x=0 $ , when $ a\ne \pm 1 $
C) $ \underset{x\to 1}{\mathop{\lim }},(1-x+[x-1]+[1-x]) $ is continuous at $ x=a $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to 0}{\mathop{\lim }},f(x)=\frac{{{\sin }^{2}}ax}{{{(ax)}^{2}}}a^{2}=a^{2} $ and $ f(0)=1. $ Hence $ f(x) $ is discontinuous at $ x=0 $ , when $ a\ne 0 $ .
BETA
