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
Correct Answer: C
Solution :
\[f(0)=0,\,\underset{x\to 0+}{\mathop{\lim }}\,f(x)=\underset{x\to 0-}{\mathop{\lim }}\,f(x)=\underset{x\to 0}{\mathop{\lim }}\,\,x\,\left[ \frac{\sin {{x}^{2}}}{{{x}^{2}}} \right]=0\].
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