A) \[f(x)\]is continuous at \[x=2\]
B) \[f(x)\]is discontinuous at \[A=0,\,B=1\]
C) \[f(x)\]is continuous at\[x=3\]
D) None of these
Correct Answer: A
Solution :
\[\underset{x\to 2-}{\mathop{\lim }}\,f(x)=3,\,\underset{x\to 2+}{\mathop{\lim }}\,\,f(x)=3\] and \[\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,{f}'(x)=\underset{h\to 0}{\mathop{\lim }}\,{f}'(0-h)=0\].
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