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