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