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