A) \[f\text{(}1\text{)}\]
B) \[f\text{(0)}\]
C) \[f\left( -\infty \right)\]
D) Does not exist
Correct Answer: D
Solution :
[d] \[\{{{e}^{x}}\}=\left[ \begin{matrix} {{e}^{x}}-1, & x>{{0}^{+}} \\ {{e}^{x}}, & x<{{0}^{-}} \\ \end{matrix} \right.\] \[\underset{x\to {{0}^{-}}}{\mathop{lim}}\,{{\left( {{e}^{x}} \right)}^{\frac{1}{{{e}^{x}}}}}=1\] \[\underset{x\to {{0}^{+}}}{\mathop{lim}}\,{{\left( {{e}^{x}} \right)}^{\frac{1}{{{e}^{x}}-1}}}=e\] \[\Rightarrow \] limit does not exist at x = 0
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