A) \[{{e}^{1/m}}\]
B) \[{{e}^{-1/m}}\]
C) \[{{e}^{m}}\]
D) \[{{m}^{e}}\]
Correct Answer: A
Solution :
Let \[y=\underset{x\to \,\infty }{\mathop{\lim }}\,\,{{\left( 1+\frac{1}{mx} \right)}^{x}}=\underset{x\to \,\infty }{\mathop{\lim }}\,\,{{\left( 1+\frac{1}{mx} \right)}^{mx\cdot \frac{1}{m}}}\] \[\Rightarrow \,\,y={{e}^{1/m}},\,\,\,\left( \because \underset{x\to \,\infty }{\mathop{\lim }}\,\,{{\left( 1+\frac{1}{x} \right)}^{x}}=e \right)\].
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