A) 0
B) 1
C) 1/v
D) \[{{e}^{-y}}\]
Correct Answer: D
Solution :
\[\underset{n\to \infty }{\mathop{\lim }}\,\,{{\left( \frac{n}{n+y} \right)}^{n}}=\underset{n\to \infty }{\mathop{\lim }}\,\,{{\left( \frac{1}{1+\frac{y}{n}} \right)}^{n}}\] \[=\underset{n\to \infty }{\mathop{\lim }}\,\,{{\left( 1+\frac{y}{n} \right)}^{-n}}\]\[=\underset{n\to \infty }{\mathop{\lim }}\,\,{{\left[ {{\left( 1+\frac{y}{n} \right)}^{n}} \right]}^{-1}}={{e}^{-y}}\].
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