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Question: \(\lim_{n \rightarrow \infty}\left( \frac{e^{n}}{\pi} \right)^{1/n}\) is...

lim⁡n→∞(enπ)1/n\lim_{n \rightarrow \infty}\left( \frac{e^{n}}{\pi} \right)^{1/n} is

A

1

B

e

C

e2

D

ep

Answer

e

Explanation

Solution

y=lim⁡n→∞(enπ)1ny = \lim_{n \rightarrow \infty}\left( \frac{e^{n}}{\pi} \right)^{\frac{1}{n}}

Žy=lim⁡n→∞1n.log⁡(enπ)y = \lim_{n \rightarrow \infty}\frac{1}{n}.\log\left( \frac{e^{n}}{\pi} \right)

Ž log y = 1 Ž y =e