Question

$\lim_{n \to \infty} \left( 1 + \frac{e^y}{n} \right)^{-n}$

          $\lim_{n \to \infty} \left( 1 + \frac{e^y}{n} \right)^{-n}$

limn →∞( 1 + (e^y)/(n))^-n

Added by Laurie N.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Fuzail Shakir

07/23/2019

Step 1

Step 1: We can rewrite the expression as: $$\lim_{n \to \infty} \left( 1 + \frac{e^y}{n} \right)^{-n} = \lim_{n \to \infty} \left( \frac{n + e^y}{n} \right)^{-n}$$ Show more…

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Thanks for your feedback!

Can you explain me this limit?\lim_(n->\infty )(1-y^(-2))^(n)=0 and \lim_(n->\infty )(1+(e^(y))/(n))^(-n)=exp(-exp(-y)) $$\lim_{n \to \infty} \left( 1 + \frac{e^y}{n} \right)^{-n}$$

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