A nice limit

Calculus Level 2

$\large \lim_{x \to \infty} \left(1+\frac 1x\right) e^{-\frac 1x} = \ ?$

+infinity 1/e 0 1

2 solutions

Chew-Seong Cheong
May 2, 2018

$\displaystyle L = \lim_{x \to \infty} \left(1+\frac 1x\right) e^{-\frac 1x} = (1+0)e^{-0} = \boxed{1}$ .

X X
May 2, 2018

$\frac1x$ approaches 0 when $x$ approaches $\infty$ ,so this limit approaches $(1+0)e^0=1$