Question

find the limit limx->+infinity
$x {e}^{ - x}$
​

Answer 1

Answer:

lim (x → ∞) x e⁻ˣ

= lim (x → ∞) x / eˣ [ ∞/∞ form ]

= lim (x → ∞) 1 / eˣ

[ using L' Hospital's Rule ]

= 1 / e^∞

= 1 / ∞

= 0 (Ans.)

L' Hospital's Rule:

If lim (x → ∞) f(x) = ∞

and lim (x → ∞) g(x) = ∞

and if lim (x → ∞) f'(x)/g'(x) exists, then

lim (x → ∞) f(x)/g(x) = lim (x → ∞) f'(x)/g'(x).

Answer 2

$\huge\underline\mathfrak\purple{Answer}$