What is the limit as x approaches infinity of xe^{-sx} ?

The limit as x approaches infinity of xe^{-sx} is 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches infinity of xe^{-sx}

x \to \infty lim (x e^{- s x})

0

Solution steps

x \to \infty lim (x e^{- s x})

Rewrite for L'Hopital

= x \to \infty lim (\frac{x}{\frac{1}{e ^{- x s}}})

Apply L'Hopital's Rule

: x \to \infty lim (\frac{1}{e ^{s x} s})

= x \to \infty lim (\frac{1}{e ^{s x} s})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{s} \cdot x \to \infty lim (\frac{1}{e ^{s x}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{1}{s} \cdot \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( e ^{s x} )}

x \to \infty lim (1) = 1

x \to \infty lim (e^{s x}) = \infty

= \frac{1}{s} \cdot \frac{1}{\infty}

Simplify

\frac{1}{s} \cdot \frac{1}{\infty} : 0

= 0

\frac{d}{d x} (\frac{x ^{2} - 16}{x - 4})

\int \frac{x ^{2} + 10 x + 2}{x ^{3} + 15 x ^{2} + 6 x + 9} d x

f (x) = 3 - 2 x

x \to 0 lim (tan (2 x) csc (4 x))

y = x^{4} + 5 e^{x}, (0, 5)

What is the limit as x approaches infinity of xe^{-sx} ?
The limit as x approaches infinity of xe^{-sx} is 0