What is the limit as x approaches infinity of e^x*x ?

The limit as x approaches infinity of e^x*x is infinity

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 e^x*x

x \to \infty lim (e^{x} \cdot x)

\infty

Solution steps

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

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

With the exception of indeterminate form

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

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

x \to \infty lim (x) = \infty

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

x \to 0 + lim (x^{3} ln (2 x))

x \to 3 lim (x^{2} + 7)

x \to 2 + lim (\frac{x - 2}{x - 2})

x \to 0 lim (\frac{\frac{0}{x ^{2}}}{x})

x \to 1 lim (x^{2} + 4 x - 5)

What is the limit as x approaches infinity of e^x*x ?
The limit as x approaches infinity of e^x*x is infinity