What is the limit as x approaches infinity of xe^{1/x} ?

The limit as x approaches infinity of xe^{1/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 xe^{1/x}

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

\infty

Solution steps

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

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

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

= \infty \cdot 1

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\int cos (y) sin (x) d x

\int x 3 x^{2} + 1 d x

x \to 0 lim (\frac{sin ( 9 x )}{x})

(2 x y + 3 y^{2}) d x - (2 x y + x^{2}) d y = 0

\int \frac{1}{( x ^{2} + z ^{2} ) ^{\frac{3}{2}}} d x

What is the limit as x approaches infinity of xe^{1/x} ?
The limit as x approaches infinity of xe^{1/x} is infinity