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

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

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

in v erse l a pl a ce \frac{s ^{2} + 4}{( s ^{2} - 4 ) ^{2}}

5 x - 8 y x^{2} + 1 \frac{d y}{d x} = 0

s im pl i f y 2 ln (\frac{3 x ^{2}}{2})

\frac{d}{d x} ((4 x^{2} + 9) (8 x + x^{\frac{1}{2}}))

d er i v a t i v e y = 7 x^{\frac{1}{2}} + x^{\frac{3}{2}}

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