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

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

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limit as x approaches infinity of (x)(e^{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

t \to 1 lim (t + 4)

x \to 5 lim (- (x - 3)^{2})

\frac{d}{d t} (1.1 t + 6.3 t^{3})

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

f (x) = \frac{x ^{3} + 7}{x}

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