What is the limit as x approaches 0+of e^{1/x}*x ?

The limit as x approaches 0+of e^{1/x}*x is infinity

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limit as x approaches 0+of e^{1/x}*x

x \to 0 + lim (e^{\frac{1}{x}} \cdot x)

\infty

Solution steps

x \to 0 + lim (e^{\frac{1}{x}} x)

Rewrite for L'Hopital

= x \to 0 + lim (\frac{e ^{\frac{1}{x}}}{\frac{1}{x}})

Apply L'Hopital's Rule

: x \to 0 + lim \frac{- \frac{e ^{\frac{1}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}}

= x \to 0 + lim \frac{- \frac{e ^{\frac{1}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}}

Simplify

\frac{- \frac{e ^{\frac{1}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}} : e^{\frac{1}{x}}

= x \to 0 + lim (e^{\frac{1}{x}})

Apply the Limit Chain Rule:

\infty

= \infty

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

x \to 4 lim (5 x + 6)

n \to \infty lim (\frac{n}{3})

\frac{d}{d x} (\frac{sin ( \frac{1}{x} ) \cdot x ^{3}}{ln ( x )})

\frac{d y}{d x}, (x - y)^{2} = 2 a x

What is the limit as x approaches 0+of e^{1/x}*x ?
The limit as x approaches 0+of e^{1/x}*x is infinity