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 (\frac{e ^{\frac{1}{x}}}{x})

\infty

Solution steps

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

\frac{e ^{\frac{1}{x}}}{x} = e^{\frac{1}{x}} \frac{1}{x}

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

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

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

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

(3 x + 4)^{2}

\frac{d}{d t} (2 t - 1)

\frac{\partial}{\partial x} (- x e^{\frac{y}{x}})

t^{3} \frac{d y}{d t} + 3 t^{2} y = 9 cos (t), y (π) = 0

cos (10 t)

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