What is the limit as x approaches 0+of (e^x)/x ?

The limit as x approaches 0+of (e^x)/x is infinity

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limit as x approaches 0+of (e^x)/x

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

\infty

Solution steps

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

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

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

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

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

= 1 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 5 lim (8 x + 9)

\int \frac{( x + 6 ) ^{5}}{2 x} d x

\int \frac{1}{x ( ln ( x ) ) ^{9}} d x

\frac{\partial}{\partial x} (x^{2} - 2 x y + 3 y^{2} - 8 y)

\frac{d}{d x} ((f (x))^{3})

What is the limit as x approaches 0+of (e^x)/x ?
The limit as x approaches 0+of (e^x)/x is infinity