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

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