What is the limit as x approaches+0-of (e^x)/(x^3) ?

The limit as x approaches+0-of (e^x)/(x^3) is -infinity

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limit as x approaches+0-of (e^x)/(x^3)

x \to + 0 - lim (\frac{e ^{x}}{x ^{3}})

- \infty

Solution steps

x \to 0 - lim (\frac{e ^{x}}{x ^{3}})

\frac{e ^{x}}{x ^{3}} = e^{x} \frac{1}{x ^{3}}

= x \to 0 - lim (e^{x} \frac{1}{x ^{3}})

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 ^{3}})

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

x \to 0 - lim (\frac{1}{x ^{3}}) = - \infty

= 1 \cdot (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

n \to \infty lim (5^{n})

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

\int \frac{x}{( x + 2 ) ( x - 4 )} d x

\int sec (2 x) \cdot tan (2 x) d x

\int \frac{2 x - 3}{x ^{2} + 4} d x

What is the limit as x approaches+0-of (e^x)/(x^3) ?
The limit as x approaches+0-of (e^x)/(x^3) is -infinity