What is the limit as x approaches 0-of (7e^x)/(x^5) ?

The limit as x approaches 0-of (7e^x)/(x^5) is -infinity

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limit as x approaches 0-of (7e^x)/(x^5)

x \to 0 - lim (\frac{7 e ^{x}}{x ^{5}})

- \infty

Solution steps

x \to 0 - lim (\frac{7 e ^{x}}{x ^{5}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 7 \cdot x \to 0 - lim (\frac{e ^{x}}{x ^{5}})

\frac{e ^{x}}{x ^{5}} = e^{x} \frac{1}{x ^{5}}

= 7 \cdot x \to 0 - lim (e^{x} \frac{1}{x ^{5}})

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

= 7 \cdot x \to 0 - lim (e^{x}) \cdot x \to 0 - lim (\frac{1}{x ^{5}})

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

x \to 0 - lim (\frac{1}{x ^{5}}) = - \infty

= 7 \cdot 1 \cdot (- \infty)

Apply Infinity Property:

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

= - \infty

\frac{d y}{d x} = \frac{x y + 3 x - y - 3}{x y - 2 x + 4 y - 8}

(3 ln (x))^{^{'}}

\frac{d}{d x} (sin (\frac{1}{x ^{2} - 5}))

\frac{d}{d x} (ln (\frac{1}{cos ( x )}))

x \to a lim (\frac{0}{0})

What is the limit as x approaches 0-of (7e^x)/(x^5) ?
The limit as x approaches 0-of (7e^x)/(x^5) is -infinity