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

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

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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