What is the limit as x approaches infinity of (e^{4x})/(5x) ?

The limit as x approaches infinity of (e^{4x})/(5x) is infinity

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limit as x approaches infinity of (e^{4x})/(5x)

x \to \infty lim (\frac{e ^{4 x}}{5 x})

\infty

Solution steps

x \to \infty lim (\frac{e ^{4 x}}{5 x})

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

= \frac{1}{5} \cdot x \to \infty lim (\frac{e ^{4 x}}{x})

Apply L'Hopital's Rule

= \frac{1}{5} \cdot x \to \infty lim (\frac{e ^{4 x} \cdot 4}{1})

Simplify

= \frac{1}{5} \cdot x \to \infty lim (4 e^{4 x})

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

= \frac{1}{5} \cdot 4 \cdot x \to \infty lim (e^{4 x})

Apply the Limit Chain Rule:

\infty

= \frac{1}{5} \cdot 4 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

What is the limit as x approaches infinity of (e^{4x})/(5x) ?
The limit as x approaches infinity of (e^{4x})/(5x) is infinity