What is the limit as x approaches infinity of ((e^{2x}))/(x^2) ?

The limit as x approaches infinity of ((e^{2x}))/(x^2) is infinity

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limit as x approaches infinity of ((e^{2x}))/(x^2)

x \to \infty lim (\frac{( e ^{2 x} )}{x ^{2}})

\infty

Solution steps

x \to \infty lim (\frac{e ^{2 x}}{x ^{2}})

Apply L'Hopital's Rule

= x \to \infty lim (\frac{e ^{2 x} \cdot 2}{2 x})

Apply L'Hopital's Rule

= x \to \infty lim (\frac{4 e ^{2 x}}{2})

Simplify

= x \to \infty lim (2 e^{2 x})

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

= 2 \cdot x \to \infty lim (e^{2 x})

Apply the Limit Chain Rule:

\infty

= 2 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

What is the limit as x approaches infinity of ((e^{2x}))/(x^2) ?
The limit as x approaches infinity of ((e^{2x}))/(x^2) is infinity