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

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

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

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

\infty

Solution steps

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

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

= \frac{1}{2} \cdot x \to \infty lim (\frac{e ^{x}}{x ^{2}})

Apply L'Hopital's Rule

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

= \frac{1}{2} \cdot x \to \infty lim (\frac{e ^{x}}{2 x})

Apply L'Hopital's Rule

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

= \frac{1}{2} \cdot x \to \infty lim (\frac{e ^{x}}{2})

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

= \frac{1}{2} \cdot \frac{1}{2} \cdot x \to \infty lim (e^{x})

Apply the common limit:

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

= \frac{1}{2} \cdot \frac{1}{2} \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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