What is the limit as x approaches infinity of (x^3)/(1e^{x/2)} ?

The limit as x approaches infinity of (x^3)/(1e^{x/2)} is 0

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limit as x approaches infinity of (x^3)/(1e^{x/2)}

x \to \infty lim (\frac{x ^{3}}{1 e ^{\frac{x}{2}}})

0

Solution steps

x \to \infty lim (\frac{x ^{3}}{1 \cdot e ^{\frac{x}{2}}})

Simplify

= x \to \infty lim (\frac{x ^{3}}{e ^{\frac{x}{2}}})

Apply L'Hopital's Rule

: x \to \infty lim (\frac{3 x ^{2}}{e ^{\frac{x}{2}} \frac{1}{2}})

= x \to \infty lim (\frac{3 x ^{2}}{e ^{\frac{x}{2}} \frac{1}{2}})

Apply L'Hopital's Rule

: x \to \infty lim (\frac{6 x}{\frac{1}{4} e ^{\frac{x}{2}}})

= x \to \infty lim (\frac{6 x}{\frac{1}{4} e ^{\frac{x}{2}}})

Apply L'Hopital's Rule

: x \to \infty lim (\frac{6}{\frac{1}{8} e ^{\frac{x}{2}}})

= x \to \infty lim (\frac{6}{\frac{1}{8} e ^{\frac{x}{2}}})

Simplify

\frac{6}{\frac{1}{8} e ^{\frac{x}{2}}} : \frac{48}{e ^{\frac{x}{2}}}

= x \to \infty lim (\frac{48}{e ^{\frac{x}{2}}})

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

= 48 \cdot x \to \infty lim (\frac{1}{e ^{\frac{x}{2}}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= 48 \cdot \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( e ^{\frac{x}{2}} )}

x \to \infty lim (1) = 1

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

= 48 \cdot \frac{1}{\infty}

Simplify

48 \cdot \frac{1}{\infty} : 0

= 0

\int 2 x^{3} x^{4} + 2 d x

3 \cdot 2

- 4 x^{2} + 9, x + 7, x = 0

ln (6 x - 1)

\frac{d y}{d x} = \frac{6 y ^{2}}{x ^{2}}

What is the limit as x approaches infinity of (x^3)/(1e^{x/2)} ?
The limit as x approaches infinity of (x^3)/(1e^{x/2)} is 0