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

The limit as x approaches infinity of (x^3)/(2^x) is 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches infinity of (x^3)/(2^x)

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

0

Solution steps

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

Apply L'Hopital's Rule

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

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

Apply L'Hopital's Rule

: x \to \infty lim (\frac{6 x}{ln ^{2} ( 2 ) \cdot 2 ^{x}})

= x \to \infty lim (\frac{6 x}{ln ^{2} ( 2 ) \cdot 2 ^{x}})

Apply L'Hopital's Rule

: x \to \infty lim (\frac{6}{ln ^{3} ( 2 ) \cdot 2 ^{x}})

= x \to \infty lim (\frac{6}{ln ^{3} ( 2 ) \cdot 2 ^{x}})

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

= \frac{6}{ln ^{3} ( 2 )} \cdot x \to \infty lim (\frac{1}{2 ^{x}})

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

= \frac{6}{ln ^{3} ( 2 )} \cdot \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( 2 ^{x} )}

x \to \infty lim (1) = 1

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

= \frac{6}{ln ^{3} ( 2 )} \cdot \frac{1}{\infty}

Simplify

\frac{6}{ln ^{3} ( 2 )} \cdot \frac{1}{\infty} : 0

= 0

\int sin (- 2 x) d x

x \to 6 lim (6)

x \to - 1 lim (\frac{3 + x}{x ^{2} - 1})

\int e^{- 3 x} cos (4 x) d x

\int (9 x^{5} - 3 x^{2} + 7) d x

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