What is the limit as x approaches infinity of x-3x^{1/3} ?

The limit as x approaches infinity of x-3x^{1/3} is infinity

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limit as x approaches infinity of x-3x^{1/3}

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

\infty

Solution steps

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

Factor out

x

from

x - 3 x^{\frac{1}{3}} : x (1 - \frac{3 x ^{\frac{1}{3}}}{x})

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

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

With the exception of indeterminate form

= x \to \infty lim (x) \cdot x \to \infty lim (1 - \frac{3 x ^{\frac{1}{3}}}{x})

x \to \infty lim (x) = \infty

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

= \infty \cdot 1

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

(- 7.2) (8.2)

\frac{7 - e ^{\frac{- t}{5}}}{6}

\frac{d}{d x} (1^{\frac{1}{2}})

y^{^{''}} + 12 y^{^{'}} + 36 y = e - 7 x (x^{2} + 3 x + 6)

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

What is the limit as x approaches infinity of x-3x^{1/3} ?
The limit as x approaches infinity of x-3x^{1/3} is infinity