What is the limit as x approaches infinity of 3\sqrt[3]{x-3} ?

The limit as x approaches infinity of 3\sqrt[3]{x-3} is infinity

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limit as x approaches infinity of 3\sqrt[3]{x-3}

x \to \infty lim (3 3 x - 3)

\infty

Solution steps

x \to \infty lim (3 3 x - 3)

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

= 3 \cdot x \to \infty lim (3 x - 3)

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= 3 3 x \to \infty lim (x - 3)

Apply Infinity Property:

x \to \infty lim (a x^{n} + \dots + b x + c) = \infty, a > 0,

n is odd

a = 1, n = 1

= 3 3 \infty

Simplify

3 3 \infty : \infty

= \infty

x \to 4 lim (\frac{1}{x} + x^{- 1})

x \to 0 lim (\frac{( 1 + x ) \cdot 1}{x})

x \to 0 + lim (\frac{1}{0})

x \to - \infty lim (- 5 \cdot (x))

x \to 6 lim (\frac{x}{3})

What is the limit as x approaches infinity of 3\sqrt[3]{x-3} ?
The limit as x approaches infinity of 3\sqrt[3]{x-3} is infinity