What is the limit as x approaches infinity of \sqrt[3]{x^3+3x^2-x} ?

The limit as x approaches infinity of \sqrt[3]{x^3+3x^2-x} is infinity

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limit as x approaches infinity of \sqrt[3]{x^3+3x^2-x}

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

\infty

Solution steps

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

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

With the exception of indeterminate form

= 3 x \to \infty lim (x^{3} + 3 x^{2} - x)

Apply Infinity Property:

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

n is odd

a = 1, n = 3

= 3 \infty

Apply Infinity Property:

\infty^{c} = \infty

= \infty

\frac{1}{s ^{2} ( s ^{2} + 1 )}

\int \frac{6 - x}{6 + x} d x

n = 0 \sum \infty \frac{2 ^{n}}{1 ^{n}}

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

x \to 1 lim (1 \cdot 0)

What is the limit as x approaches infinity of \sqrt[3]{x^3+3x^2-x} ?
The limit as x approaches infinity of \sqrt[3]{x^3+3x^2-x} is infinity