What is the limit as x approaches-infinity of x^3-x ?

The limit as x approaches-infinity of x^3-x is -infinity

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limit as x approaches-infinity of x^3-x

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

- \infty

Solution steps

x \to - \infty lim (x^{3} - 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

= - \infty

x \to \infty lim (x^{- 6})

\int - x \cdot e^{3 x} d x

\int x^{2} - y^{2} d y

\int \frac{4 x ^{3} - 6 x ^{4}}{2 x ^{6}} d x

y^{^{'}} = 2 y - x^{2}

What is the limit as x approaches-infinity of x^3-x ?
The limit as x approaches-infinity of x^3-x is -infinity