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

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

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

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

\infty

Solution steps

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

= \infty

x \to 5 lim (\frac{x ^{2} - 3 x - 10}{x ^{2} - 4 x - 5})

x \to 2 lim ((x - 2)^{(x - 2)})

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

x \to 4 lim (0)

x \to \infty lim ((\frac{x + 3}{x})^{2 x - 7})

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