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

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

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

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

\infty

Solution steps

x \to - \infty lim (3 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 0 lim (- 2 x + x^{4} - x^{2} - 1)

x \to - \infty lim (x^{2} + 6 x - x)

n \to 1 lim (n x (1 - x^{2})^{n})

x \to 0 lim (\frac{( 4 x - x ^{2} )}{x})

x \to - 2 lim (3 x^{3} + x - 2021)

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