What is the limit as x approaches-infinity of 2x-x^2 ?

The limit as x approaches-infinity of 2x-x^2 is -infinity

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limit as x approaches-infinity of 2x-x^2

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

- \infty

Solution steps

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

Apply Infinity Property:

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

n is even

a = - 1, n = 2

= - \infty

What is the limit as x approaches-infinity of 2x-x^2 ?
The limit as x approaches-infinity of 2x-x^2 is -infinity