Can-someone-please-explain-why-lim-x-x-x-2-

Question Number 5286 by FilupSmith last updated on 05/May/16

Can someone please explain why :

\lim_{x \to \infty} (x - x^{2}) = - \infty

Commented by FilupSmith last updated on 05/May/16

i normally undwrstand limits but

i dont remember how to do this

Answered by 123456 last updated on 05/May/16

write it as

- x^{2} + x = x^{2} (- 1 + \frac{1}{x})

\lim_{x \to \infty} x - x^{2}

= \lim_{x \to \infty} x^{2} (- 1 + \frac{1}{x})

\frac{1}{x} \to 0 when x \to \infty so

= \lim_{x \to + \infty} - x^{2} = - \infty

Commented by FilupSmith last updated on 05/May/16

T h a n k s!!!

Answered by enigmeyou last updated on 18/Jun/16

\lim_{x \to - \infty} (x - x^{2}) = \lim_{x \to - \infty} x (1 - x) = - \infty \times (+ \infty) = - \infty

\lim_{x \to + \infty} (x - x^{2}) = \lim_{x \to + \infty} x (1 - x) = + \infty \times (- \infty) = - \infty