Find the limits:
As $x\to \mathrm{\infty},\frac{-2x({x}^{2}+4)}{-7-7{x}^{4}}$

Answer & Explanation

Lacey-May Snyder

Skilled2021-01-17Added 88 answers

The given function is $\frac{-2x({x}^{2}+4)}{(-7-7{x}^{4}}$
Evaluate the limits at the endpoints as shown below.
$\underset{x\to \mathrm{\infty}}{lim}\frac{-2x({x}^{2}+4)}{-7-7{x}^{4}}$ $=\underset{x->\mathrm{\infty}}{lim}\frac{{x}^{3}(-2-\frac{8}{{x}^{2}})}{{x}^{4}(\frac{-7}{{x}^{4}}-7)}$ $=\underset{x->oo}{lim}\frac{{x}^{3}(-2-\frac{8}{{x}^{2}})}{{x}^{4}(\frac{-7}{{x}^{4}}-7)}$ $=\underset{x\to \mathrm{\infty}}{lim}\frac{(-2-\frac{8}{{x}^{2}})}{(x(\frac{-7}{{x}^{4}}-7)}=0$