Jason Farmer

2021-01-16

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

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.

$\underset{x\to \mathrm{\infty}}{lim}\frac{-2x({x}^{2}+4)}{-7-7{x}^{4}}$

$=\underset{x->\mathrm{\infty}}{lim}\frac{{x}^{3}(-2-\frac{8}{{x}^{2}})}{{x}^{4}(\frac{-7}{{x}^{4}}-7)}$

$=\underset{x->oo}{lim}\frac{{x}^{3}(-2-\frac{8}{{x}^{2}})}{{x}^{4}(\frac{-7}{{x}^{4}}-7)}$

$=\underset{x\to \mathrm{\infty}}{lim}\frac{(-2-\frac{8}{{x}^{2}})}{(x(\frac{-7}{{x}^{4}}-7)}=0$

Evaluate the limits at the endpoints as shown below.

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function

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