defazajx

2021-10-31

SImplify the indicated limits on the following.

$\underset{x\to \mathrm{\infty}}{lim}\frac{3{x}^{2}+5}{{x}^{2}+1}$

grbavit

Skilled2021-11-01Added 109 answers

According to the given information, it is required to find the limit.

$\underset{x\to \mathrm{\infty}}{lim}\frac{3{x}^{2}+5}{{x}^{2}+1}$

Now find the value of limit.

$\underset{x\to \mathrm{\infty}}{lim}\frac{3{x}^{2}+5}{{x}^{2}+1}=\underset{x\to \mathrm{\infty}}{lim}\frac{{x}^{2}(3+\frac{5}{{x}^{2}})}{{x}^{2}(1+\frac{1}{{x}^{2}})}$

$=\underset{x\to \mathrm{\infty}}{lim}\frac{3+\frac{5}{{x}^{2}}}{1+\frac{1}{{x}^{2}}}$

$=\frac{3+\frac{5}{\mathrm{\infty}}}{1+\frac{1}{\mathrm{\infty}}}$

$=\frac{3+0}{1+0}$

$\underset{x\to \mathrm{\infty}}{lim}\frac{3{x}^{2}+5}{{x}^{2}+1}=3$

Now find the value of limit.

Jeffrey Jordon

Expert2022-06-24Added 2605 answers

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