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

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.
$\underset{x\to \mathrm{\infty }}{lim}\frac{3{x}^{2}+5}{{x}^{2}+1}=\underset{x\to \mathrm{\infty }}{lim}\frac{{x}^{2}\left(3+\frac{5}{{x}^{2}}\right)}{{x}^{2}\left(1+\frac{1}{{x}^{2}}\right)}$
$=\underset{x\to \mathrm{\infty }}{lim}\frac{3+\frac{5}{{x}^{2}}}{1+\frac{1}{{x}^{2}}}$
$=\frac{3+\frac{5}{\mathrm{\infty }}}{1+\frac{1}{\mathrm{\infty }}}$
$=\frac{3+0}{1+0}$
$\underset{x\to \mathrm{\infty }}{lim}\frac{3{x}^{2}+5}{{x}^{2}+1}=3$

Jeffrey Jordon