SImplify the indicated limits on the following. limx→∞3x2+5x2+1

defazajx

Answered question

2021-10-31

SImplify the indicated limits on the following.
$\underset{x\to \mathrm{\infty}}{lim}\frac{3{x}^{2}+5}{{x}^{2}+1}$

Answer & Explanation

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