Question

Find $\underset{x\to \infty }{lim}\left(\frac{5x^2+1}{x^2+10}\right)$

Answer 1

We have,

$\underset{x\to \infty }{lim}\left(\frac{5x^2+1}{x^2+10}\right)$

$\underset{x\to \infty }{lim}\left(\frac{x^2(5+\frac{1}{x^2})}{x^2(1+\frac{10}{x^2})}\right)$

$\underset{x\to \infty }{lim}\left(\frac{(5+\frac{1}{x^2})}{(1+\frac{10}{x^2})}\right)$

$=\frac{(5+\frac{1}{\infty })}{(1+\frac{10}{\infty })}$

$=\frac{(5+0)}{(1+0)}$

$=5$

Hence, this is the answer.