Question

Evaluate : $\underset{x\to \infty }{lim}\frac{5x^2+1}{x^2+10}$

Answer 1

We have, $\underset{x\to \infty }{lim}\frac{5x^2+1}{x^2+10}$

Let $L=\underset{x\to \infty }{lim}\frac{5x^2+1}{x^2+10}$

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

$=\underset{x\to \infty }{lim}\frac{5+\frac{1}{x^2}}{1+\frac{10}{x^2}}$

$=\frac{5+\frac{1}{{\infty }^2}}{1+\frac{10}{{\infty }^2}}$

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

$L=\frac{5}{1}=5$

Hence, this is the answer.