Question

Evaluate $\underset{x\to \infty }{lim}\frac{5x^2+4}{\sqrt{2x^4+1}}$

Answer 1

We have,

$\underset{x\to \infty }{lim}\frac{5x^2+4}{\sqrt{2x^4+1}}$

$\underset{x\to \infty }{lim}\frac{x^2(5+\frac{4}{x^2})}{x^2\sqrt{2+\frac{1}{x^4}}}$

$\underset{x\to \infty }{lim}\frac{(5+\frac{4}{x^2})}{\sqrt{2+\frac{1}{x^4}}}$

$\Rightarrow \frac{(5+\frac{4}{(\infty {)}^2})}{\sqrt{2+\frac{1}{(\infty {)}^4}}}$

$\Rightarrow \frac{(5+0)}{\sqrt{2+0}}$

$\Rightarrow \frac{5}{\sqrt{2}}$

Hence, this is the answer.