Question

Evaluate the limit $\underset{x\to \infty }{lim}(\sqrt{4x^2-x}+2x)dx$

Answer 1

$li{m}_{x\to \infty }\frac{(\sqrt{4x^2-x}+2x)(\sqrt{4x^2-2}-2x)}{\sqrt{4x^2-2}-2x}$

$=li{m}_{x\to \infty }\frac{4x^2-x-4x^2}{x[\sqrt{4-2/x}-2/x]}=li{m}_{x\to \infty }\frac{-1}{\sqrt{4-\frac{1}{x}}-\frac{2}{x}}=\frac{-1}{\sqrt{4}}=\frac{-1}{2}$