Question

\(\lim\limits_{x\rightarrow\pm\infty}\dfrac{\sqrt{2x^2+3}}{4x+2}\)

Answer 1

TH1: \(\lim\limits_{x\rightarrow+\infty}\dfrac{\sqrt{2x^2+3}}{4x+2}\)

\(=\lim\limits_{x\rightarrow+\infty}\dfrac{\sqrt{2+\dfrac{3}{x^2}}}{4+\dfrac{2}{x}}\)

\(=\dfrac{\sqrt{2+0}}{4+0}=\dfrac{\sqrt{2}}{4}\)

TH2: \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt{2x^2+3}}{4x+2}\)

\(=\lim\limits_{x\rightarrow-\infty}\dfrac{-\sqrt{2+\dfrac{3}{x^2}}}{4+\dfrac{2}{x}}\)

\(=\dfrac{-\sqrt{2+0}}{4+0}=-\dfrac{\sqrt{2}}{4}\)