Answer
$\displaystyle \frac{2}{3}$
Work Step by Step
$\displaystyle \lim_{x\rightarrow\infty}\frac{2x^{2}}{3x^{2}+5}= \displaystyle \lim_{x\rightarrow\infty}[\frac{2x^{2}\div x^{2}}{3x^{2}+5\div x^{2}}$
$=\displaystyle \lim_{x\rightarrow\infty}\frac{2}{3+\frac{1}{x^{2}}}\qquad$... the term $\displaystyle \frac{1}{x^{2}}$ approaches 0 when $ x\rightarrow\infty$
$=\displaystyle \frac{2}{3+0}=\frac{2}{3}$
