1) $\lim_{x \to -\infty} \frac{1+3x}{\sqrt{2x^2+3}}=\lim_{x \to -\infty} \frac{\frac{1}{x}+3}{\frac{\sqrt{2x^2+3}}{x}}$
$=\lim_{x \to -\infty} \frac{\frac{1}{x}+3}{-\sqrt{2+\frac{3}{x^2}}}$
$=\frac{0+3}{-\sqrt{2+0}}=\frac{-3}{\sqrt{2}} $
2) $ \lim_{x \to -\infty} \frac{2x^2-1}{3-x^2}=lim_{x \to -\infty} \frac{2-\frac{1}{x^2}}{\frac{3}{x^2}-1}$
$=\frac{2-0}{0-1}=-2$
3) $\lim_{x \to +\infty} \frac{5}{3x+2}=\lim_{x \to +\infty} \frac{\frac{5}{x}}{3+\frac{2}{x}}$
$=\frac{0}{3+0}=0$
