Question

POR FAVOR, ME AJUDEM EM CÁLCULO DE limite 

( exercício na imagem)

Answer 1

$\displaystyle\lim_{x \to +\infty} \dfrac{2x}{3x-6} = \displaystyle\lim_{x \to \infty} \dfrac{\frac{2x}{x}}{\frac{3x}{x}-\frac{6}{x}} = \displaystyle\lim_{x \to \infty} \dfrac{2}{3-\frac{6}{x}} = \dfrac{2}{3}\\ \\\displaystyle\lim_{x \to -\infty} \dfrac{2x}{3x-6} = \displaystyle\lim_{x \to \infty} \dfrac{\frac{2x}{x}}{\frac{3x}{x}-\frac{6}{x}} = \displaystyle\lim_{x \to \infty} \dfrac{2}{3-\frac{6}{x}} = \dfrac{2}{3} \\ \\ \displaystyle\lim_{x \to 2^+} \dfrac{2x}{3x-6}=\displaystyle\lim_{x \to 2^+} \dfrac{4}{0^+} = +\infty\\ \\ \displaystyle\lim_{x \to 2^-} \dfrac{2x}{3x-6}=\displaystyle\lim_{x \to 2^-} \dfrac{4}{0^-} = -\infty$