Question

Lim x³ + 8 / x + 2...... x -> -2

lim x³- x² - 2x / x²- 3x + 2..... x-> 2

Podem me ajudar nessas questões de limite? Obrigado.

Answer 1

$\lim_{x \to -2} \frac{x^{3}+8}{x+2}= \lim_{x \to -2}\frac{x^{3}+2^{3}}{x+2} = \lim_{x \to -2}\frac{(x+2)(x^{2}-2x+4)}{x+2}\\ = \lim_{x \to -2}(x^{2}-2x+4) = (-2)^{2}-2*(-2)+4=4+4+4=12 \\ \\ x\neq -2$

$\lim_{x \to 2} \frac{x^{3}-x^{2}-2x}{x^{2}-3x+2}=\lim_{x \to 2} \frac{x(x^{2}-x-2)}{(x-2)(x-1)}=\lim_{x \to 2} \frac{x(x-2)(x+1)}{(x-2)(x-1)}=\lim_{x \to 2} \frac{x(x+1)}{x-1}=\frac{2(2+1)}{2-1}=\frac{6}{1}=6 \\ \\ x\neq 2$