Question

lim x➡2 x3 -8/x2 +x-6

Answer 1

$\lim_{x \to 2} \frac{x^3-8}{x^2+x-6} = \lim_{x \to 2} \frac{(x-2)(x^2+2x+4)}{(x+3)(x-2)} =\lim_{x \to 2} \frac{x^2+2x+4}{x+3} = \frac{2^2+2*2+4}{2+3} \\= \frac{4+4+4}{5} = \frac{12}{5} =2.4$