Question

lim x^3-8/x^2-4
x->2

Answer 1

$\lim_{x \to \ 2} \ \ \frac{x^{3}-8 }{ x^{2}-4} \ \ factorizamos \ para \quitar \ la \ indeterminacion \\ \\ \frac{(x-2)( x^{2}+2x+4 )}{(x-2)(x+2)} \ cancelamos \ (x-2) \ y \ evaluamos \\ \\ \lim_{x \to \ 2} \ \ \frac{ x^{2} +2x+4}{x+2}....... \frac{(2)^{2}+2(2)+4 }{2+2}........ \frac{4+4+4}{4}....... \frac{12}{4}=3 \\ \\ \\ \lim_{x \to \ 2} \ \ \frac{x^{3}-8}{ x^{2}-4} =3$