Question

Como se calcula o seguinte limite:
lim x3-x-6/2x2+x-10
x->2

Answer 1

$\lim_{x \to \ 2} \frac{x^3-x-6}{2x^2+x-10}=\\\\ \lim_{x \to \ 2} \frac{(x-2)(x^2+2x+3)}{(x-2)(x+ \frac{5}{2}) }= \lim_{x \to \ 2} \frac{x^2+2x+3}{x+ \frac{5}{2} }\\\\ \frac{2^2+2*2+3}{2+ \frac{5}{2} }= \frac{4+4+3}{ \frac{9}{2} }= \frac{11}{ \frac{9}{2} }=11* \frac{2}{9}= \frac{22}{9}$