Question

limite: (x²+3x-10) / (2x²-x-6) x>2 







$\lim_{x \to \ 2} \frac{ x^{2}+3x-10}{2 x^{2} -x-6}$

Answer 1

Decompondo a equação:
$\frac{ x^{2} +3x-10}{ 2x^{2}-x-6 } = \frac{(x-2).(x+5)}{(x-2).(x+ \frac{3}{2} )}$
Para $x \neq 2$,
$\frac{(x-2).(x+5)}{(x-2).(x+ \frac{3}{2} )} =\frac{(x+5)}{(x+ \frac{3}{2} )}$
Aplicando a definição de limite:
$\lim_{x \to 2} \frac{(x+5)}{(x+ \frac{3}{2} )}$=$\frac{(2+5)}{(2+ \frac{3}{2} )}$=2
Logo,
$\lim_{x \to 2} \frac{ x^{2} +3x-10}{ 2x^{2}-x-6 }$=2