Question

Limite de Função

x^2-x-2/x^2-1
x = -1

Answer 1

Siga os passos:
$\displaystyle i)~~~~\lim_{x\to-1}\frac{x^2-x-2}{x^2-1}\\\\ii)~~~(x-2)(x+1)=x^2+x-2x-2=x^2-x-2:~\text{fatorei}\\\\iii)~~\lim_{x\to-1}\frac{x^2-x-2}{x^2-1}=\lim_{x\to-1}\frac{(x-2)(x+1)}{(x^2-1)}\\\\iv)~~(x^2-1)=(x+1)(x-1)=x^2-x+x-1=x^2-1~:\text{fatorei}\\\\v)~~~\lim_{x\to-1}\frac{(x-2)(x+1)}{(x+1)(x-1)}=\lim_{x\to1}\frac{x-2}{x-1}\\\\vi)~~~\lim_{x\to-1}\frac{x-2}{x-1}=\frac{-1-2}{-1-1}=\boxed{\boxed{-\frac{3}{2}}}$

logo

$\boxed{\boxed{\lim_{x\to-1}\frac{x^2-x-2}{x^2-1}=-\frac{3}{2}}}$