Question

Вычислите:
$\lim_{x \to \ -1} \frac{ (x^{3}-2x-1)(x+1)}{ x^{4}+4x^{2}-5 }$

Answer 1

$\lim_{x \to -1} \frac{(x^3-2x-1)\cdot(x+1)}{x^4 +4x^2-5}= \lim_{x \to -1} \frac{(x^2-x-1) \cdot (x+1)\cdot(x+1)}{(x^2+1)\cdot (x^2+5)}=\\ \\= \lim_{x \to -1} \frac{(x^2-x-1)\cdot(x+1)}{(x-1)\cdot (x^2+5)}=\frac{((-1)^2+1-1)\cdot(-1+1)}{(-1-1)\cdot ((-1)^2+5)}=\frac{(x^2-x-1)\cdot(x+1)}{(x-1)\cdot (x^2+5)}=0$