Question

Calcule o Lim (x³+1)/(x²-1) quando x-»-1

Answer 1

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

conhecendo os produtos notaveis

$A^2-B^2 = (A-B)*(A+B)\\\\(A^3+B^3)=(A+B)*(A^2-AB+B^2)$

como 
1² = 1
1³ =1

podemos escrever como
$\lim_{x \to -1} \frac{x^3+1^3}{x^2-1^2} \\\\ \lim_{x \to -1} \frac{(x+1)*(x^2-1x+1^2)}{(x-1)*(x+1)} \\\\ \lim_{x \to -1} \frac{(x^2-1x+1^2)}{(x-1)} = \frac{(-1)^2-(-1)+1}{(-1) -1 }= \frac{3}{-2}= - \frac{3}{2}$

Answer 2

$Ol\acute{a}~~\mathbb{CHRISTIAN} \\ \\ M= \lim _{x \to -1}\Bigg( \frac{x\³+1}{x\²-1}\Bigg) \\ \\ M=\lim_{x \to -1}\Bigg( \frac{(x+1).(x\² -x+1)}{(x+1).(x-1)} \Bigg)~~--\ \textgreater \ simplificando~fica: \\ \\ M=\lim_{x \to -1} \Bigg( \frac{ x^{2} -x+1}{x-1}\Bigg) \\ \\ M=\Bigg( \frac{(-1)\² -(-1)+1}{-1-1} \Bigg)$

$M=\Bigg( \frac{1+1+1}{-2} \Bigg) \\ \\ \boxed{ \boxed{M= - \frac{3}{2} }} \\ \\ \mathbb{xxxxxxxxxxxxxxxxxxxxxxxxxxx}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$