Question

calcular o limite de x tendendo a -2 = x elevado a quinta=32 / x+2

Answer 1

$\lim_{x \to -2} \frac{x^5+32}{x+2} = \frac{0}{0}$

fazendo a divisão de polinomios usando briot ruffini

$\boxed{-2}\;\;\boxed{1_{x^5}}\boxed{0_{x^4}}\boxed{0_{x^4}}\boxed{0_{x^3}}\boxed{0_{x^2}}\boxed{0_{x}}\boxed{32}\\ .........\boxed{1_{x^4}}\boxed{-2_{x^3}}\boxed{4_{x^2}}\boxed{-8_{x}}\boxed{16_{}}\boxed{0}}\\\\\\ \text{chegamos a conclusao que:}\\\\\frac{x^5-32}{x+2}= x^4-2x^3+4x^2-8x+16$


temos:

$\lim_{x \to -2} \frac{x^5+32}{x+2}\\\\ = \lim_{x \to -2} (x^4-2x^3+4x^2-8x+16) \\\\ = (-2)^4-2*(-2)^3+4*(-2)^2-8*(-2)+16 = 80\\\\\\\\\boxed{\boxed{\lim_{x \to -2} \frac{x^5+32}{x+2}=80}}$