Question

Solucione esse limite :

lim x^2 + x - 2 / x^5 - 1
x -> 1

Answer 1

Use a Regra de L' Hospital que diz:

$\boxed{\lim_{x \to a} \frac{f(x)}{g(x)}= \lim_{x \to a} \frac{f('x)}{g'(x)}}$

Assim:


$\lim_{x \to 1} \frac{x^2+x-2}{x^5-1}= \lim_{x \to 1} \frac{2x+1}{5x^4}=\frac{2*1+1}{5*1^4}=\frac{3}{5}$