Question

lim x→−4 |x|−4 / x2−16

Answer 1

|x| = x se x > ou |x | = -x , se s < 0
$\frac{|x|-4}{x^2-16} = \frac{-x-4}{(x+4)(x-4)} =- \frac{x+4}{(x+4)(x-4)} = - \frac{1}{x-4}$$\lim_{n \to \-4} \frac{|x^2-4|}{x^2-16} = \lim_{n \to \-4} =- \frac{1}{x-4} = \frac{-1}{-4-4} = \frac{1}{8}$