Question

lim x->4 5x-x^2-4/x2-2x-8

Answer 1

$f(x) = \dfrac{-x^2+5x-4}{x^2-2x-8}\\\\ \lim_{x \to 4} \dfrac{-x^2+5x-4}{x^2-2x-8} = \lim_{x \to 4} \dfrac{-(x-4)(x-1)}{(x-4)(x+2)} = \lim_{x \to 4} \dfrac{-(x-1)}{x+2} = f(4)= \dfrac{-(4-1)}{4+2} = \dfrac{-3}{6}=-\dfrac{1}{2}$