Question

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

Answer 1

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