Question

Dada a função f (x) = 1/x, mostrar que f (1 + h) — f (1) — h / (1 + h). Calcular f (a + h) — f (a).

Answer 1

f(1 + h) - f(1) = 1 / (1 + h) - 1/1 = [1 - 1(1 + h)] / (1 + h) = (1 - 1 - h) / (1 + h) =

= -h / (1 + h)

f(a + h) - f(a) = 1 /(a + h) - 1/a = [a - (a + h)] / a(a + h) = (a - a - h) / (a² + ah) = 
= -h / (a² + ah)