Question

Calcule o quociente de
f(a+h) - f(a)
---------------
h

Para o
f(x)= x^2 - 1
----------
X - 1

Answer 1

$\dfrac{f(a+h)-f(a)}{h}~=\\\\\\\\=~\dfrac{\left(~(a+h)^2-1~\right)~-~\left(~a^2-1~\right)}{h}\\\\\\\\=~\dfrac{\left(~(a^2+2.a.h+h^2)-1~\right)~-~\left(~a^2-1~\right)}{h}\\\\\\\\=~\dfrac{a^2+2.a.h+h^2-1~-a^2+1}{h}\\\\\\\\=~\dfrac{2.a.h+h^2}{h}\\\\\\\\=~\dfrac{h\,.\,(2a+h)}{h}\\\\\\\\=~\dfrac{h\!\!\!\backslash\,.\,(2a+h)}{h\!\!\!\backslash}\\\\\\\\=~\boxed{2a+h}$