Respostas

  • Usuário do Brainly
2014-08-31T04:37:21-03:00
Olá, Francine !

f(x)=\dfrac{2}{3}x-\dfrac{1}{3}

f(p)=f(10^8)=\dfrac{2}{3}\cdot10^8-\dfrac{1}{3}

f(q)=f(10^{10})=\dfrac{2}{3}\cdot10^{10}-\dfrac{1}{3}

Assim:

f(p)-f(q)=\dfrac{2}{3}\cdot10^8-\dfrac{1}{3}-\dfrac{2}{3}\cdot10^{10}+\dfrac{1}{3}=\dfrac{2}{3}\cdot10^8-\dfrac{2}{3}\cdot10^{10}.

Note que, \dfrac{2}{3}\cdot10^8-\dfrac{2}{3}\cdot10^{10}=\dfrac{2}{3}\cdot10^8\cdot(1-10^2})

E q-p=10^{10}-10^{8}=10^{8}\cdot(10^2-1);

Logo:

\dfrac{f(p)-f(q)}{q-p}=\dfrac{\dfrac{2}{3}\cdot10^8\cdot(1-10^{2})}{10^8\cdot(10^2-1)}=\dfrac{\dfrac{2}{3}\cdot(1-10^2)}{10^2-1}=\dfrac{\dfrac{2}{3}\cdot(-99)}{99}

\dfrac{f(p)-f(q)}{q-p}=-\dfrac{2}{3}

Espero ter ajudado, até mais ^^