Question

Mostre que se f(x) = 2x/x-1 então f(x + h) - f(x)/h = -2/(x-1)(x + h -1)

Answer 1

f(x) = 2x/x-1

f(x + h) = [2(x+h)/(x+h-1)]

f(x+h) - f(x) = [2(x+h)/(x+h-1)] - [2x/(x-1)]

f(x+h) - f(x) = [2x² -2x + 2hx - 2h - 2x² - 2hx + 2x] / (x-1)(x+h-1)

f(x+h) - f(x) = -2h/(x-1)(x+h-1)

Portanto fica:

[f(x+h) - f(x)]/h = [-2h/(x-1)(x+h-1)]/h

[f(x+h) - f(x)]/h = -2/(x-1)(x+h-1) ■

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05/10/2016
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