Question

Ajudaaa ...
,...........

.

Answer 1

Resposta:

Explicação passo-a-passo:

a) f(x) = x²

f'(x) = lim f(x + Δx) - f(x)/Δx

Δx⇒0

lim (x+Δx)² - x² /Δx

Δx⇒0

lim x² +2x.Δx +(Δx)² - x² /Δx

Δx⇒0

lim 2xΔx +( Δx)²/Δx

Δx⇒0

lim Δx(2x + Δx / Δx

Δx⇒0

lim 2x + Δx = 2x + 0 = 2x, portanto

Δx⇒0

f(x) = x² ⇒f'(x) = 2x

b) f'(x) = lim f( x + Δx) - f(x) / Δx

Δx⇒0

lim 2(x +delta x) + 1 - [2.x + 1]/delta x

Δ⇒0

lim 2x + 2Δx + 1 - 2x -1/Δx

Δx⇒0

lim 2Δx/Δx = 2

Δx⇒0

portanto, f(x) = 2x +1 ⇒ f'(x) = 2

Answer 2

Resposta:

Explicação passo-a-passo:

a) f(x) = x²

f'(x) = lim f(x + Δx) - f(x)/Δx

Δx⇒0

lim (x+Δx)² - x² /Δx

Δx⇒0

lim x² +2x.Δx +(Δx)² - x² /Δx

Δx⇒0

lim 2xΔx +( Δx)²/Δx

Δx⇒0

lim Δx(2x + Δx / Δx

Δx⇒0

lim 2x + Δx = 2x + 0 = 2x, portanto

Δx⇒0

f(x) = x² ⇒f'(x) = 2x

b) f'(x) = lim f( x + Δx) - f(x) / Δx

Δx⇒0

lim 2(x +delta x) + 1 - [2.x + 1]/delta x

Δ⇒0

lim 2x + 2Δx + 1 - 2x -1/Δx

Δx⇒0

lim 2Δx/Δx = 2

Δx⇒0

portanto, f(x) = 2x +1 ⇒ f'(x) = 2