Question

calcule f(x) pela definição : f (x) = √x

Answer 1

Ficaria assim f(x)=√x

Answer 2

Resposta:

Explicação passo-a-passo:

$f'(x)= \lim_{h \to 0}\dfrac{f(x+h)-f(x)}{h}\\\\\\f'(x)= \lim_{h \to 0}\dfrac{\sqrt{x+h}-\sqrt{x}}{h}\\\\\\f'(x)= \lim_{h \to 0}\dfrac{\sqrt{x+h}-\sqrt{x}}{h}.\dfrac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}\\\\\\f'(x)= \lim_{h \to 0}\dfrac{x+h-x}{h.(\sqrt{x+h}+\sqrt{x})}\\\\\\f'(x)= \lim_{h \to 0}\dfrac{h}{h.(\sqrt{x+h}+\sqrt{x})}\\\\\\f'(x)= \lim_{h \to 0}\dfrac{1}{\sqrt{x+h}+\sqrt{x}}\\\\f'(x)=\dfrac{1}{\sqrt{x+0}+\sqrt{x}}$

$f'(x)=\dfrac{1}{\sqrt{x}+\sqrt{x}}\\\\\\f'(x)=\dfrac{1}{2.\sqrt{x}}$