Question

Dada a função f(x) = $\sqrt{2x+3}$, calcule $\frac{f(x+h) - f(x)}{h}$

Answer 1

Resposta:

$f(x)=\sqrt{2x+3}\\f'(x)= \lim_{x \to 0} \frac{f(x+h)-f(x)}{h} \\f(x+h)=\sqrt{2(x+h)+3}=\sqrt{2x+2h+3} \\f'(x)=\lim_{x \to 0} \frac{\sqrt{2x+2h+3}-\sqrt{2x+3}}{h}*\frac{\sqrt{2x+2h+3}+\sqrt{2x+3}}{\sqrt{2x+2h+3}+\sqrt{2x+3}}\\f'(x)=\lim_{x \to 0} \frac{2x+2h+3-2x+3}{h(\sqrt{2x+2h+3}+\sqrt{2x+3})} =\lim_{x \to 0} \frac{2h}{h(\sqrt{2x+2h+3}+\sqrt{2x+3})} =\lim_{x \to 0} \frac{2}{\sqrt{2x+2h+3}+\sqrt{2x+3}} \\f'(x)=\frac{2}{\sqrt{2x+3}+\sqrt{2x+3} } =\frac{2}{2\sqrt{2x+3} } =\frac{1}{\sqrt{2x+3} }$

Qualquer dúvida só perguntar.