Question

simplifique f(x+h)-f(x)/h sendo f(x)=x^2+3x e h diferente de 0

Answer 1

$\boxed{\begin{array}{l}\sf f(x)=x^2+3x\\\sf\dfrac{f(x+h)-f(x)}{h}=\dfrac{(x+h)^2+3(x+h)-(x^2+3x)}{h}\\\\\sf\dfrac{f(x+h)-f(x)}{h}=\dfrac{\diagup\!\!\!\!x^2+2hx+h^2+\diagup\!\!\!\!3x+3h-\diagup\!\!\!\!x^2-\diagup\!\!\!3x}{h}\\\\\sf\dfrac{f(x+h)-f(x)}{h}=\dfrac{h^2+2hx+3h}{h}\\\\\sf\dfrac{f(x+h)-f(x)}{h}=\dfrac{h(h+2x+3)}{h}\\\\\sf~como~h\ne0,podemos~''cortar''\end{array}}$

$\Large\boxed{\begin{array}{l}\sf\dfrac{f(x+h)-f(x)}{h}=\dfrac{\backslash\!\!\!h(h+2x+3)}{\backslash\!\!\!h}\\\\\sf\dfrac{f(x+h)-f(x)}{h}=h+2x+3\end{array}}$