Question

lim de h tendendo a 0 se f(x+h)-f(x)/h quando f(x)= x^3

Answer 1

$\lim_{h \to 0} \frac{(x+h)^3-x^3}{h}= \lim_{h \to 0} \frac{x^3+3x^2h+3xh^2+h^3-x^3}{h}= \lim_{h \to 0} \frac{3x^2h+3xh^2+h^3}{h}$ $=\lim_{h \to 0} \frac{h(3x^2+3xh+h^2)}{h}=\lim_{h \to 0} 3x^2+3xh+h^2=3x^2+3x(0)+(0)^2$ $=\boxed{3x^2}$