Question

Calcule os seguintes limites limx->0 (x+h)^3- x^3/ h

Answer 1

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