Avalie o limite $lim_ (h rarr 0) {(xh) ^ 3-x ^ 3} / h$ ?

$lim_(h rarr 0) {(x-h)^3-x^3}/h = -3x^2$

Procuramos:

$L = lim_(h rarr 0) {(x-h)^3-x^3}/h$

Assim sendo:

$L = lim_(h rarr 0) {x^3-3x^2h+3xh^2-h^3-x^3}/h$
$= lim_(h rarr 0){-3x^2h+3xh^2-h^3}/h$

$= lim_(h rarr 0)-3x^2+3xh-h^2$

$= -3x^2 +0 + 0$

$= -3x^2$

Avalie o limite lim_ (h rarr 0) {(xh) ^ 3-x ^ 3} / h lim_ (h rarr 0) {(xh) ^ 3-x ^ 3} / h ?