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

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 #