Evaluate the limit #lim_(h rarr 0) {(x-h)^3-x^3}/h#?
1 Answer
Sep 14, 2017
# lim_(h rarr 0) {(x-h)^3-x^3}/h = -3x^2 #
Explanation:
We seek:
# L = lim_(h rarr 0) {(x-h)^3-x^3}/h #
Therefore:
# 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 #
