If limit of #f(x)=4# as #x->c#, what the limit of #(f(x))^3# as #x->c#?
1 Answer
Nov 13, 2016
# lim_(x rarr c) { f(x) }^3 = 64 #
Explanation:
Limits obey a multiplication law, so that if both the limits
# lim_(x rarr c) f(x) # and# lim_(x rarr c) g(x) #
exist, then
# lim_(x rarr c) { f(x)g(x) } = {lim_(x rarr c) f(x)} {lim_(x rarr c) g(x)} #
Hence,
# lim_(x rarr c) { f(x) }^3 = { lim_(x rarr c) f(x) }^3 #
# :. lim_(x rarr c) { f(x) }^3 = { 4 }^3 #
# :. lim_(x rarr c) { f(x) }^3 = 64 #
