If limit of #f(x)=4# as #x->c#, what the limit of #(f(x))^3# as #x->c#?

1 Answer
Steve M
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 #

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