What is the value of : [(x - 64)^(1/3) - 4]/x for x tending to 0?

In other words, we'll have to evaluate the limit of the
fraction, if x approaches to 0:

We'll replace x by 0, we'll
get:

lim [(x - 64)^(1/3) - 4]/x = [(0 - 64)^(1/3) -
4]/0

lim [(x - 64)^(1/3) - 4]/x = [(-64)^(1/3) -
4]/0

But (-64)^(1/3) = -4

lim
[(x - 64)^(1/3) - 4]/x = (-4 - 4)/0

lim [(x - 64)^(1/3) -
4]/x = -8/0

lim [(x - 64)^(1/3) - 4]/x = -
infinite

When x approches to 0, the value of
the fraction [(x - 64)^(1/3) - 4]/x tends to -
infinite.