Find the first step in the following "Proof" that is incorrect, and provide an explanation why this is the case. As part of your explanation provide an example that shows the step is not valid.

Statement: If lim_xzf(x)g(x)=A then there are numbers B and C such that lim_xz f(x) = B and lim_xzg(x)=C and A=BC.

Proof: We are given that lim_xzf(x)g(x) = A. Then

(1) lim_xzf(x)g(x)=(lim_xzf(x)) (lim_xzg(x))

Then let B be the value of lim_xzf(x) in (1)and lat C be the value of lim_xzg(x) in (1) so that lim_xzf(x) = B and lim_xzg(x) = C. It needs to be shown that A = BC.

What does this mean please explain. I am very confused.

Also, the (1) is the equation.