Assume that \lim_x\to3g(x) exists, \lim_x\to3f(x) = 7, and \lim_x\to3(f(x)g(x)) = 28.
Since the limits of both f and g exist, the limit of the product is the product of the limits.
28& = \lim_x\to3(f(x)g(x))
& = &(\lim_x\to3f(x))\cdot(\lim_x\to3g(x))
& = &7\cdot\lim_x\to3g(x)
4& = &\lim_x\to3g(x).
as long as all limits involved exist, this "limit of a product is the product of the limits'' also works even when the product involves several factors.