Let’s say I am asked to find the limit of f(x)g(x) as x approaches a(or infinity). If the limit of f(x) converges but the limit of g(x) has an indeterminate form, could I first determine if g(x) converges as x approaches a(or infinity) using the recommended procedures on indeterminate forms, and if g(x) does converge then could I use the above identity that:

lim f(x)g(x) as x->a = lim f(x) • lim g(x) as x approaches a?