Thread: limit of f(x) * g(x) = limit (f(x)) * limit (g(x)) proof

Here is the proof of limit of f(x) * g(x) = limit (f(x)) * limit (g(x))



I don't understand why don't take:

|f(x) - L1| < e/3

and

|g(x)-L2|<e/3


and he takes

|f(x)-L1|< e/3(1+|L1|)


Could you please tell me?

Thanks in advance.[/tex]

Using you'll prove that . Which is the same but less elegant.