Find f(x) and g(x) that do not have a limit at x=0, but (fg)(x) does have a limit at x=0

Question

 The two individual functions have no limit at x=0 but their product does have a limit at x=0

Answer 1

An example of this would be 2 odd functions such as 1/X and 1/x^3. neither of these have a limit at 0 bc if u approach it from the left it is -infinity but if you approach it from the right it is positive infinity. But multiply the functions together and get 1/x⁴ does have a limit of positive infinity From both directions.