Well, for what about ? That is bounded and continuous but not uniformly continuous. Can you see how to generalize?

It isn't true, takeAlso, if f and g are uniformly continuous maps of R to R, must the product f*g be uniformly continuous? What if f and g are bounded.

I think this one is true...since you're just multiplying two continuous functions together...but I don't know how to prove this either

Thanks.