find examples to show that if

a) lim x->c [f(x)+g(x)] exists, this does not imply that either lim x->c [f(x)] or lim x->c [g(x)] exists.

b) lim x->c [f(x)*g(x)] exists, this does not imply that either lim x->c [f(x)] or lim x->c [g(x)] exists.

any help would be great