Question

Let f and g be functions that are differentiable for all real numbers, with g(x)=/=0 and x=/=0. If lim as x approaches 0 of f(x)=lim of x approaches 0 of g(x)=0 and the limit as x approaches 0 of f'(x)/g'(x) exists, then what is the limit as x approaches 0 of f(x)/g(x)?