Arnold F. answered • 09/24/15

College Professor & Expert Tutor In Statistics and Calculus

Yes to both.

Let f(x)=x

^{2}and let g(a)=1/x with a=0. Lim f(x)=0; lim g(x) DNE but lim f(x)g(x)=lim (x) = 0.For the same functions f(x)/g(x)=x

^{3}and this lim is also 0.