It's taught that $\lim_{h\rightarrow 0}g(h)f(h) = \lim_{h\rightarrow 0} g(h) \lim_{h\rightarrow 0}f(h)$.
If I consider $f(h) = 1/h^2$ and $g(h)=h$ then their product is$ 1/h$, and as $h$ tends to zero it blows up to infinity. But if I use the result I get limit of $g=0$ as $h$ tends to zero and thus product becomes zero. What is wrong with my thought process? Please help if the result is not applied as expected.