Indeterminate Forms

I suspect you mean that you can have functions f(x), g(x), f'(x), and g'(x) such that $\lim_{x\to a} f(x)= 0$. $\lim_{x\to a} g(x)= \infty$, $\lim_{x\to a} f'(x)= 0$, and $\lim_{x\to a} g'(x)= \infty$ such that $\lim_{x\to a} f(x)g(x)$ and $\lim_{x\to a} f'(x)g'= 0$ converge to different limits.