# indeterminate form intuition

I'd been reading about indeterminate forms for some time, so it became quite intuitive to me that $$(\rightarrow 0 )\cdot( \rightarrow \infty), \quad (1)$$ is indeterminate.

But then I came across this $$\frac {\rightarrow 0}{\rightarrow \infty}, \quad (2)$$ which my book tells me is determinate and is equal to $$(\rightarrow 0)$$. To me, it seems that the intuition I developed to explain myself why $$(1)$$ is determinate tells me that $$(2)$$ can't be determinate.

Can someone give an intuitive explanation as to why these two forms/expressions are indeterminate and determinate, respectively?

As opposed to if you take something small and multiply by something large. That could be either small, large, or in-between, depending on how small the small thing is and how large the large thing is. This is what makes $$(\to0)\cdot(\to\infty)$$ indeterminate.