Help me understand limits

Good day

I'm currently doing some math homework (don't worry I won't ask anyone to solve anything) and I don't think I'm understanding limits correctly. More precisely how the l'Hôpital rule works.

I know I can/should be able to apply it if it is either $\infty/\infty$ or $0/0$ but I was wondering does it have anything to do with $0/\infty$ or $\infty/0$?
Anything you think might help me better understand limits would be appreciated.

P.S. I'm sorry if this is a simple question, math is not my strongest point.

• No, you don't use l'Hôpital on anything you can't reduce to the indeterminate $0/0$ or $\infty/\infty$ cases. Usually other techniques will be much more transparent than l'Hôpital anyway. Commented Oct 1, 2011 at 14:47
• Can you name the other techniques? And can I assume that if I have a limit of a function f(x) that is 0/infinity that it is just 0? Commented Oct 1, 2011 at 15:01
• The "other techniques" come out on a case-to-case basis... Commented Oct 1, 2011 at 15:16

No, because $0/\infty$ and $\infty/0$ are not indeterminate cases. Symbolically one can write $0/\infty=0\times 0=0$ and $\infty/0=\infty\times \infty=\infty$ (without sign).
For instance, the function $f(x)=1/x\to 0$ (as $x\to \infty$) and the function $g(x)=x\to \infty$, (as $x\to \infty$). And we have, as $x\to \infty$, $$f(x)/g(x)=(1/x)/x=1/x^2\to 0$$ and $$g(x)/f(x)=x/(1/x)=x^2\to \infty.$$