3
$\begingroup$

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.

  • 0
    The "other techniques" come out on a case-to-case basis...2011-10-01

1 Answers 1

5

I was wondering does it have anything to do with 0/infinity or infinity/0?

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 $g(x)/f(x)=x/(1/x)=x^2\to \infty.$

  • 0
    @J.M. Th$a$nks! (I have corrected it).2011-10-01