Talk:L'Hôpital's Rule

first discussion

Let's talk before we fill up the history of this page with a big ol' discussion.

I contend that the limit of f'/g' will exist, so long as the derivatives exist. is this not right?

also, i think that my previous list of categories was overkill (i do that sometimes), but "Limits" is a legitimate category, since they are a part of calculus, AND analysis --Jehan60188 16:55, 4 October 2008 (UTC)

"Limits" is good for me as a category.

I'm racking my memory from many-years-ago study, but I believe that the limit of f/g = limit of f'/'g as long as the limit of f'/g' exists. In practice you often get f'/g' = 0. No problem, just diff again: the limit of f'/g' = limit of f"/g" and so on up the drivs till you get a pair that make sense.

Feel free to get cracking on the calculus, I'm still bogged down in defining the number systems. --Matt Westwood 17:01, 4 October 2008 (UTC)

The limit does not have to exist. Take for instance $f(x)=x+sin(x)$ and take $g(x)=x$. Then the derivatives of $f$ and $g$ will exist, but the limit as $x\rightarrow\infty$ of $\frac{f^'(x)}{g^'(x)}$ will not exist.

As for the categories, I agree, but make sure you separate categories with a ';'. It might also be nice to mention the indeterminate form of the limit and show the other types, which will all reduce to either $\frac{0}{0}$ or $\frac{\infty}{\infty}$. --Joe 17:05, 4 October 2008 (UTC)

Wikipedia and Mathworld both agree that lim f'/g' has to exist, so I'm adding that to the page. -RickettsAM 14:16, 5 October 2008 (UTC)