Re: Problem with Limits; basic calculus
- To: mathgroup at smc.vnet.net
- Subject: [mg39077] Re: Problem with Limits; basic calculus
- From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
- Date: Sun, 26 Jan 2003 18:44:27 -0500 (EST)
- References: <b0jfs1$t8q$1@smc.vnet.net> <b0lu3e$4v5$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"David W. Cantrell" <DWCantrell at sigmaxi.org> wrote: I just noticed something strange, closely related to the original question in this thread, which I can't explain. Using version 4.2.0 for Windows: Limit[(Exp[-x]-Exp[-2x])/(Exp[-x]+Exp[-2x]), x-> Infinity] does not give an answer (although the built-in Limit function _should_ of course be able to do so) but, merely using an alternative notation, Limit[(E^(-x)-E^(-2x))/(E^(-x)+E^(-2x)), x-> Infinity] yields, incorrectly, 0 . [The correct answer is 1 .] The reason I think of these notations as alternatives is that both Exp[x] and E^x have FullForm of Power[E, x]. So what's going on? Why does the first not give an answer, while the second gives a wrong answer? BTW, using the Standard Add-on Package Calculus`Limit`, _both_ give the incorrect answer 0 . PLEASE do not respond with "workarounds". I know several already, the easiest of which is to just do the problem in my head! David Cantrell