Re: One to the power Infinity
- To: mathgroup at smc.vnet.net
- Subject: [mg36037] Re: One to the power Infinity
- From: Selwyn Hollis <slhollis at earthlink.net>
- Date: Tue, 13 Aug 2002 05:23:00 -0400 (EDT)
- References: <aitfon$cfu$1@smc.vnet.net> <aj01qv$18l$1@smc.vnet.net> <aj17ad$2kh$1@smc.vnet.net> <aj5bfk$abr$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
All I can say about my last post on this topic is: Nevermind. I was looking at the graph of Abs[(1-x)^(1/x^2)] near 1 instead of 0. Aargg. Mathematica's answers (Infinity) for both Limit[Abs[(1-x)^(1/x^2)], x->0, Direction-> +1] and Limit[Abs[(1-x)^(1/x^2)], x->0, Direction-> +1] are correct. --- Selwyn Selwyn Hollis wrote: >>Selwyn Hollis <slhollis at earthlink.net> wrote: > > Actually it seems you've discovered a bug in Limit. If we allow complex > values, then Limit[(1-x)^(1/x^2), x->0, Direction-> +1] should be 0, > which is evident from the graph of Abs[(1-x)^(1/x^2)]. Mathematica gives > Infinity for Limit[Abs[(1-x)^(1/x^2)], x->0, Direction-> +1] as well. If > we don't allow complex values, then Limit[(1-x)^(1/x^2), x->0, > Direction-> +1] can't exist at all (even as Infinity or -Infinity). > >