RE: Re: Limit[Sin[a*x]/(a*x), x -> Infinity]
- To: mathgroup at smc.vnet.net
- Subject: [mg35820] RE: [mg35796] Re: Limit[Sin[a*x]/(a*x), x -> Infinity]
- From: "DrBob" <majort at cox-internet.com>
- Date: Fri, 2 Aug 2002 02:42:12 -0400 (EDT)
- Reply-to: <drbob at bigfoot.com>
- Sender: owner-wri-mathgroup at wolfram.com
There are many values of a for which the limit doesn't exist... a==I and a==0, for instance. You can eliminate the first possibility by setting a=Re[b] where b is unknown, but that still leaves the second possibility, so Mathematica still doesn't find the limit you want. Here's an answer, in which we assume a is greater than or equal to some small delta (surrogate for greater than zero). delta = 10^(-25); a = Abs[b] + delta; Limit[Sin[a*x]/(a*x), x -> Infinity] 0 This also works, though it shouldn't: delta = 10^-25; a = Re[b] + delta; Limit[Sin[a*x]/(a*x), x -> Infinity] 0 Perhaps THIS is the best way to assume a>0: a = Exp[Re[b]]; Limit[Sin[a*x]/(a*x), x -> Infinity] 0 Bobby -----Original Message----- From: JM [mailto:j_m_1967 at hotmail.com] To: mathgroup at smc.vnet.net Subject: [mg35820] [mg35796] Re: Limit[Sin[a*x]/(a*x), x -> Infinity] Sorry for 'refreshing' this message but does anyone know if I can define the assumption below. I don't want to write specific assumptions for each term in Limit since I have many different variables and forms of a. Is it possible to generalise the assumption? it would really help me (and I really don't want to have to buy any additional maths software). timreh719 at yahoo.com.tw (bryan) wrote in message news:<ahdf97$i36$1 at smc.vnet.net>... > Hi All : > I am also interesting in the solution of how to make an asumption > in Mathematica. I can't find any method in Mathematica. If anybody has > the approch to do this , please send it to my e-mail too , Thank you all .. > > j_m_1967 at hotmail.com (JM) wrote in message news:<ah8otr$aut$1 at smc.vnet.net>... > > I know that this should be 0 but why can't I get mathematica to think > > likewise. > > > > > > In[4]:= Limit[Sin[a*x]/(a*x),x->Infinity] > > > > Sin[a x] > > Out[4]= Limit[--------, x -> Infinity] > > a x > > > > Is the problem a? How can I specify the properties of or assumptions > > that may be made about a?