Re: Limit Question
- To: mathgroup at smc.vnet.net
- Subject: [mg66465] Re: Limit Question
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Sun, 14 May 2006 02:58:01 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <e43vun$90e$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Blimbaum, Jerry CIV NSWC PC wrote: > Why do these give no output? > > Simplify[Limit[Exp[-a t],t->Infinity],a>0] > > and same for > > Simplify[Limit[Exp[a t],t->Infinity],a<0] Hi Jerry, First, *Simplify* evaluates its arguments. The assumption 'a > 0' is not passed on to the *Limit* function. Since the limit statement returned unevaluated -- the result depends on the value of the parameter 'a' and *Limit* does nothing about 'a' at this stage -- *Simplify* has nothing to simplify. You can see this process using the *Trace* function (see In[2]). To pass the assumption to the limit statement, wrap it inside an *Assuming* function [1], as in In[3] and In[4]. In[1]:= Limit[Exp[(-a)*t], t -> Infinity] Out[1]= -a t Limit[E , t -> Infinity] In[2]:= Trace[Simplify[Limit[Exp[(-a)*t], t -> Infinity], a > 0]] In[3]:= Assuming[a > 0, Limit[Exp[(-a)*t], t -> Infinity]] Out[3]= 0 In[4]:= Assuming[a < 0, Limit[Exp[(-a)*t], t -> Infinity]] Out[4]= Infinity In[5]:= $Version Out[5]= 5.2 for Microsoft Windows (June 20, 2005) Best regards, Jean-Marc [1] http://documents.wolfram.com/mathematica/functions/Assuming