RE: Problem with Limits; basic calculus
- To: mathgroup at smc.vnet.net
- Subject: [mg38942] RE: [mg38952] Problem with Limits; basic calculus
- From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
- Date: Wed, 22 Jan 2003 06:09:42 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
>-----Original Message----- >From: sophtwarez at hotmail.com [mailto:sophtwarez at hotmail.com] To: mathgroup at smc.vnet.net >Sent: Tuesday, January 21, 2003 1:40 PM >To: mathgroup at smc.vnet.net >Subject: [mg38942] [mg38952] Problem with Limits; basic calculus > > >Hey all - I'm taking a basic calculus course that uses Mathematica. >We have been studying limits and I have been using the Limit function >to check if my answers are correct. >We were given the following function and asked to determine a limit: >(3E^(-x) - E^(-3x)) / (E^(-3x) + E^(-x)) > >Usually the approach is to select the dominant terms, factor and then >determine the limit. My initial reason had me select -E^(-3x) in the >numerator and E^(-3x) in the denominator. Factoring the terms would >yield -1, thus the limit for x->infinity. But I plotted the function >and the real answer is somewhere near 3. >I then tried to use the Limit function which is not producing an >answer (perhaps I'm not sure of the usage). > >Any help is greatly appreciated, > >David Seruyange > David, as you told, factor and determine the limit: In[1]:= expr = (3E^(-x) - E^(-3x))/(E^(-3x) + E^(-x)); In[9]:= Limit[expr, x -> -Infinity] Out[9]= -1 In[10]:= Limit[Factor[expr], x -> Infinity] Out[10]= 3 You might be interested in the identity In[11]:= Factor[expr] === Together[TrigToExp[2Tanh[x] + 1]] Out[11]= True What you have to look for is the appropriate form to "simplify". -- Hartmut Wolf