Re: Problem with Limits; basic calculus
- To: mathgroup at smc.vnet.net
- Subject: [mg38955] Re: Problem with Limits; basic calculus
- From: atelesforos at hotmail.com (Orestis Vantzos)
- Date: Wed, 22 Jan 2003 06:11:22 -0500 (EST)
- References: <b0jfs1$t8q$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Since Exp[-x] goes to zero as x goes to +infinity, the dominant term is not Exp[-3x]==Exp[-x]^3 but Exp[-x], so 3 is the real value of the limit. Using Simplify on the original expression yields: -1 + 3 Exp[2x] --------------- 1+ 2 Exp[2x] It is clear (use L'Hospital rule for formal proof) that the limit is indeed 3. Finally, by applying FullSimplify we get 1 + 2Tanh[x] and since Limit[Tanh[x],x->inf]==1 we also get 3. Orestis sophtwarez at hotmail.com (David Seruyange) wrote in message news:<b0jfs1$t8q$1 at smc.vnet.net>... > 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