Re: Problem with Limits; basic calculus
- To: mathgroup at smc.vnet.net
- Subject: [mg38938] Re: Problem with Limits; basic calculus
- From: Tom Burton <tburton at brahea.com>
- Date: Wed, 22 Jan 2003 06:09:30 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Clean those wiper blades :) For large positive x, the dominant term is E^(-x), hence 3. I'm not sure why Mathematica cannot find the limit directly of your expression, but if you Simplify first, you do indeed get 3. Tom Burton On 1/21/03 4:53 AM, in article b0jfs1$t8q$1 at smc.vnet.net, "David Seruyange" <sophtwarez at hotmail.com> wrote: > 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