Date: Tue, 29 Jan 2002 18:42:26 -0600 (CST)
From: jr <organism>
Subject: Re: project

e^(t^2/2), being continuous, has an anti-derivative.  just what that 
anti-derivative is, though, can't be described in terms of a finite 
combination of +, -, *, /, log, exp, and sin.  even though you can't get 
such an expression doesn't mean you're stuck: you still have a lot of 
information about the function in its derivative.  you can still make 
graphs of the function from this information, and you can still ascertain 
its behavior as t gets large (what you want in this homework).  a hint: 
you're not quite interested in this anti-derivative in isolation.  in 
determining the behavior of this anti-derivative in combination with 
another function, l'hoptial's rule will be useful.

in finding the value of the solution to the IVP at t=4, you will need to 
employ an approximation.  you can use your direction field to make this 
estimation, a numerical integration scheme, or whatever else you deem 
appropriate (it might be easiest to think graphically here).  please 
be sure to justify your methods!

j


> We have been working on our project and we do not know how to integrate
> e^(t^2/2).  In class you started to explain our problem with example 1;
> however, the bell rang before you could finish.  Is it possible you could
> explain this, or could I somehow make a brief appointment with you.  Thank
> you.