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MathGroup Archive 1994

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Error(?) in Limit Evaluation

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Error(?) in Limit Evaluation
  • From: NATARAJ at ucis.vill.edu (Nat C. Nataraj)
  • Date: Tue, 5 Jul 1994 09:51 EST

Hello Folks!

I am new to Mathematica (although I have used Macsyma for almost ten
years), and the very first thing I tried gave me an erroneous answer.  
It was a definite integral, and quite involved.  After fooling around
for two days, I reduced the possible Mma problem down to the following.

    In: Limit[ArcTan[Tan[x]], x -> Pi/2]

gives
 
    Out: -Pi/2

as the answer, which is of course wrong.  The reason is that tangent
is a multivalued function, and the limit really depends upon the direction
of approach.

However, this limit was buried inside the integral, and Mma did not even 
give me a warning.  The only reason I knew something was amiss was because 
I knew what to expect from the physics of the problem.

By the way, I tried the above on Macsyma, and it gave me `No Limit Exists'
as the answer.

Am I missing something?  Is there some control parameter I should
have set?  Any comments will be most appreciated.

Thanks.

Nat

 -------------------------------------------------------------------
| Dr. "Nat" C. Nataraj                          Off: (610) 519-4994 |
| Department of Mechanical Engineering          FAX: (610) 519-7312 |
| Villanova University                                              |
| Villanova, PA 19085                                               |
|                                                                   |
| e-mail:   nataraj at vuvaxcom (bitnet)                               |
|           nataraj at ucis.vill.edu (internet)                        |
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