       unwarranted assumption?

• To: mathgroup at yoda.physics.unc.edu
• Subject: unwarranted assumption?
• From: steves at bnlux1.bnl.gov (stephen e schwartz)
• Date: Mon, 27 Jun 1994 14:29:56 -0400

```Dear Mathgroup

The following expression

Simplify[x*D[x^(1/3)/(k+x^(1/3)), x]/((x^(1/3)/(k+x^(1/3)))*
(1-(x^(1/3)/(k+x^(1/3)))))]

gives the possibly surprising and rather elegant result

Out [] =

1
-
3

[Turns out that this expression approximates dependence of cloud
reflectivity on number concentration of cloud drops]

I was surprised however that mathematica didn't choke on this expression.
My question is how does mathematica know that k is not zero?  I would have
expected mathematica to consider all possible values of k and at least flag
the possibility.

Feel free to knock me over the head if this is a trivial question.  I was
kinda surprised that mma gave me the answer I "expected" instead of a bunch
of red flags.

Generally my experience with mathematica is the contrary; that I would have
had to have told it that k was not zero.

mathematically yours  -steve

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Stephen E. Schwartz                    Phone:     (516) 282-3100
Environmental Chemistry Division       Fax:       (516) 282-2887
Brookhaven National Laboratory         Secretary: (516) 282-3275
Bldg. 426 (51 Bell Ave.) PO Box 5000   Internet:  steves at BNLUX1.BNL.GOV
Upton NY 11973-5000                    Bitnet:    steves at BNLUX1
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```

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