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 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -