From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik) Subject: Re: functions which are hard to plot Date: 22 Nov 1999 12:22:43 -0500 Newsgroups: sci.math.num-analysis Keywords: headaches for graphic calculators In article <38395507@news.uia.ac.be>, Johan.Vervloet wrote: :Dear all, : :When one tries to plot the function f(x)=log (1-x)/x for x in :[-10^-15, 10^-15], Mathematica (and other programs which use floating :point arithmetic) delivers a plot which is locally 100% erroneous. : :I'm looking for more examples like these; functions which are hard to :plot correctly. : :Thank you. : :Johan :-- In addition to what others suggested, let me mention a modification of a Conte-deBoor example: (x-1)^7, but expanded by the binomial formula: x^7 - 7 * x^6 + 21 * x^5 - 35 * x^4 + 35 * x^3 - 21 * x^2 + 7 * x - 1 in the interval [0.99, 1.01] MATLAB shows dozens of false roots. Also, try 1/x^2 - 1/(sin(x))^2 near 0, with 1/3 as the limit as x goes to 0. Good luck, ZVK(Slavek).