Re: Limit problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg51130] Re: Limit problem*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Tue, 5 Oct 2004 04:37:29 -0400 (EDT)*Organization*: The University of Western Australia*References*: <cjr9ce$osq$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <cjr9ce$osq$1 at smc.vnet.net>, Mike Zeitzew <pdop at yahoo.com> wrote: > Why is Limit giving me the wrong answer for this simple divided difference? > I am using 5.0.1.0 / > XP > > In[1]:= > Clear[f,h,x] > > In[2]:= > f[x_]:=Sin[12*x^2]/(3*x^2) > > In[3]:= Limit[(f[0.4 + h] - f[0.4])/h, h -> 0] > > Out[3]= > -∞ I assume that this output is -Infinity under XP? > In[4]:= > f'[0.4] > > Out[4]= > -16.631 Instead of computing the limit using Limit, have a look at the output of (f[0.4 + h] - f[0.4])/h + O[h] Now compare this with (f[a + h] - f[a])/h + O[h] In the first case you will see that, due to round-off error, the first term in the series expansion, involving 1/h, is not identically zero, and it is this term that leads to the limit of -Infinity. Note: adding an order term, O[h], coerces the input to a Maclaurin series expansion in h. You can, of course, use Series instead: Series[(f[a + h] - f[a])/h, {h, 0, 0}] In general, I find that using Series is preferable to using Limit. Cheers, Paul -- Paul Abbott Phone: +61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul