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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
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