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MathGroup Archive 2004

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Re: Limit problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51107] Re: [mg51098] Limit problem
  • From: "David Park" <djmp at earthlink.net>
  • Date: Tue, 5 Oct 2004 04:36:51 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Mike,

I don't know why Mathematica didn't get that limit. But quite often, with
functions like Limit or Solve, Mathematica does much better with exact
expressions, or with symbolic expressions where values are substituted
later.

f[x_] := Sin[12*x^2]/(3*x^2)

Limit[(f[4/10 + h] - f[4/10])/h, h -> 0]
% // N
20*Cos[48/25] - (125/12)*Sin[48/25]
-16.631

Or...

Limit[(f[x + h] - f[x])/h, h -> 0]
% /. x -> 0.4
(8*Cos[12*x^2])/x - (2*Sin[12*x^2])/(3*x^3)
-16.631

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/





From: Mike Zeitzew [mailto:pdop at yahoo.com]
To: mathgroup at smc.vnet.net

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]=
-&#8734;

In[4]:=
f'[0.4]

Out[4]=
-16.631




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