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]= -∞ In[4]:= f'[0.4] Out[4]= -16.631