Re: Limit problem
- To: mathgroup at smc.vnet.net
- Subject: [mg51109] Re: Limit problem
- From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
- Date: Tue, 5 Oct 2004 04:36:53 -0400 (EDT)
- References: <cjr9ce$osq$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
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 can't read that output. I think it was supposed to appear as -Infinity. This result may seem surprising at first. However, since we're taking a limit in which both numerator and denominator approach 0, we must have them represented _precisely_; otherwise, we risk getting nonsense, like the output of -Infinity above. Here are two good ways to do essentially what you had intended: In[5]:= Limit[(f[2/5 + h] - f[2/5])/h, h -> 0] Out[5]= 20*Cos[48/25] - (125/12)*Sin[48/25] In[6]:= N[%] Out[6]= -16.631 In[7]:= Limit[(f[x + h] - f[x])/h, h -> 0] Out[7]= (8*Cos[12*x^2])/x - (2*Sin[12*x^2])/(3*x^3) In[8]:= %/. x -> 0.4 Out[8]= -16.631 HTH, David Cantrell > In[4]:= > f'[0.4] > > Out[4]= > -16.631