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]=
> -&#8734;

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

```

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