       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:=
> Clear[f,h,x]
>
> In:=
> f[x_]:=Sin[12*x^2]/(3*x^2)
>
> In:= Limit[(f[0.4 + h] - f[0.4])/h, h -> 0]
>
> Out=
> -&#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:= Limit[(f[2/5 + h] - f[2/5])/h, h -> 0]

Out= 20*Cos[48/25] - (125/12)*Sin[48/25]

In:= N[%]

Out= -16.631

In:= Limit[(f[x + h] - f[x])/h, h -> 0]

Out= (8*Cos[12*x^2])/x - (2*Sin[12*x^2])/(3*x^3)

In:= %/. x -> 0.4

Out= -16.631

HTH,
David Cantrell

> In:=
> f'[0.4]
>
> Out=
> -16.631

```

• Prev by Date: Re: Print with limited precision
• Next by Date: keymap and mouse problems with 5.0 frontend under linux
• Previous by thread: Re: Limit problem
• Next by thread: Re: Limit problem