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Re: Discontinuity
*To*: mathgroup at smc.vnet.net
*Subject*: [mg6437] Re: Discontinuity
*From*: Pasquale Nardone <pnardon at ulb.ac.be>
*Date*: Fri, 21 Mar 1997 22:59:21 -0500 (EST)
*Organization*: Université Libre de Bruxelles
*Sender*: owner-wri-mathgroup at wolfram.com
Larry Smith wrote:
>
> I have the following function which is defined as:
>
> f(t)=t +10t^2 Sin[1/t]
>
> When you take the derivative of this function and evaluate it at
> f'[0] it is indeterminate at t=0, I would like to adjust the function
> so that the function is differentiable at t=0. I'm trying to state a
> function y=f(t) such that f'(0)=1 but t is not a function of y in any
> neighborhood of 0. If you look at the plot of the derivative like
>
> Plot[Evaluate[D[f[t],t],{t,-.02,-0.01}]] or
> Plot[Evaluate[D[f[t],t],{t,-.002,-0.001}]] where
> f[t] is defined as f[t_]:=t-10t^2Sin[1/t].
>
> I want to use the function as defined and adjust it so that I get a
> derivative of 1 at f'(0) without using a step function.
>
> Larry
>
> 601-939-8555 extension 255
>
> larry.smith at clorox.com
Why don't you try the following
f[t_]:=t +10t^2 Sin[1/t]
g[t_]=D[f[t],t]
hh[t_]:=g[t]/;(t>0 || t<0);
hh[0]:=1;
hh[0.0]:=1;
then you can Plot what you want:
Plot[hh[x],{x,-1,2}]
--------------------------------------------
Pasquale Nardone *
*
Université Libre de Bruxelles *
CP 231, Sciences-Physique *
Bld du Triomphe *
1050 Bruxelles, Belgium *
tel: 650,55,15 fax: 650,57,67 (+32,2) *
http://homepages.ulb.ac.be/~pnardon/ *
,,,
(o o)
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