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MathGroup Archive 1997

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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)
----ooO-(_)-Ooo----


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