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----