Discontinuity

*To*: mathgroup at smc.vnet.net*Subject*: [mg6416] Discontinuity*From*: Larry.Smith at clorox.com (Larry Smith)*Date*: Tue, 18 Mar 1997 22:16:28 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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