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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
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