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MathGroup Archive 1997

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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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