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MathGroup Archive 1993

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Re: conditional limits

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: conditional limits
  • From: belopols at marie.mit.edu (Alexander Belopolsky)
  • Date: Tue, 7 Sep 1993 14:28:58 -0400

>   I have a function of two variables, f[x, y], which when evaluated for values of
>   x=y results in:
>						  1
>		 Power::infy: Infinite expression -- encountered.
>						  0.              
>
>   As there is an (x-y) term in the denominator of the function.  However,
>   the Limit[f[x,y], x-y] does exist, and evaluates to a finite number.
>
>
>   The question is, how do I construct a rule that conditionally evaluates
>   the limit of f[x,y] rather than f[x,y] whenever x=y?

Here is my solution:
In[1]:= f[x_,y_]:=Sin[x-y]/(x-y)

In[2]:= f[3,3]

                                 1
Power::infy: Infinite expression - encountered.
                                 0

Infinity::indet: Indeterminate expression 0 ComplexInfinity encountered.

Out[2]= Indeterminate

In[3]:= f[x_,x_]:=Limit[f[x,y],y->x]

In[4]:= f[3,3]

Out[4]= 1







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