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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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