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mathematica gets a simple limit wrong?


Could anyone explain the following output of mathematica 4.0:

In[]:= 1+Limit[a-Sqrt[a^2-a],a->Infinity]
Out[]:= 3/2

In[]:=Limit[1+a-Sqrt[a^2-a],a->Infinity]
Out[]:= 1  ????!!!!!!!!!!!


Huh? I just moved the 1 inside the brackets and got a wrong answer?
Makes me wonder about mathematica.

bye,

D.


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