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seen Sep 23 at 18:11

Jan
31
awarded  Scholar
Jan
31
accepted Calculating a limit with constraints
Jan
29
comment Calculating a limit with constraints
It is weird why my numerical answer differs from your analytical answers (is there maybe a third limit?). With $x=y=10^{-10}, z=1, w=-\sqrt{2 \cdot 10^{-20} + 1^2}$ and 4096 bits precision I still obtain about $ 1 + i $.
Jan
29
awarded  Supporter
Jan
29
comment Calculating a limit with constraints
Thanks for your reply! Maybe it helps if I explain a bit of the context. The formula is used in a numerical program and obviously it is not defined for $(x,y,z,w) = (0,0,-z,z)$. Now my questions basically is: What do I do in this case (there is data that has exactly this form). And now that we have two limits, which one do I choose?
Jan
29
revised Calculating a limit with constraints
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Jan
29
awarded  Student
Jan
29
comment Calculating a limit with constraints
$z$ is a fixed real number and may be negative. If it helps, the denominator is $\sqrt{|w+z|}$.
Jan
29
revised Calculating a limit with constraints
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Jan
29
revised Calculating a limit with constraints
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Jan
29
comment Calculating a limit with constraints
I am really sorry, you're right. I hope my question makes sense now.
Jan
29
revised Calculating a limit with constraints
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Jan
29
awarded  Editor
Jan
29
revised Calculating a limit with constraints
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Jan
29
asked Calculating a limit with constraints