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Possible error? Simple Limit discrepancy between W|A and Mathematica

Agustin Covarrubias
Posted 6 years ago

The error

It's very straight-forward; the same piece of code (presumably interpreted the same way between both) outputs a different answer. I did the limit with polar coordinates and the answer is, indeed, 1/4. If you know what may have happened here, let me know.
POSTED BY: Agustin Covarrubias
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Possibly Alpha is running an older version that does not have more recent methods for handling multivariate limits.
POSTED BY: Daniel Lichtblau

Have you guys at Wolfram recently created methods for multivariate limits? When?
POSTED BY: Agustin Covarrubias

When I called Wolfram|Alpha it gave the answer 1/4. You can check that it is correct with an estimate:

f[x_, y_] = (x^2*(1 + Sin[y]) + y^2)/(4 x^2 + 4 y^2);
Plot3D[f[x, y],
 {x, -1, 1}, {y, -1, 1}]
Reduce[RealAbs[f[x, y] - 1/4] <= RealAbs[x]/8, Reals]
POSTED BY: Gianluca Gorni

I pasted the query once again on the W|A web app, and it still returns the same answer query

Thanks for your answer, but my main concern is not about the limit itself, which can be easily calculated via the polar coordinates method I mentioned. My concern is that the same code (presumably interpreted the same way) gave back very different answers between Wolfram Mathematica and W|A.
POSTED BY: Agustin Covarrubias
Bill Nelson
Bill Nelson
Posted 6 years ago
POSTED BY: Bill Nelson
POSTED BY: Agustin Covarrubias 
Limit[(x^2*(1 + Sin[y]) + y^2)/(4 x^2 + 4 y^2), {x, y} -> {0, 0}]
POSTED BY: Agustin Covarrubias

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