Wikipedia:Reference desk/Archives/Mathematics/2016 January 15

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January 15

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Alzebra

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Solve it (a+b)^4 — Preceding unsigned comment added by 49.126.0.41 (talk) 00:39, 15 January 2016 (UTC)[reply]

There's nothing to solve, but you can expand it to a^4 + 4(a^3)b + 6(a^2)(b^2) + 4a(b^3) + b^4 using the Binomial theorem. --  02:25, 15 January 2016 (UTC)[reply]
From the title, I assumed that this was a strip(p)ed-down problem86.139.120.76 (talk) 12:36, 18 January 2016 (UTC)[reply]

Multivariate Limit

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Let  . Assume that f is continuous at   (the "minus" sign denotes set difference), and that   the limit   exists (and finite). Then, the multivariate limit   exists? 213.8.204.40 (talk) 08:48, 15 January 2016 (UTC)[reply]

I believe the classical counterexample is
 
around the origin .Dmcq (talk) 10:41, 15 January 2016 (UTC)[reply]
Another counterexample is  . Here, not only does the limit   exist, it's the same (0) for all v. But the function is still discontinuous at the origin.
(I've started with the known example   and modified it to be continuous everywhere except the origin. I hope I didn't mess it up.) -- Meni Rosenfeld (talk) 11:24, 15 January 2016 (UTC)[reply]