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#5670 limit() at a bigfloat point returns ind for a continuous function

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open
nobody
5
2026-10-13
2026-10-13
No

By Claude:

limit(atan(x), x, 1.1b0) returns ind, although atan is continuous at 1.1b0. Both one-sided limits give the right value, and with the float 1.1 the limit is fine:

(%i1) limit(atan(x), x, 1.1b0);
(%o1)                                 ind
(%i2) [limit(atan(x), x, 1.1b0, plus), limit(atan(x), x, 1.1b0, minus)];
(%o2)            [8.329812666744316b-1, 8.329812666744316b-1]
(%i3) limit(atan(x), x, 1.1);
(%o3)                         0.8329812666744317

The two one-sided limits differ in the last bit of the bigfloat, and the two-sided limit treats them as different. The same happens for acos at every bigfloat point, for example limit(acos(x), x, 0.3b0) returns ind while limit(acos(x), x, 0.3b0, minus) returns %pi - 1.875488980810294b0.

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