[Rafael-SOWNet]

1/abs(x) at 0 was NaN, which claims the limit does not exist. It is +oo, and 2.6.0 says NaN too.

The sign a vanishing divisor keeps was read off its derivatives. The derivative of abs(x) is sgn(x), 0 at 0, and there is nothing after it. So each side was left unevaluated, and the two descents not matching made the two-sided limit NaN.

An absolute value is now never negative by its form, and so is a real power, product or quotient of such things. A divisor of that kind vanishes from above, and a power of it to an exponent tending to a negative number tends to +oo.

Two sides that agree are promoted to the two-sided limit only for an expression shown real on both sides. That check knew nothing of an absolute value, a sine, a cosine, an arctangent or an arcsine, nor of a real power of something never negative. So sin(arcsin(x)) * (tan(-1) + 2/x), which is 2 from each side, was NaN, and sqrt(x^2)^(-3/2), which is +oo, was NaN too. Those are read now. Where the sides differ, as for x / abs(x), the limit is still NaN. The test pins five such cases, including the x^x convention.

One cost had to be paid back. Reading the sine and cosine as real makes tan(x/2) at pi real on both sides. Each time, it then asked its two sides in full again, though the descent had already answered them +oo and -oo. The one-sided path returns the descent's value first, so asking again can only give the same pair. The definite integral of 1/(2 + cos(x)) over [0, pi] ran out of its budget of limits on that. Both sides are now asked again only where one of them came back NaN.

limitcheck, DEPTH=3, seeds 14, 16, 19, 23, 26 and 29, against master 53ce725:

	master	this branch
compared	30 980	30 987
the limit is NaN where the values settle	79	75
the limit is another value	7	7

Every answer that changed is recorded in BREAKING-CHANGES.md. Suite, AOT and the harnesses are green locally.

Found by limitcheck at SEED=29; no issue was filed.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 81.81818% with 6 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.79%. Comparing base (53ce725) to head (76468fc).

Files with missing lines	Patch %	Lines
...ns/Continuous/Limits/Solvers/Solvers.Definition.cs	80.00%	2 Missing and 2 partials ⚠️
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	66.66%	0 Missing and 1 partial ⚠️
...ath/Functions/Continuous/Limits/Transformations.cs	90.00%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2364      +/-   ##
==========================================
- Coverage   86.79%   86.79%   -0.01%     
==========================================
  Files         312      312              
  Lines       68825    68855      +30     
  Branches    20053    20063      +10     
==========================================
+ Hits        59735    59761      +26     
- Misses       4907     4910       +3     
- Partials     4183     4184       +1     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.33% <81.81%> (-0.01%)	⬇️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	75.36% <66.66%> (+1.73%)	⬆️
...ath/Functions/Continuous/Limits/Transformations.cs	88.29% <90.00%> (+<0.01%)	⬆️
...ns/Continuous/Limits/Solvers/Solvers.Definition.cs	89.67% <80.00%> (-1.62%)	⬇️

... and 6 files with indirect coverage changes

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