[Rafael-SOWNet]

Found while checking a limit limitcheck reported. No issue was filed.

at 0	2.6.0 and master	now
(sin(x)/x)^2	NaN	1
exp(sin(x)/x)	NaN	e
limitright(exp(sin(x)/x), x, 0)	unevaluated	e
sin(sin(x)/x)	NaN	sin(1)
exp((cos(x) - 1)/x^2)	NaN	e ^ (-1/2)
sin(x)/x, exp(x/x), (2^x - 1)/x	1, e, ln(2)	unchanged

A function of a quotient took the quotient's limit from the descent alone. The descent reads 0/0 or oo/oo off the two parts as NaN, the claim that there is no limit, where it only cannot tell. The whole limit reaches sin(x)/x = 1 through the first remarkable limit, but a function wrapped round it never asked the whole limit. Sums and products of it already worked.

The change. Where a quotient's descent would return NaN for an indeterminate form and nothing else answers, the quotient's whole limit is asked once, and only a value is taken; otherwise what was answered is kept. So the change can turn a NaN from 0/0 or oo/oo into a value, and nothing else. Three things keep it from costing what it answers, each found by the suite:

• One level. No whole limit is asked inside another.
• Not under a caller's budget of limits (remainingLimits), which it would spend.
• The form is folded. A limit can come back holding the infinity it was taken at: -4/9 * 0 * (1 - (1 + (1/+oo)^2)^(1/3)) for a quotient in a definite integral's antiderivative. Handed on as written, it left integral(1/((1 + x^2)^(1/3) (9 + x^2)), x, -1, 1) unevaluated after two minutes, where master gives it in 4 s. Folded, that form is 0, and ln(2) * 2^(1/+oo) is ln(2). A form is taken as its number only where an infinity is still in it.

limitcheck at SEED=14 and 16, and at DEPTH=3 on 19 and 23 (the last rebased onto #2357), gains cos(sin(x)/x), (x/arctan(x))^3 and 1/(x/abs(x)) at 0 from each side, each agreeing with the values. It has the same number of limits of another value as master on every seed, and fewer NaNs where the values settle. 4180 limit and integration tests pass.

Still NaN, and not reached by this: the 1^oo powers (cos(x))^(1/x^2) and (sin(x)/x)^(1/x^2), which take the indeterminate-power route.

Tests: AFunctionOfAnIndeterminateQuotientTest, 8 cases. 6 fail on master; the 2 controls pass on both. The full suite, AOT and the nine harnesses pass. There is a BREAKING-CHANGES entry, measured on 2.6.0.

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[codecov]

Codecov Report

❌ Patch coverage is 81.81818% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.78%. Comparing base (f86d0a2) to head (dadaaf4).

Files with missing lines	Patch %	Lines
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	80.95%	2 Missing and 2 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2358      +/-   ##
==========================================
+ Coverage   86.76%   86.78%   +0.02%     
==========================================
  Files         312      312              
  Lines       68786    68807      +21     
  Branches    20039    20045       +6     
==========================================
+ Hits        59679    59712      +33     
+ Misses       4923     4910      -13     
- Partials     4184     4185       +1     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.32% <81.81%> (+0.02%)	⬆️
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
...ns/Continuous/Limits/Solvers/Solvers.Definition.cs	90.86% <100.00%> (+0.04%)	⬆️
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	73.33% <80.95%> (+0.53%)	⬆️

... and 7 files with indirect coverage changes

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