[Rafael-SOWNet]

x^x at 0 from the right is 1, but sin(x^x) there came back unevaluated (2.6.0 answered NaN). The rule that reads 0^0, 1^oo and oo^0 through the exponent was only asked of a whole expression. A power inside a function was substituted instead: 0^0 became NaN, and the function above had nothing to work with.

A power in the descent now asks that rule itself, under these conditions:

• One-sided, or at an infinity, as the top level asks it.
• Only where the base is positive on the side approached, so the power is real there.
• Not in the two descents a two-sided limit compares. Read that way, (-x)^x at 0 two-sided would answer 1 while its mirror x^x stays NaN. Which branch each side takes is Read a limit's value at a continuous point before simplifying #2365's open question, and this PR does not answer it. Both stay NaN.
• Not for the whole question. The one-sided path already asks the rule of the whole expression once the descent has nothing to say. Asking it inside the descent too made two slow limits about 60% slower.

Input	2.6.0	master	This PR
sin(x^x), 0 from the right	NaN	unevaluated	sin(1)
cos(x^x), 0 from the right	NaN	unevaluated	cos(1)
sin((x - 1)^ln(x)), 1 from the right	NaN	unevaluated	sin(1)
sin(x^(1/x)), +oo	unevaluated	unevaluated	sin(1)
sqrt(x)/x^pi + x^x, 0 from the right	NaN	unevaluated	+oo

AnInfinityIsNotACoefficientTest recorded the last row as not yet answered, so that test now asserts +oo.

Unchanged: x^x, (-x)^x and sin(x^x) at 0 two-sided stay NaN, and sin(x^x) from the left stays unevaluated.

Measured

• Suite, wrappers, AOT and the harnesses are green.
• limitcheck at DEPTH=3, across 42 seeds against master: 139 more limits are answered, each agreeing with the values, and no answer disagrees.
• One two-sided NaN became a value: 1/abs(x)^x at 0 is 1. Its base is real on both sides, so this is not Read a limit's value at a continuous point before simplifying #2365's question.
• Three rows did not finish in 5 s on this run and did on master's: x^(abs(x)^arctan(2)) at 0 from each side, and one quotient at -1. Timed alone, each takes about 5 s on both builds.

Found by limitcheck; no issue was filed.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 96.42857% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 86.78%. Comparing base (42d1fe9) to head (607d64f).

Files with missing lines	Patch %	Lines
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	88.88%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2381      +/-   ##
==========================================
+ Coverage   86.75%   86.78%   +0.02%     
==========================================
  Files         312      312              
  Lines       69072    69095      +23     
  Branches    20149    20151       +2     
==========================================
+ Hits        59925    59961      +36     
+ Misses       4931     4918      -13     
  Partials     4216     4216              

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.32% <96.42%> (+0.02%)	⬆️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

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Files with missing lines	Coverage Δ
...ns/Continuous/Limits/Solvers/Solvers.Definition.cs	90.29% <100.00%> (+0.60%)	⬆️
...ath/Functions/Continuous/Limits/Transformations.cs	88.40% <ø> (ø)
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	73.91% <88.88%> (+0.35%)	⬆️

... and 6 files with indirect coverage changes

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