Pin the limits #231 asked for, including the one still unticked (#231)

[Rafael-SOWNet]

Closes #231.

All three cases answer, including the one still unticked

the issue's list
lim (1 + 1/x)^x as x → +oo	e
lim sin(x)/x as x → 0	1
lim e^x - x as x → +oo	+oo — its box is still unchecked on the issue

Measured rather than read off: this workspace has had recorded verdicts turn out stale seven times, so an old checklist is a hypothesis.

Why tests rather than just closing it

An issue's list is not a test. Closing #231 on three passing examples leaves nothing that fails if one of them stops working — and a limit solver is a search over several methods, where which one answers depends on the shape of the input. Three cases say almost nothing about the capability.

So the file covers twenty, chosen to exercise different paths rather than to be numerous:

• the two remarkable limits with their constants moved — (1 + 2/x)^x → e^2, (1 + 1/x)^(2x) → e^2 — so a rule is applied rather than a value recognised
• indeterminate powers: (1 + 1/x)^(x^2) → +oo
• differences of infinities: x - ln(x), e^x - x^2
• polynomial against exponential, both ways: x^2/e^x → 0, e^x/x^100 → +oo
• a root cancelling a linear term: sqrt(x^2 + x) - x → 1/2
• an oscillation damped by its argument: sin(1/x)·x → 1
• the higher-order expansions: (sin(x) - x)/x^3 → -1/6, (1 - cos(x))/x^2 → 1/2
• (2^x - 1)/x → ln(2), arctan(x) → pi/2

One thing worth stating

x * ln(x) and x^x at zero answer NaN two-sided, and answer correctly — 0 and 1 — one side at a time. That is a decision, not a gap: ln(x) is not real to the left of zero, so there is no two-sided limit to report, and OneSidedLimitTest already records the reasoning.

It is pinned in both directions here, so that "does not answer" and "answers correctly" cannot later be mistaken for one another by someone reading only the two-sided result.

Failed: 0, Passed: 23 on net10.0, against clean master — these pin existing behaviour and depend on nothing else in flight.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura