0
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Version 12.0 produces a generic result

Limit[Cos[a*x], x -> Infinity, Assumptions -> a \[Element] Reals]

Indeterminate

and

Limit[Cos[a*x], x -> Infinity, Assumptions -> a \[Element] Reals, GenerateConditions -> True]

Indeterminate

instead of

ConditionalExpression[Indeterminate, a != 0]

and

Limit[Cos[a*x], x -> Infinity, Assumptions -> a \[Element] Reals, GenerateConditions -> None]

Indeterminate

instead of the returned input, though the documentation to the Limit command (see Examples/Options/GenerateConditions there) says

With GenerateConditions->True, even these non-generic conditions are reported

and states that with GenerateConditions->None the command returns unevaluated if the results depend on the value of parameters.

The following commands produce correct results:

Limit[D[Cos[a/x^2], x]*x, x -> 0, Assumptions -> a \[Element] Reals]

Indeterminate

Limit[D[Cos[a/x^2], x]*x, x -> 0, Assumptions -> a \[Element] Reals, GenerateConditions -> True]

ConditionalExpression[Indeterminate, a != 0]

Are these bugs or I'm missing something?

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    $\begingroup$ Not a bug but the documentation wording could be better. As the relevant documentation example shows, only result for the condition that gives the generic case is shown. This effectively implies that the "non-generic conditions are reported". What is not given is the limit (0, in this case) for the non-generic condition. $\endgroup$ – Daniel Lichtblau Mar 22 at 19:26
  • $\begingroup$ @DanielLichtblau: Sorry, don't understand you. $\endgroup$ – user64494 Mar 23 at 10:22
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    $\begingroup$ The only part of my comment that matters is the first three words. $\endgroup$ – Daniel Lichtblau Mar 23 at 14:17

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