I tried to evaluate the following limit:

Limit[Sin[x]^n, n -> Infinity]

However, Mathematica doesn't evaluate it, and just reprints the original problem:

Limit[Sin[x]^n, n -> ∞].

I was expecting as result a function that oscillates between 0 and 1.

  • $\begingroup$ How would you represent such a function in Mathematica? $\endgroup$ – AccidentalFourierTransform Sep 7 '18 at 0:26
  • $\begingroup$ I guess: value: 1 when x = 2kPi+Pi/2, with k=0,1,2,3... and value: 0? otherwise. $\endgroup$ – JohnS Sep 7 '18 at 0:46
  • $\begingroup$ Not in words, but in Mathematica. $\endgroup$ – AccidentalFourierTransform Sep 7 '18 at 1:15

You appear to be assuming in your mind that n is an integer and x is real, but Mathematica makes no such assumption by default. If you were to make these assumptions explicit you will get a result.

Limit[Sin[x]^n, n -> Infinity, Assumptions -> n ∈ Integers && x ∈ Reals]
ConditionalExpression[0, Log[Sin[x]] < 0]

That is not the answer as you conceived it, but it is not unreasonable.

  • $\begingroup$ The condition can be expressed also as the output of Reduce[Log[Sin[x]] < 0, x, Reals] $\endgroup$ – Bob Hanlon Sep 7 '18 at 4:29

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