Mathematica doesn't evaluate my Limit expression

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.

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

1 Answer

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.

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