What's the limit of sin squared (x) as x approaches infinity?

Answer 1

There isn't one. sin² x continues to oscillate between 0 and 1 indefinitely.

Answer 2

In order for a limit of f(x) while x -> infinity to exist, you have to show that the difference between f(x) and your limit will always be less than any arbitrarily small number for ALL x greater than some corresponding arbitrarily large number. Obviously this is impossible in this situation becasue for any number, you can find an infinate number of arbitrarily large x whereby f(x) is at least 1/2 away from that number. So you say this function simply does not tend to a limit as x -> infinity.
You do have to assume, however, that there are numbers smaller that 1/2.

Answer 3

somewhere between 0 and 1. but it doesn't converge to a particular asymptotic value.