How do you evaluate the limit sin(x^2) as x approaches oo?

1 Answer
Jan 21, 2017

This limit doesn't exist. Explanation below.

Explanation:

sin x constantly changes, taking values between 1 and -1 and back ("oscillates") as x increases. sin x^2 also has this oscillation effect, only the graph is a little different, and in fact, it oscillates more rapidly as x approaches infinity, since the rate of change of x^2 also increases. Because of that, since sin x^2 neither goes unbounded, nor does it approach a set value as x approaches infinity, its limit at infinity doesn't exist.