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

$\sin x$ 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.