Take the 2-minute tour ×  What is the limit as $x\to\infty$ of
$\cos x$?  Thanks in advance.  share|improve this question In
the immortal words of Lindsay Lohan... –  Qiaochu Yuan Jan 19
'11 at 15:21 @Qiaochu: your joke eludes me. Citation please? – 
Willie Wong Jan 19 '11 at 19:18 @Willie:
youtube.com/watch?v=QIMSC-RWvF8 (skip to 7:40 for the problem
and 8:10 or so for its solution). –  Qiaochu Yuan Jan 19 '11 at
19:22 thank you Qiaochu! Damn that was worth wasting 9 minutes
of my life! –  Arjang Jan 21 '11 at 8:50 add comment  4 Answers
The limit does not exist. It oscillates between -1 and 1. Just
so that you know, the limit supremum or infimum as $x \to
\infty$ is given as  $$\lim \sup_{x\to\infty} \cos(x) = 1$$
$$\lim \inf_{x\to\infty} \cos(x) = -1$$  share|improve this
answer add comment  The limit does not exist because $\cos{(2\pi
n)} = 1$ for $n \in \mathbb{Z}$ and $\cos{(\pi + 2 \pi n)} = -1$
for $n \in \mathbb{Z}$.  share|improve this answer add comment
There is no limit, $\lim_{x \to \infty} \co