Question

lim(x->2 pi) (ceil(cosx))

Answer 1

Well, \(\cos(2\pi) = 0\), so if you take your right and left hand limits, you're going to have:
\[ \Large
\lim_{x\rightarrow 2\pi^-}\cos(x) = -1
\]\[\Large
\lim_{x\rightarrow 2\pi^+}\cos(x) = 1

\]What does that tell you about the limit?