mary, a parent:
i was trying to find the limit of this problem
the limit as x approches infinity of x minus cosx divided by x
For any x, -1 ≤ cos x ≤ 1 and hence -1/x ≤ cosx/x ≤ 1/x
lim -1/x = lim 1/x = 0 as x -> infinity and hence you can apply the sandwich theorem.