This is what I want to say: The squeeze theorem may be used when direct substitution and factoring (or simplification of any sort) doesn't help in finding a limit. An example would be lim x->0 of x2sin(pi/x). Limit laws wouldn't work and we can't simplify the expression. What we can do is recognize -1<= sin(pi/x)<= 1, so -(x2) <= x2sin(pi/x) <= x2. According to the squeeze theorem, if the function in question is bounded by two other function at x near a, and the lmits of these bounding functions equal eachother at some a, then the limit of the bounded function also takes that value at a.