- #1

MurdocJensen

- 47

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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 x

^{2}sin(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 -(x

^{2}) <= x

^{2}sin(pi/x) <= x

^{2}. 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 each other at some a, then the limit of the bounded function also takes that value at a.