The Squeeze Theorem

AP Calculus · Axiom Academy

Find limits of complex functions by sandwiching them between simpler ones Sometimes a function is trapped between two others whose limits we know. We can use this to find the limit of the trapped function. In other words: if g(x) and h(x) squeeze f(x) between them, and both squeeze limits agree, then f(x) must approach that same value. Think of it graphically: if f(x) is always between two curves, and those curves both meet at a point L, then f(x) must reach that point too. This limit is not easy to compute directly. But we can squeeze it:

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