Squeeze theorem

Math

Definition

A theorem stating that if a function g(x) is trapped between two other functions f(x) and h(x) near a point, and f and h have the same limit L at that point, then g must also have limit L. It is especially useful for limits involving oscillating functions.

Examples

  • Proving lim(x→0) x²sin(1/x) = 0 by squeezing between −x² and x²
  • Proving lim(x→0) sin(x)/x = 1 using the squeeze theorem with geometric areas
Key Fact

If f(x) ≤ g(x) ≤ h(x) and lim f(x) = lim h(x) = L, then lim g(x) = L.

Related Terms

Limit definition Continuity Ivt

Study This Concept

Practice squeeze theorem with free review games in these units:

AP Calculus AB Unit 1: Limits and Continuity