Math
Squeeze theorem.
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
Real-world.
- 1 Proving lim(x→0) x²sin(1/x) = 0 by squeezing between −x² and x²
- 2 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.