Squeeze Theorem

Updated April 3, 2021

Example:

Sal always eats ≥ calories than Alex, and Sal always ≤ calories than Bill.

On Tuesday, Alex ate 300 calories and Bill ate 300 calories. The Squeeze Theorem says that Sal ate 300 calories on Tuesday (Sal is squeezed between Alex and Bill).

Rigorous description:

g(x)f(x)h(x)g(x) \leq f(x) \leq h(x)
limxag(x)=L\lim_{x \to a} g(x) = L
limxah(x)=L\lim_{x \to a} h(x) = L

The Squeeze Theorem tells us that:

limxaf(x)=L\lim_{x \to a} f(x) = L