Part 1/5:

Understanding the Squeeze Theorem in Calculus

The Squeeze Theorem is a powerful concept in calculus that is useful for finding limits of functions that are difficult to evaluate directly. In this article, we will provide a brief explanation of the Squeeze Theorem and an illustrative example to clarify how it can be effectively applied.

What is the Squeeze Theorem?

The Squeeze Theorem states that if you have three functions, (f(x)), (g(x)), and (h(x)), such that:

(f(x) \leq g(x) \leq h(x)) for all (x) near a point (a) (but not necessarily at (x = a)),
The limits of (g(x)) and (h(x)) as (x) approaches (a) are equal to some limit (L):

[

\lim_{x \to a} g(x) = L \quad \text{and} \quad \lim_{x \to a} h(x) = L,

]

then it follows that:

[