Out of the many techniques there are for solving limits, the squeeze theorem is a fairly famous theorem that has the ability to evaluate certain limits by comparing with other functions. For those who do not know the squeeze theorem, it states the following:
Let A be some domain containing the point c, and let f, g, and h be defined on this common domain (except possibly at c). Suppose that for every x in A, f(x) ≤ g(x) ≤ h(x). Then, if lim(x → c) f(x) = lim(x → c) h(x) = L, it follows that lim(x → c) g(x) = L.
In this post, I will be going through a simple proof of this theorem using the epsilon delta definition for limits, and will finish with a simple application of this theorem.