what is sandwhich rule?

The Sandwich Theorem (also known as the Squeeze Theorem or the Pinching Theorem) is a theorem in calculus. It states that if for all x in an interval I, f(x) ≤ g(x) ≤ h(x), and the limits as x approaches a certain value c of f(x) and h(x) are equal, then the limit of g(x) as x approaches c is also equal to that same value.

Here are the steps to use the Sandwich Theorem:

1. Identify three functions f(x), g(x), and h(x) such that f(x) ≤ g(x) ≤ h(x) for all x in an interval around the point c (excluding possibly c itself).

2. Calculate the limit as x approaches c of f(x) and h(x). If these limits are equal, then you can proceed to the next step. If not, then the Sandwich Theorem cannot be applied.

3. Since the limits of f(x) and h(x) as x approaches c are equal, the limit of g(x) as x approaches c is also equal to this value. This is the conclusion given by the Sandwich Theorem.