The Squeeze Theorem, also known as the Sandwich Theorem, is a mathematical tool used to find the limit of a function when the limit of another function is known. It is often used to evaluate limits of functions that are difficult to solve directly.
To use the Squeeze Theorem, you must have two functions, f(x) and g(x), where f(x) is always greater than or equal to g(x) and the limit of f(x) and g(x) is the same. Then, the limit of f(x) and g(x) will also be the limit of the squeezed function in between.
The Squeeze Theorem can only be used when the two functions, f(x) and g(x), are close to each other and the limit of both functions exists and is equal. Additionally, the two functions must be defined on the same interval, except possibly at the point where the limit is being evaluated.
Yes, the Squeeze Theorem can be used to find both two-sided and one-sided limits. When using the Squeeze Theorem for one-sided limits, the two functions, f(x) and g(x), must be approaching the same limit from the same side.
The Squeeze Theorem is commonly used in calculus and real analysis to evaluate complex limits. It also has practical applications in physics and engineering, such as finding the velocity of an object or the rate of change of a system.