The Squeeze Theorem, also known as the Sandwich Theorem, is a fundamental concept in calculus that states that if a function is sandwiched between two other functions that have equal limits, then the original function also has the same limit as the bounds.
The Squeeze Theorem can be used to prove the limit of a function indirectly, i.e. without having to evaluate the limit directly. By finding two other functions that bound the original function, and showing that the limits of those functions are the same, one can conclude that the limit of the original function is also that value.
The Squeeze Theorem is a powerful tool that can be used to prove a wide variety of limits in calculus. It is a key concept in understanding the behavior of functions as x approaches a certain value and is used in many branches of mathematics, including analysis and differential equations.
In conclusion, the Squeeze Theorem states that if a function is sandwiched between two other functions that have equal limits, then the original function also has the same limit as the bounds. It is a powerful tool to prove limits of function by bounding it with two other known limit functions.