The Squeeze Theorem is a method for finding the limit of a function that's trapped between two other functions with known limits.
Imagine you have three functions: f(x), g(x), and h(x).
If f(x) ≤ g(x) ≤ h(x) for all x near a point, and the limits of f(x) and h(x) as x approaches that point are equal, then the limit of g(x) must be the same.
The mechanism here is straightforward: the 'squeezed' function inherits the limit of its 'bounding' functions.
The difficulty arises in setting up the problem correctly.
You might struggle to identify suitable bounding functions or prove the necessary inequalities.
Another trap is assuming the theorem applies without checking all conditions, especially continuity at the point of interest.
Misapplying the theorem leads to incorrect limits, and those errors can cascade through more complex problems.
Precision in setup is not optional — it's the only way this theorem works.