The Squeeze Theorem is a method for finding the limit of a function when direct evaluation is impossible.
It works by pinning the function between two others that have known limits at a particular point.
If both bounding functions converge to the same limit, the squeezed function must also converge to that limit.
This mechanism relies on the inequality: if f(x) ≤ g(x) ≤ h(x) for all x near a point, and if the limits of f(x) and h(x) as x approaches that point are equal, then the limit of g(x) is the same.
The tricky part is identifying suitable bounding functions.
You might think you can always use simple functions, but sometimes you need creative choices or trigonometric identities.
The cognitive trap is assuming any two functions will work without checking the limit conditions.
If your bounding functions don't converge to the same value, the theorem doesn't apply, and you're left with an unsolved problem.