Question

state and proof squeeze principle​

Answer 1

The squeeze (or sandwich) theorem states that if f(x)≤g(x)≤h(x) for all numbers, and at some point x=k we have f(k)=h(k), then g(k) must also be equal to them. We can use the theorem to find tricky limits like sin(x)/x at x=0, by "squeezing" sin(x)/x between two nicer functions and using them to find the limit at x=0.

Answer 2

Answer:

The squeeze theorem is used in calculus and mathematical analysis. It is typically used to confirm the limit of a function via comparison with two other functions whose limits are known or easily computed.

Theorem 0.1 (The Squeeze Theorem). Suppose that g(x) ≤ f(x) ≤ h(x) for all x in some open interval containing c except possibly at c itself. If limx→c g(x) = L = limx→c h(x) then limx→c f(x) = L. Proof.