Question

Squeeze Theorem In your own words, explain the Squeeze Theorem.

Short answer

The Squeeze Theorem in calculus states that if a function is 'squeezed' between two other functions that converge to the same limit at a certain point, then the squeezed function must also converge to the same limit. Think of it as a car trapped between two other cars on a highway. If the front and back cars slow down simultaneously, the middle car also has to slow down to avoid collision.

Step-by-step solution

Understanding the Squeeze theorem

The Squeeze Theorem is a concept in calculus which states that if function f is 'squeezed' between two other functions g and h at a certain point, and if g and h converge to the same limit at that point, then the squeezed function f must also converge to the same limit.

Breaking Down the Theorem

On the number line, if you have three points a, b, and c such that a <= b <= c, then you can say that b is squeezed between a and c. In the Squeeze Theorem, instead of points on a line, we have functions on a graph. If function f(x) is always between functions g(x) and h(x) and if g(x) and h(x) converge to the same limit when x approaches a certain value, then f(x) must also converge to the same limit.

Relating Squeeze Theorem to Real Life

A real-life scenario for the Squeeze Theorem could be a car trapped in between two other cars on a highway all moving at the same speed. If the cars in front and back decide to simultaneously slow down, assuming the car in the middle doesn't want to collide, it has to also slow down to the same speed.