Squeeze Theorem and Limits

The video tutorial by Mr. Bean introduces the squeeze theorem, also known as the sandwich or pinching theorem, explaining its concept and application in calculus. The tutorial covers the theorem's use in determining limits when a function is squeezed between two others. It includes a detailed example problem, practice problems similar to those on AP exams, and discusses the limitations of the theorem with unbounded functions.

What is another name for the Squeeze Theorem?

• Boundary Theorem

• Graph Theorem

• Limit Theorem

• Sandwich Theorem

In the Squeeze Theorem, which function is always between the other two?

• g

• f

• None of the above

• h

What is the limit of x^2 * cos(1/x^2) as x approaches 0?

• 1

• Undefined

• Infinity

• 0

When applying the Squeeze Theorem, what must be true about the limits of g and h?

• They must be undefined

• They must be different

• They must be equal

• One must be greater than the other

In an AP exam problem, if g(x) < f(x) < h(x) and the limits of g and h are known, what can be said about the limit of f?

• It cannot be determined

• It is equal to the limits of g and h

• It is less than the limit of h

• It is greater than the limit of g

What happens if one of the boundary functions in the Squeeze Theorem is unbounded?

• The limit becomes zero

• The theorem cannot be applied

• The limit becomes infinite

• The theorem can still be applied

What is the behavior of the graph of 1/x as x approaches zero?

• It approaches a horizontal asymptote

• It creates a vertical asymptote

• It remains constant

• It oscillates