AP Calculus AB Review: Limits

What is a limit in calculus?

• A limit is a value that a function approaches as the input approaches some value.

• A limit is the maximum value a function can reach.

• A limit is the minimum value a function can reach.

• A limit is the difference between two function values.

How do you find the limit of a polynomial function as x approaches a number?

• Substitute the number directly into the polynomial function.

• Take the derivative of the polynomial function.

• Evaluate the polynomial function at x = 0.

• Use L'Hôpital's rule to find the limit.

What is the limit of a constant function?

• The limit is always zero.

• The limit is the constant itself.

• The limit does not exist.

• The limit approaches infinity.

How do you evaluate limits using substitution?

• Replace the variable in the function with the value that x is approaching.

• Use L'Hôpital's rule to find the limit.

• Factor the function and cancel common terms.

• Graph the function and observe the behavior at the limit.

What is a removable discontinuity?

• A point where a function is defined but not continuous.

• A removable discontinuity occurs when a function is not defined at a point, but can be made continuous by defining it at that point.

• A discontinuity that cannot be removed by redefining the function.

• A point where the function approaches infinity.

What is the Squeeze Theorem?

• A theorem that states a function can be evaluated at any point without limits.

• A theorem that states if a function is squeezed between two other functions that have the same limit at a point, then the squeezed function also has that limit.

• A theorem that describes the behavior of functions that are not continuous.

• A theorem that states that limits can only be evaluated from one side.

What is the limit of sin(x)/x as x approaches 0?

• 0

• 1

• undefined

• infinity

What is the limit of a rational function as x approaches a value that makes the denominator zero?

• The limit is always zero.

• The limit may be infinite or may not exist (DNE) depending on the behavior of the function near that point.

• The limit is always a finite number.

• The limit approaches the value of the numerator.

What does it mean for a limit to exist?

• A limit exists if the function approaches a specific value as the input approaches a certain point from both the left and right.

• A limit exists if the function is continuous at that point.

• A limit exists if the function has a defined value at that point.

• A limit exists if the function approaches infinity as the input approaches a certain point.

What is the limit at infinity?

• The limit at infinity refers to the behavior of a function as the input grows without bound.

• The limit at infinity is the maximum value a function can reach.

• The limit at infinity is always zero for continuous functions.

• The limit at infinity is the point where a function becomes undefined.