AP Calculus AB Review: Limits

Front

What is a limit in calculus?

Back

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

Front

What does it mean for a limit to exist?

Back

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

Front

What is the limit at infinity?

Back

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

Front

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

Back

Substitute the number directly into the polynomial function.

Front

What is the Squeeze Theorem?

Back

The Squeeze Theorem states that 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.

Front

What is the limit of a constant function?

Back

The limit of a constant function as x approaches any value is the constant itself.

Front

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

Back

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

Front

What is L'Hôpital's Rule?

Back

L'Hôpital's Rule is a method for finding limits of indeterminate forms by taking the derivative of the numerator and denominator.

Front

What does DNE stand for in limits?

Back

DNE stands for 'Does Not Exist', indicating that the limit does not approach a specific value.

Front

How do you evaluate limits using substitution?

Back

To evaluate limits using substitution, replace the variable in the function with the value that x is approaching.