AP Calculus AB Review: Limits

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

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

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

Substitute the number directly into the polynomial function.

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.

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

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

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

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

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