Math

AP Calculus AB: Semester Review Notes Name: ____________________Per____

Information in the box are MASTERY CONCEPTS.

Be prepared to apply these concepts on your final.

I. Limits and Continuity

Definition of Average Rate of Change (…Slope)

The average rate of change of [pic] from x to x+h is [pic] Geometrically the average rate of change is the slope of the secant line. …slope formula

If [pic]is the position function of a particle that is moving on a straight line, then the average velocity of the particle over the time interval a < time < a+h is

Average velocity = [pic]

Example #1: The displacement of a particle moving in a straight line is given by the equation of motion [pic]. Find the average velocity of the particle over the time interval 0 < t < 5.

Definition of One-Sided Limits & The Existence of a Limit

The right-hand limit means that x approaches c from values greater than c. [pic]

The left-hand limit means that x approaches c from values less than c. [pic]

The limit of [pic] as x approaches c is L if and only if the right and the left hand limits are both equal to L.

Limits that FAIL to Exists

|The left and the right hand limits are NOT EQUAL.|The y-values increase without bound. |The y-values oscillate infinitely between y = -1 to|

|[pic] |[pic] |y = 1 |

| | |[pic] |

Definition of Continuity

A function f is continuous at c if the following three conditions are met.

(1) [pic] (1) The y-value exists at x = c

(2) [pic] (2) The limit exists as x approaches c

(3) [pic] (3) The limit equals the...