1. AP Calculus BC Chapter 2

2. 2.1 Rates of Change & Limits Average Speed =Instantaneous Speed is at a specific time - derivative Rules of Limits: 1.If you can plug in the value, plug it in. 2.Answer to a limit is a y-value. 3.Holes can be limits. Sandwich Theorem 1 Example: A rock is dropped off a cliff. The equation: Models the distance the rock falls. FIND: 1.The average speed during the 1 st 3 seconds. 2.The Instantaneous speed at t=2 sec.

3. 2.1 cont’d. #1 – slope, #2 – Definition of Derivative Properties of Limits: 1.Sum/Difference 2.Product 3.Constant Mult. 4.Quotient 5.Power GIVEN: 1-sided limits & 2-sided limits Rt. Hand Left Hand Overall Do some examples, including Step-Functions

4. 2.2 Limits involving Infinity Horizontal Asymptote occurs if:H.A. –> y = b Compare Powers: If N(x)=D(x)-> y = coeff. If N(x) y = 0 If N(x)>D(x) -> y = slant (use leading terms) Infinity as an answer: Then, x = a is a V.A. End-Behavior Models: Right & Left End Models

5. 2.3 Continuity Being able to trace a graph without lifting your pencil off the paper. Draw a graph, answer questions. 2-sided limits, 1-sided limits. Continuity at a point: Interior point: Rt.End point: Left End point: Types of Discontinuities Removable Jump Infinite Oscillating A continuous (cts.) function is cts. at every point in its domain. An example of an extended function. Composition of functions. Intermediate Value Thm. for cts. Functions.

6. 2.4 Rates of Change & Tangent Lines Average Rate of Change: (think : SLOPE) Definition of the Derivative: The first derivative will give you the slope of the tangent line at any x-value. Normal Line is perpendicular to the Tangent Line Examples: Find the T.L. and N.L. at x = 1. Long way 