AP Calculus BC Chapter 2. 2.1 Rates of Change & Limits Average Speed =Instantaneous Speed is at a specific time - derivative Rules of Limits: 1.If you.

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AP Calculus BC Chapter 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.

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

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

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.

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 