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Stuff you MUST know Cold for the AP Calculus Exam In the morning of Tuesday, May 3, 2005. AP Physics & Calculus Covenant Christian High School 7525 West.

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Presentation on theme: "Stuff you MUST know Cold for the AP Calculus Exam In the morning of Tuesday, May 3, 2005. AP Physics & Calculus Covenant Christian High School 7525 West."— Presentation transcript:

1 Stuff you MUST know Cold for the AP Calculus Exam In the morning of Tuesday, May 3, AP Physics & Calculus Covenant Christian High School 7525 West 21st Street Indianapolis, IN Phone: 317/ x104 Website: Psalm 111:2 Sean Bird

2 Curve sketching and analysis y = f(x) must be continuous at each: critical point: = 0 or undefined. And dont forget endpoints local minimum: goes (–,0,+) or (–,und,+) or > 0 local maximum: goes (+,0,–) or (+,und,–) or < 0 point of inflection: concavity changes goes from (+,0,–), (–,0,+), (+,und,–), or (–,und,+)

3 Basic Derivatives

4 Basic Integrals

5 More Derivatives

6 Differentiation Rules Chain Rule Product Rule Quotient Rule

7 The Fundamental Theorem of Calculus Corollary to FTC

8 Intermediate Value Theorem. Mean Value Theorem. If the function f(x) is continuous on [a, b], AND the first derivative exists on the interval (a, b), then there is at least one number x = c in (a, b) such that If the function f(x) is continuous on [a, b], and y is a number between f(a) and f(b), then there exists at least one number x = c in the open interval (a, b) such that f(c) = y.

9 If the function f(x) is continuous on [a, b], AND the first derivative exists on the interval (a, b), then there is at least one number x = c in (a, b) such that If the function f(x) is continuous on [a, b], AND the first derivative exists on the interval (a, b), AND f(a) = f(b), then there is at least one number x = c in (a, b) such that f '(c) = 0. Mean Value Theorem & Rolles Theorem

10 Approximation Methods for Integration Trapezoidal Rule Simpsons Rule Simpson only works for Even sub intervals (odd data points) 1/3 ( )

11 Theorem of the Mean Value i.e. AVERAGE VALUE If the function f(x) is continuous on [a, b] and the first derivative exists on the interval (a, b), then there exists a number x = c on (a, b) such that This value f(c) is the average value of the function on the interval [a, b].

12 Solids of Revolution and friends Disk Method Washer Method General volume equation (not rotated) Arc Length * bc topic

13 Distance, Velocity, and Acceleration velocity =(position) (velocity) speed = displacement = average velocity = acceleration = *velocity vector = *bc topic

14 Values of Trigonometric Functions for Common Angles 0–10π,180° 01,90°,60° 4/33/54/553° 1,45° 3/44/53/537°,30° 0100° tan θcos θsin θθ π/3 = 60° π/6 = 30° sine cosine

15 Trig Identities Double Argument

16 Double Argument Pythagorean sine cosine

17


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