Barrons AP Calculus

Triangle: Trapezoid: Parallelogram: Circle: C = 2πr; A = πr 2. Circular secto ...

13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. TRIGONOMETRY BASIC IDENTITIES sin^2 θ + cos^2 θ = 1. 1 ...

sin (π + α) = −sin α; cos (π + α) = −cos α. LAW OF COSINES. c 2 = a^2 + b 2 − ...

32. 33. 34. 35. INVERSE TRIGONOMETRIC FUNCTIONS ANALYTIC GEOMETRY Rectangular Coordinates DISTANCE The distance d betwe ...

INTERCEPT FORM. With x- and y-intercepts of a and b, respectively: GE ...

47. 48. 49. 50. 51. 52. Center at (h, k), major axis horizontal, and vertices at (h ± a, k): Center at (h, k), ...

x = r cos θ; y = r sin θ; r^2 = x^2 + y^2 ; SOME POLAR EQUATIONS r = a ci ...

r = sin 2θ. cardioids (specific examples below) r = a (1 ± cos θ). r = a (1 ± sin θ). ...

63. 64. 65. r 2 = cos 2θ, lemniscate, symmetric to the x-axis. (r 2 = sin 2θ is a lemniscate symmetric to ...

FUNCTIONS PROPERTIES INVERSE PROPERTIES f (x) = e x and f −1(x) = ln x are inverses of each other: f −1(f(x)) ...

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ANSWERS EXPLAINED Diagnostic Test Calculus AB Section I Multiple-Choice ...

1. 2. 3. 4. 5. 6. 7. Part A (A) Use the Rational Function Theorem; the ratio of the coefficients of the highest ...

(B) (B) Let . Then f ′ increases for 1 < x < 2, then begins to decrease. ...

y′ = 2(x − 3)−^2 and , y′′ is positive when x < 3. (C) represents the rate of ...

f ′(1) exists and is equal to 2. (B) Since |x − 2| = 2 − x if x < 2, th ...

(A) (B) Separate to get , Since −(−1) = 1 + C implies that C = 0, the solution is . T ...

(A) At x = 3, the equation of the tangent line is y − 8 = −4(x − 3), so f (x) −4(x ...

31. 32. 33. Part B (B) The sign diagram shows that f changes from increasing to decreasing at x = 4 and thu ...

The slope of the secant line is . Find c in [0,1] such that, f ′(c) = e − 2, or f ′(c) − ...