Barrons AP Calculus

(B) , so v = 3t^3 + c. Since v = 1 when t = 0, c = 1. Now , so s = t^3 ...

(B) The velocity is graphed in [−1,11] × [−15,5]. The object reverses direction when th ...

43. 44. 45. so apply L’Hôpital’s Rule. You get , which is still of the form ; therefore, apply L’Hôpital’s ...

AB/BC 1. (b) (c) (d) AB 2. Part A (a) (Review Chapter 3) After 15 minutes the rate at which grain is leaking ...

(a) (b) (c) The object moves to the left when the velocity is negative, namely, on the interval p & ...

AB/BC 3. (b) (c) (d) (e) AB 4. (b) Part B (a) The average value of . The line tangent to the graph of A at x ...

(c) AB/BC 5. (b) (c) At Q = (4,4) the curve has a local maximum because y′ = 0 and y′′ < 0. (Review Cha ...

AB 6. (b) (Review Chapter 7) (a) The differential equation is separable: If y = 0 when x = 2, then ...

7. 9. 12. 15. 18. 19. Part A (B) The volume is given by , an improper integral. (D) . Series fails the nth Term ...

(B) Since function f is increasing on the interval [2,6], rectangles based on left endpoints of t ...

31. 32. 33. 34. Part B (A) Use the Ratio Test: which equals zero if x ≠ 1. The series also converges if x ...

(here R = 4 and r = sec x). Symmetry allows us to double the volume generated by t ...

45. (D) The first quadrant area is . Section II Free-Response ...

BC 1. BC 2. (b) (c) (d) Part A See solution for AB/BC 1. Review Chapter 4. (a) . . . . . (Review Chapters 4, 6, & ...

BC 3. BC 4. (b) (c) Part B See solution for AB/BC 3, Review for Chapter 3. (a) Using the differential equation, ...

BC 5. BC 6. (b) (c) (d) 1. 2. 3. See solution for AB/BC 5, Review Chapter 7. (a) The series is a geometric series ...

(E) Since g(x) = 2, g is a constant function. Thus, for all f(x), g(f(x)) ...

(B) Since f(q) = 0 if q = 1 or q = −2, f(2x) = 0 if 2x, a repl ...

(E) Interchange x and y: x = y 3 + 2 Solve for y: y 3 = x − 2, so . ...

29. 30. 31. 32. 33. 34. 35. 1. and (except 0), there are two x’s in the domain. (D) The domain of the ln func ...