Barrons AP Calculus

equal to (circumference × width), so the area is 2πrk Δr or 4πrk . The population in the ring ...

27. 28. 29. and that the areas for x < 0 and x > 3 are unbounded. Using the calculator, we get (E) The FTC yie ...

30. 31. 2–3 P.M. 70 100 3–4 P.M. 120 220 The table shows one approach, based on the Midpoint Rule. We estimate t ...

1. 2. 3. 4. 9 Differential Equations (C) v(t) = 2t^2 − t + C; v(1) = 3; so C = 2. (B) If a(t) ...

(C) From Answer 4 s(t) = −16t 2 + 40t + 96. Then s′(t) = −32t + 40, which is z ...

(E) (A), (B), (C), and (D) are all true. (E) is false: see Answer 9. (A) Integrating ...

(E) yields ln |y| = x + c; hence the general solution is y = kex, k ≠ 0. (A) ...

(B) It’s easy to see that the answer must be choice (A), (B), or (C), because the slope fiel ...

25. 26. 27. 28. 29. Since y(0) = 0, C = 0. Verify that (A) through (D) are incorrect. NOTE: In matching s ...

(A) From Answer 25, we know that the d.e. for slope field II is y′ = y. The gener ...

(A) The slope segments are not parallel in either the x or y direction, so the d.e. must ...

(A) We let S equal the amount present at time t; using S = 40 when t = 0 yields . ...

(C) Logistic growth is modeled by equations of the form , where L is the upper limit. The g ...

(D) If Q is the concentration at time t, then . We separate variables and integrate: We ...

54. 55. 1. 2. 3. 4. (A) The description of temperature change here is an example of Case II: the rate of change ...

that lim by repeated application of L’Hôpital’s rule. (C). (E) The harmonic series ...

(D). (A) If , then f(0) is not defined. (C) unless x = 3. (B) The integrated ...

(E) Now the first omitted term, , is positive for x < 0. Hence P 9 (x) is le ...

(B) See Example 52 in Chapter 10. (D) Note that every derivative of ex is e at x = 1. ...

(C) Since the series converges when , that is, when , the radius of convergence is . (C) ...