Barrons AP Calculus

(b) (c) (d) (e) One estimate might be . f(x) = F′(x); F′(x) = 0 at x = 4. f ′(x) = F ′′(x). F ...

3. 6. 12. 13. Part A (D) Here, (C) (B) Note that, when x = 2 sin θ, x 2 = 4 sin^2 θ, dx = 2 cos ...

(D) Separating variables yields so ln y = −ln cos x + C. With y = 3 when x = ...

since diverges, (C) diverges. For (D), we would like to compare to , so by the Comparison ...

36. 37. 38. Part B (A) Using disks, ΔV = πR^2 Δy = π(ln y)^2 Δy. Evaluate The required volume is 0.592. (C) ...

The Lagrange remainder R, after n terms, for some c in the interval |x| 2, is Since R is grea ...

41. 44. length is (C) See series (2) in Example 43 in Chapter 10. (B) At t = 0, we know H = 120, so 120 = ...

1. 2. Part A See solution for AB/BC 1. See solution for AB 2. ...

3. (b) (c) 4. Part B (a) Because , which never equals zero, the object is never at rest. so the object’s s ...

(b) (c) (b) By the Ratio Test, the series converges when Thus, the radius of convergence is e. (a) To find ...

(c) fractions. Let F = 0; then A = . Let F = 600; then B = . Since F = 100 when The solu ...

BC Practice Examination 2 The explanations for questions not given below will be found in the ...

1. 2. 3. 6. Part A (B) Since to render f (x) continuous at x = 1, define f (1) to be 1. (C) The limit ...

and the magnitude of the acceleration, |a|, is given by (B) By the Ratio Test the series converges ...

= e ln e − e − (1 ln 1 − 1) = e − e − (0 − 1) = 1. (C) Use the method of p ...

II. (C) Using separation of variables: Given initial point (0,0), we have 0 = tan(0 + C); h ...

III. diverges by the Limit Comparison Test: therefore both series diverge since we know that th ...

31. 32. 38. Part B (B) Since the equation of the spiral is r = ln θ, use the polar mode. The formula for area ...

(A) f (x) is differentiable on [−3, −1] so MVT guarantees that there exists at least one x value ...

43. 44. (C) The endpoints of the arc are and (e,1). The arc length is given by (A) Find k such that cos x ...