Barrons AP Calculus - David Bock
34. (B) Use disks; then ΔV = πR^2 H = π(ln y)^2 Δy. Note that the limits of the definite integral are 1 and 2. Evaluate the inte ...
(C) Note that the rate is people per minute, so the first interval width from midnight to 6 A.M. is 360 minutes. The total numb ...
(C) so v = 3t^3 + c. Since v = 1 when t = 0, c = 1. Now so s = t^3 + t + c. Since, s = 3 when t = 0, c = 3; then s = t^3 + t + ...
(A) Let u = x^2. Then ...
38. (C) To find a, the point of intersection of y = x^2 and y = cos (x), use your calculator to solve the equation x^2 − cos (x) ...
(D) If x = 2t + 1, then When t = 0, x = 1; when t = 3, x = 7. ...
(E) Use A(t) = A 0 ekt, where the initial amount A 0 is 50. Then A(t) = 50ekt. Since 45 g remain after 9 days, 45 = 50ek·9, whi ...
(C) See the figure above. Since x^2 + y^2 = 26^2 , it follows that at any time t. When x = 10, then y = 24 and it is given tha ...
(E) Let u = 2x and note that Then ...
43. (D) −v(0) = −π + 3; so v(0) = π − 3. ...
44. (C) ...
(D) Let y = (x^3 − 4x^2 + 8)ecos(x^2 ). The equation of the tangent at point (2, y (2)) is y − y(2) = y ′(2)(x − 2). Note that ...
Free-Response Part A AB 1/BC 3. (a) (Review Chapter 3) (b) After 15 minutes the rate at which grain is leaking is slowing down a ...
AB/BC 2. (a) Graph y = (x + ex) sin (x^2 ) in [1, 3] × [−15, 20], Note that y represents velocity v and x represents time t. (b) ...
Part B AB 3. One possible graph of h is shown; it has the following properties: continuity on [−4,4], symmetry about the y-axis ...
AB 4. (a) Draw elements as shown. Then (b) (c) Revolving the element around the x-axis generates disks. Then (Review Chapter 7) ...
AB 5. (a) The differential equation is separable: If y = 0 when x = 2, then thus c = 3, and Solving for y gives the solution: No ...
AB/BC 6. (a) (c) The line tangent to the graph of A at x = 6 passes through point (6, A(6)) or (6, 9π). Since A ′(x) = f (x), th ...
Answers Explained The explanations for questions not given below will be found in the answer section for Calculus AB Diagnostic ...
(B) Let y = xx and take logarithms. ln this function has the indeterminate form ∞/∞. Apply L’Hôpital’s rule: So y → e^0 or 1. ...
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