Barrons AP Calculus - David Bock
(A) Use the Parts Formula with u = x and dv = ex dx. Then du = dx and v = ex, and ...
(B) The arc length is given by the integral dx which is ...
(E) Separating variables yields Integrating gives ln x = kt + C. Since x = 2 when t = 0, ln 2 = C. Then ln x = kt + ln 2. Using ...
(B) y ′ = x + 2x ln x and ...
18. (D) ...
(C) At (0, 2), With step size the first step gives where so the next step produces ...
(B) Since function f is increasing on the interval [2,6], rectangles based on left endpoints of the subintervals will all lie c ...
Part B (B) Set ...
(E) S is the region bounded by y = sec x, the y-axis, and y = 4. We send region S about the x-axis. Using washers, Δ V = π(R^2 ...
(A) Use the Ratio Test: which equals zero if x ≠ 1. The series also converges if x = 1 (each term equals 0). ...
(C) The absolute value function f (x) = |x| is continuous at x = 0, but f ′(0) does not exist. ...
(B) The Maclaurin series is When an alternating series satisfies the Altering Series Test, the sum is approximated by using a ...
34. (B) Graph x = 4 − t^2 and y = 2t for −3 ≤ t ≤ 3 in the window [−1, 5] × [−1, 5]. Now ΔA = x Δy; the limits of integration ar ...
35. (E) ...
36. (B) ...
(C) = cos θ dx = cos θ dθ, sin−1 0 = 0, ...
(C) The power series for ln (1 − x), if ...
(B) Solve by separation of variables; then Use P(0) = 200; then c = 1000, so P(x) = 1200 − 1000e−0.16t. Now P(2) = 473.85. ...
(E) As the water gets deeper, the depth increases more slowly. Hence, the rate of change of depth decreases: d^2 h/dt^2 < 0. ...
(E) The first quadrant area is (3 sin 2θ)^2 d ≈ 3.53. ...
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