Barrons AP Calculus - David Bock
38. (E) ...
(E) In the figure above, S is the region bounded by y = sec x, the y axis, and y = 4. Send region S about the x-axis. Use washe ...
(A) The curve falls when f ′(x) < 0 and is concave up when f ′′(x) > 0. ...
(B) To find g ′(0), find x such that f (x) = 0. By inspection, ...
(D) It is given that you want where Since y^2 = 25 −x^2 , it follows that and, when x = 3, y = 4 The function f (x) = 2 sin x ...
(E) Since f (0) = f (π) and f is both continuous and differentiable, Rolle’s Theorem predicts at least one c in the interval su ...
(B) Since a positive constant, where c is a positive constant. Then which is also positive. ...
(C) If Q(t) is the amount of contaminant in the tank at time t and Q 0 is the initial amount, then = kQ and Q(t) = Q 0 ekt. Si ...
Free-Response Part A AB/BC 1. (a) This is the graph of f ′(x). (b) f is increasing when f ′(x) > 0. The graph shows this to b ...
AB2. (a) Since April 1 is 3 months from January 1 and June 30 is 3 months later, we form the sum for the interval [3,6]: We esti ...
Part B AB 3. (a) At (2,5), so the tangent line is y − 5 = 4(x − 2). Solving for y yields f (x) ≈ 5 + 4(x − 2). (b) f (2.1) ≈ 5 + ...
AB 4. (a) Draw a vertical element of area, as shown. (b) (i) Use washers; then ...
(ii) See the figure above. ...
AB/BC 5. f is decreasing where f ′(x) < 0, which occurs for −2 < x < 1. (b) f is decreasing on the interval −2 < x & ...
AB/BC 6. (a) S = 4πr^2 , so Substitute given values; then Since therefore Substituting known values gives (b) Regions of consist ...
Answers Explained Multiple-Choice Part A 1. (E) ...
(A) Divide both numerator and denominator by ...
(E) Since eln u = u, y = 1. ...
(D) f (0) = 3, and, ...
5. (B) ...
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