Barrons AP Calculus - David Bock
12. (A) ...
17. (E) ...
(D) See the figure below, which shows that the length of a semicircle of radius 2 is needed here. The answer can, of course, be ...
(E) using long division, ...
(C) Using parts we let u = x^2 , dv = exdx; then du = 2x dx, v = ex, and We use parts again with u = x, dv = exdx; then du = d ...
(E) will increase above the half-full level (that is, the height of the water will rise more rapidly) as the area of the cross ...
(A) The required area is lined in the figure below. ...
(D) Note that f (x) = x + 6 if x ≠ 6, that f (6) = 12, and that So f is defined and continuous at x = 6. ...
Part B (E) The velocity functions are When these functions are graphed on a calculator, it is clear that they intersect four t ...
(C) Changes in values of f ′′ show that f ′′′ may be constant. Hence f ′′ may be linear, so f′ could be quadratic and thus f cu ...
(C) Expressed parametrically, x = sin3θ cosθ, y = sin3θ sin θ. is undefined where = −sin3θ sin θ + 3 cos 3θ cos θ = 0. Use your ...
(D) See the figure below. The roots of f (x) = x^2 − 4x − 5 = (x − 5)(x + 1) are x = −1 and 5. Since areas A and B are equal, ...
(C) It is given that An antiderivative is Since the constants are c 1 = c 2 = 1. The object’s speed is Use a calculator to fin ...
(D) Use the Ratio Test: which is less than 1 if −3 < x < 3. When x = −3, the convergent alternating harmonic series is o ...
(A) Since and since v(0) = 1, C = 1. Then yields s = t^3 + t + C ′, and you can let s(0) = 0. Then you want s(3). ...
(A) Arc length is given by Here the integrand implies that hence, y = 3 ln x + C. Since the curve contains (1,2), 2 = 3 ln 1 + ...
42. (E) At x = 3; the answer is 2[2(−2) + 5^2 ] = 42. ...
(D) Counterexamples are, respectively, for (A), f (x) = |x|, c = 0; for (B), f (x) = x^3 , c = 0; for (C), f (x) = x^4 , c = 0; ...
Free-Response Part A 1. (a) The following table shows x- and y-components of acceleration, velocity, and position: The last line ...
See solution for AB-2, Free-Response in AB Practice Exam Three. ...
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