Barrons AP Calculus - David Bock
(E) Speed is the magnitude of velocity: |v(8)| = 4. ...
(E) For 3 < t < 6 the object travels to the right At t = 7 it has returned 1 unit to the left; by t = 8, 4 units to the l ...
(C) Use disks: ΔV = πr^2 Δy = πx^2 Δy, where x = ln y. Use your calculator to evaluate ...
(B) If then u^2 = x − 2, x = u^2 + 2, dx = 2u du. When x = 3, u = 1; when x = 6, u = 2. ...
(A) The tangent line passes through points (8,1) and (0,3). Its slope, is f ′(8). ...
(A) Graph f ′′ in [0,6] × [−5,10]. The sign of f ′′ changes only at x = a, as seen in the figure. ...
(C) In the graph below, the first rectangle shows 2 tickets sold per minute for 15 min, or 30 tickets. Similarly, the total is ...
(B) Graph both functions in [−8,8] × [−5,5]. At point of intersection Q, both are decreasing. Tracing reveals x −4 at Q. If you ...
(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; ...
(E) f ′(x) > 0; the curve shows that f ′ is defined for all a < x < b, so f is differentiable and therefore continuous ...
(D) Consider the blast area as a set of concentric rings; one is shown in the figure. The area of this ring, which represents t ...
Free-Response Part A AB1. (a) Since x^2 y − 3y^2 = 48, (b) At (5,3), so the equation of the tangent line is (c) (d) Horizontal t ...
AB/BC2. (a) (b) The average value of a function is the integral across the given interval divided by the interval width. Here Es ...
Part B AB/BC 3. (a) (b) Let h = the hypotenuse of an isosceles right triangle, as shown in the figure. Then each leg of the tria ...
AB/BC 4. (a) so v(0) = 0 and v(10) = 48. The average acceleration is Acceleration (b) Since Q’s acceleration, for all t in 0 ≤ t ...
AB5. (a) Using the differential equation, evaluate the derivative at each point, then sketch a short segment having that slope. ...
AB 6. (a) f (t)dt = F(2) = 4. (b) One estimate might be f (t)dt F(7) − F(2) = 2 − 4 = −2. (c) f (x) = F′ (x); F′ (x) = 0 at = 4. ...
Answers Explained The explanations for questions not given below will be found in the answer section for AB Practice Examination ...
6. (D) ...
(B) Note that, when x = 2 sin θ, x^2 = 4 sin^2 θ, dx = 2 cos dθ, and 2 cos θ. Also, ...
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