Barrons AP Calculus - David Bock
(E) [cos (x^2 )] ′ = −sin (x^2 ) · 2 x. The missing factor 2x cannot be created through introduction of constants alone. ...
(E) As the water gets deeper, the depth increases more slowly. Hence, the rate of change of depth decreases: ...
(D) The graph of f is shown in the figure above; f is defined and continuous at all x, including x = 1. Since f ′(1) exists an ...
(B) Since |x − 2| = 2 − x if x < 2, the limit as ...
20. (A) Note that the distance covered in 6 seconds is the area between the velocity curve and the t-axis. ...
(C) Acceleration is the slope of the velocity curve, ...
(D) Particular solutions appear to be branches of hyperbolas. ...
(A) Differentiating implicitly yields 2xyy ′ + y^2 − 2y ′ + 12y^2 y ′ = 0. When y = 1, x = 4. Substitute to find y ′. ...
24. (C) ...
25. (A) ...
(B) Separate to get Since −(−1) = 1 + C implies that C = 0, the solution is This function is discontinuous at x = 0. Since the ...
27. (E) ...
(C) Note that for all x. ...
Part B (B) At x = 3, the equation of the tangent line is y − 8 = −4(x − 3), so f (x) −4(x − 3) + 8. f (3.02) −4(0.02) + 8. ...
30. (C) The velocity is graphed in [−1,11] × [−15, 5]. The object reverses direction when the velocity changes sign, that is, wh ...
(D) The sign diagram shows that f changes from increasing to decreasing at x = 4 and thus f has a maximum there. Because f inc ...
(D) Since f ′ decreases, increases, then decreases, f ′′ changes from negative to positive, then back to negative. Hence, the g ...
33. (B) On the curve of f (x) − ex − x^2 , the two points labeled are (0,1) and (1, e − 1). The slope of the secant line is Find ...
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 ...
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