Barrons AP Calculus - David Bock
(C) Since v = 3t^2 + 3, it is always positive, while a = 6t and is positive for t > 0 but negative for t < 0. The speed t ...
(A) Note from the figure that the area, A, of a typical rectangle is For y = 2, Note that is always negative. ...
(B) If S represents the square of the distance from (3, 0) to a point (x, y) on the curve, then S = (3 − x)^2 + y^2 = (3 − x)^2 ...
21. (D) ...
(D) See the figure. Since the area, A, of the ring equals π (y 22 − y 12 ), A = π [(6x − x^2 )^2 − x^4 ] = π [36x^2 − 12x^3 + ...
(A) This is of type ...
(A) About the y-axis; see the figure. Washer. ...
(E) Separating variables, we get y dy = (1 − 2x) dx. Integrating gives or y^2 = 2x − 2x^2 + k or 2 x^2 + y^2 − 2x = k. ...
26. (E) 2(5) + ...
27. (E) ...
(D) Use L’Hôpital’s Rule or rewrite the expression as ...
(D) For f (x) = tan x, this is ...
(E) The parameter k determines the amplitude of the sine curve. For f = k sin x and g = ex to have a common point of tangency, ...
(D) We differentiate implicitly to find the slope At (3, 1), The linearization is ...
32. (C) ...
(A) About the x-axis. Disk. ...
(C) Let f (x) = ax; then ln a = ln a. ...
(E) is a function of x alone; curves appear to be asymptotic to the y-axis and to increase more slowly as |x| increases. ...
(D) The given limit is equivalent to where The answer is ...
37. (B) ...
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