Barrons AP Calculus - David Bock
26. (A) ...
(E) ln (4 + x^2 ) = ln (4 + (−x)^2 ); y ′ ...
(A) f (x) = (x sin πx) = πx cos πx + sin πx. ...
Part B (B) See the figure below. A = ...
(C) See the figure below. About the x-axis: Washer. ΔV = π(y^2 − 1^2 ) Δx, ...
(E) We solve the differential equation by separation: If s = 1 when t = 0, we have C = 1; hence, when t = 1. ...
32. (D) 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, therefore Thus, Solv ...
(D) If N is the number of bacteria at time t, then N = 200ekt. It is given that 3 = e^10 k. When t = 24, N = 200e^24 k. Therefo ...
(C) Since For x = 2t − 1, t = 3 yields x = 5 and t = 5 yields x = 9. ...
(C) Using implicit differentiation on the equation x^3 + xy − y^2 = 10 yields The tangent is vertical when is undefined; that ...
(D) G ′(x) = f (3x − 1) · 3. ...
(B) Since f changes from positive to negative at t = 3, G ′ does also where 3x − 1 = 3. ...
(D) Using your calculator, evaluate y ′(2). ...
39. (E) 2(3) + 2(0) + 2(4) + 2(1). See the figure above. ...
40. (E) At x = 3, the answer is 2[2(−2) + 5^2 ] = 42. ...
(A) The object is at rest when v(t) = ln(2 − t^2 ) = 0; that occurs when 2−t^2 = 1, so t = 1. The acceleration is ...
42. (D) implies that x = 3. ...
(C) represents the rate of change of the surface area; if y is inversely proportional to x, then, ...
(E) The velocity functions are v 1 = −2t sin (t^2 + 1) and Graph both functions in [0, 3] × [−5, 5]. The graphs intersect four ...
45. (B) ...
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