Barrons AP Calculus - David Bock
(B) When f ′ is positive, f increases. By the Fundamental Theorem of Calculus, f′ (x) = 1 − 2 (cos x)^3. Graph f ′ in [0, 2π] × ...
81. (C) ...
(B) The volume is composed of elements of the form ΔV = (2x)^2 Δy. If h is the depth, in feet, then, after t hr, ...
(B) Separating variables yields P(0) = 300 gives c = 700. P(5) = 500 yields 500 = 1000 − 700e−5k, so k + 0.0673. Now P(10) = 1 ...
(C) dx = 4 arctan 1 = π. H′ (1) = f (1) = 2. The equation of the tangent line is y − π = 2(x − 1). ...
(C) Using midpoint diameters to determine cylinders, estimate the volume to be V π · 8^2 · 25 + π · 6^2 · 25 + π · 4^2 · 25 + ...
86. (A) ...
(C) H′ (3) = f′ (g(3)) · g′ (3) = f′ (2) · g′ (3). ...
(E) M′ (3) = f (3) · g′ (3) + g(3) · f′ (3) = 4 · 3 + 2 · 2. ...
89. (E) ...
90. (C) ...
(D) Here are the pertinent curves, with d denoting the depth of the water: ...
(B) Use areas; then Thus, f (7) − f (1) = 7. ...
(B) The region x units from the stage can be approximated by the semicircular ring shown; its area is then the product of its c ...
(B) is positive, but decreasing; hence ...
95. (C) ...
(E) On 2 ≤ t ≤ 5, the object moved ft to the right; then on 5 ≤ t ≤ 8, it moved only ft to the left. ...
97. (B) ...
(D) Evaluate ...
99. (A) Use, also, the facts that the speed is given by and that the point moves counterclockwise; then = 4, yielding and at the ...
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