Barrons AP Calculus - David Bock
Free-Response Part A (a) Use the Ratio Test: The radius of convergence is 1. At the endpoint x = 1, Since this series converge ...
See solution for AB-2. ...
Part B See solution for AB 1. ...
(a) Using the differential equation, evaluate the derivative at each point, then sketch a short segment having that slope. For ...
(a) To find the y-intercepts of the graph of P(t) = (9 − t^2 ,2t), let x = 9 − t^2 = 0, and solve: t = −3, 3. Then and P(3) = ( ...
See solution for AB-6. ...
Answers Explained (C) f (−2) = (−2)^3 − 2(−2) − 1 = −5. ...
(E) The denominator, x^2 + 1, is never 0. ...
(D) Since x − 2 may not be negative, x 2. The denominator equals 0 at x = 0 and x = 1, but these values are not in the interval ...
(E) Since g(x) = 2, g is a constant function. Thus, for all f (x), g(f (x)) = 2. ...
(D) f (g(x)) = f (2) = −3. ...
(B) Solve the pair of equations Add to get A; substitute in either equation to get B. A = 2 and B = 4. ...
(C) The graph of f (x) is symmetrical to the origin if f (−x) = −f (x). ln (C), f (−x) = (−x)^3 + 2(−x) = −x^3 − 2x = −(x^3 + 2 ...
(C) For g to have an inverse function it must be one-to-one. Note, that although the graph of y = xe−x^2 is symmetric to the or ...
(B) Note that the sine function varies from −1 to 1 as the argument varies from ...
(E) The maximum value of g is 2, attained when cos x = −1. On [0,2π], cos x = −1 for x = π. ...
(C) f is odd if f (−x) = −f (x). ln (C), f (−x) = (−x)^3 + 1 = −x^3 + 1 ≠ −f (x) ...
(B) Since f (q) = 0 if q = 1 or q = −2, f (2x) = 0 if 2x, a replacement for q, equals 1 or −2. ...
(B) f (x) = x(x^2 + 4x + 4) = x(x + 2)^2 ; f (x) = 0 for x = 0 and x = −2. ...
(E) Solving simultaneously yields (x + 2)^2 = 4x; x^2 + 4x + 4 = 4x; x^2 + 4 = 0. There are no real solutions. ...
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