Barrons AP Calculus - David Bock
parallel to y-axis, focus at (h, k + p): (x − h)^2 = 4p(y − k). ELLIPSE With major axis of length 2a, minor axis of length 2b, ...
For the hyperbola, c^2 = a^2 + b^2 , and eccentricity which is greater than 1. POLAR COORDINATES RELATIONS WITH RECTANGULAR COOR ...
cardioids (specific examples below) r = a (1 ± cos θ). r = a (1 ± sin θ). r^2 = cos 2θ, lemniscate, symmetric to the x-axis. ...
r = θ, (double) spiral of Archimedes rθ = a (θ > 0), hyperbolic (or reciprocal) spiral EXPONENTIAL AND LOGARITHMIC FUNCTION ...
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Answers Explained Multiple-Choice Part A (C) Use the Rational Function Theorem. ...
2. (D) ...
(A) Since f ′(1) = 0 and f ′ changes from negative to positive there, f reaches a minimum at x = Although f ′(2) = 0 as well, f ...
4. (D) ...
5. (E) ...
(D) The graph must look like one of these two: ...
(E) F ′(x) = 3 cos x cos 3x − sin x sin 3x. ...
8. (B) ...
(C) Let Then f ′ increases for 1 < x < 2, then begins to decrease. In the figure above, the area below the x-axis, from 2 ...
(D) P ′(x) = 2g(x) · g ′(x) ...
(E) Note that H(3) = f −1 (3) = 2. Therefore ...
(D) Note that the domain of y is all x such that |x| 1 and that the graph is symmetric to the origin. The area is given by ...
(E) Since y ′ = 2(x − 3)−2 and = y ′′ is positive when x < 3. ...
(D) represents the rate of change of mass with respect to time; y is directly proportional to x if y = kx. ...
15. (B) ...
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