Barrons AP Calculus - David Bock
100. (A) ...
(B) The formula for length of arc is Since y = 2x, we find ...
(D) a(t) = (0, et); the acceleration is always upward. ...
(A) At (0, 1), so Euler’s method yields (0.1, 1 + 0.1(4)) = (0.1, 1.4). has particular solution y = e^4 x; the error is e4(0.1 ...
(D) Note that the series converges by the Alternating Series Test. Since the first term dropped in the estimate is the estimate ...
(C) which equals a constant times the harmonic series. ...
(D) We seek x such that Then |x| < e and the radius of convergence is e. ...
(B) The error is less than the maximum value of This maximum occurs at c = x = ...
108. (D) Note that the curve is traced exactly once by the parametric equations from t = 0 to t = 1. ...
Answers Explained Part A 1. (a) (b) It appears that the rate of change of f, while negative, is increasing. This implies that th ...
(a) 12y 0 + 0.3 = 24 yields y 0 1.975. (b) Replace x by 0.3 in the equation of the curve: The calculator’s solution to three d ...
Graph f ′(x) = 2x sin x − e(−x^2 ) + 1 in [−7, 7] × [−10, 10]. (a) Since f ′ is even and f contains (0, 0), f is odd and its g ...
In the graph below, C is the piece of the curve lying in the first quadrant. S is the region bounded by the curve C and the coo ...
See the figure, where R is the point (a, b), and seek a such that ...
Graph y = sin 2x in [−1, 3.2] × [−1, 1]. Note that y = f ′′. (a) The graph of f is concave downward where f ′′ is negative, na ...
Graph f (x) = cos x and g(x) = x^2 − 1 in [−2, 2] × [−2,2], Here, y 1 = f and y 2 = g. (a) Solve cos x = x^2 − 1 to find the t ...
(a) Use the Trapezoid Rule, with h = 60 min: (b) Draw a horizontal line at y = 20 (as shown on the graph below), representing ...
Draw a vertical element of area as shown below. (a) Let a represent the x-value of the positive point of intersection of y = x ...
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The figure above shows an elliptical cross section of the tank. Its equation is (a) The volume of the tank, using disks, is wh ...
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