Barrons AP Calculus - David Bock
(C) The given integral is equivalent to The figure shows the graph of f (x) = 1 − |x| on [−1,1]. The area of triangle PQR is e ...
(B) Let y = x1/x; then take logarithms. ln As x → ∞ the fraction is of the form ∞/∞. So y → e^0 or 1. ...
(E) Separating variables yields so ln y = −ln cos x + C. With y = 3 when x = 0, C = ln 3. The general solution is therefore (c ...
(A) Represent the coordinates parametrically as (r cos θ, r sin θ). Then Note that sin 2θ, and evaluate (Alternatively, write ...
(D) Note that v is negative from t = 0 to t = 1, but positive from t = 1 to t = 2. Thus the distance traveled is given by ...
(E) Separating variables yields y dy = (1 − 2x) dx. Integrating gives ...
(A) Use parts; then u = x, dv = cos x dx; du = dx,v = sin x. Thus, ...
(C) Using the above figure, consider a thin slice of the oil, and the work Δw done in raising it to the top of the tank: ...
(A) By Taylor’s Theorem, the coefficient is For and making the coefficient ...
(D) Here, ...
(D) Evaluate ...
Part B (E) The vertical component of velocity is = 4 cos t + 12 cos 12t. Evaluate at t = 1. ...
(B) At t = 0, we know H = 120, so 120 = 70 + ke −0.4(0), and thus k = 50. The average temperature for the first 10 minutes is ...
36. (B) The required volume is 0.592. ...
(C) The Maclaurin expansion is The Lagrange remainder R, after n terms, for some c in the interval |x| 2, is Since R is greate ...
(E) On your calculator, graph one arch of the cycloid for t in [0, 2π] and (x,y) in [0, 7] × [−1, 3]. Use disks; then the desir ...
(C) In the first quadrant, both x and y must be positive; x(t) = et is positive for all t, but y(t) = 1 − t^2 is positive only ...
(D) Chapter 10. ...
(E) Each is essentially a p-series, Such a series converges only if p > 1. ...
Free-Response Part A See solution for AB-1, Free-Response in AB Practice Exam One. ...
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