Barrons AP Calculus - David Bock
(C) The general solution of is ln y = x + C or y = cex. For a solution to pass through (2, 3), we have 3 = ce^2 and c = 3/e^2 0 ...
(C) At a point of intersection, y ′ = x + y and x + y = 0. So y ′ = 0, which implies that y has a critical point at the interse ...
(A) Although there is no elementary function (one made up of polynomial, trigonometric, or exponential functions or their inver ...
(C) Logistic growth is modeled by equations of the form where L is the upper limit. The graph shows L = 1000, so the differenti ...
(D) We start with x = 3 and y = 100. At x = 3, moving us to x = 3 + 2 = 5 and y = 100 + 5 = 105. From there so when x = 5 + 2 = ...
(C) We separate the variables in the given d.e., then solve: Since y(0) = 180, ln 112 = c. Then When t = 10, y = 68 + 112e−1.1 ...
(E) The solution of the d.e. in Question 45, where y is the temperature of the coffee at time t, is ...
(D) If Q is the concentration at time t, then We separate variables and integrate: We let Q(0) = Q 0. Then We now find t when ...
(E) Please read the sections on Applications for Restricted Growth and Applications for Logistic Growth in this chapter for the ...
(D) (A), (B), (C), and (E) are all of the form y ′ = ky(a − y). ...
(B) The rate of growth, is greatest when its derivative is 0 and the curve of is concave down. Since which is equal to 0 if or ...
(A) The description of temperature change here is an example of Case II: the rate of change is proportional to the amount or ma ...
(C) Since (A) is the correct answer to Question 51 , we solve the d.e. in (A) given the initial condition T(0) = 32: BC ONLY ...
Answers Explained (B) converges to −1. ...
(C) Note that ...
(D) The sine function varies continuously between −1 and 1 inclusive. ...
(E) Note that is a sequence of the type sn = rn with |r| < 1; also that by repeated application of L’Hôpital’s rule. ...
5. (C) ...
(E) The harmonic series is a counterexample for (A), (B), and (C). shows that (D) does not follow. ...
7. (B) ...
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