Barrons AP Calculus - David Bock
Free-Response Part A AB/BC1. (d) To work with g(x) = f −1(x), interchange x and y: x 7.6 5.7 4.2 3.8 2.2 1.6 g(x) 2.5 3.2 3.5 4. ...
AB 2. Let M = the temperature of the milk at time t. Then The differential equation is separable: where c = e −C. Find c, using ...
Part B AB 3. (a) See the figure. (b) The average value of a function on an interval is the area under the graph of the function ...
AB/BC 4. (a) The rectangular slices have base y, height 5y, and thickness along the x-axis: (b) The disks have radius x and thic ...
AB/BC 5. (a) The volume of the cord is V = πr^2 h. Differentiate with respect to time, then substitute known values. (Be sure to ...
AB/BC 6. (a) the negative of the area of the shaded rectangle in the figure. Hence F(−2) = − (3)(2) = −6. is represented by the ...
Answers Explained Multiple-Choice Part A (E) Here, ...
(C) The given limit equals where f (x) = sin x. ...
(C) Since f (x) = x ln x, f ′(x) = 1 + ln x, ...
(A) Differentiate implicitly to get Substitute (−1, 1) to find the slope at this point, and write the equation of the tangent: ...
(C) f ′(x) = 4x^3 − 12x^2 + 8x = 4x(x − 1)(x − 2). To determine the signs of f ′(x), inspect the sign at any point in each of t ...
(C) The integral is equivalent to where u = 4 + 2sinx. ...
(D) Here which is zero for x = e. Since the sign of y ′ changes from positive to negative as x increases through e, this critic ...
(E) Since is always positive, there are no reversals in motion along the line. ...
(E) The slope field suggests the curve shown above as a particular solution. ...
(E) Since is discontinuous at x = 1; the domain of F is therefore x > 1. On [2, 5] f (x) < 0, so which is positive for x ...
(B) In the graph above, W(t), the water level at time t, is a cosine function with amplitude 6 ft and period 12hr: ...
(B) Solve the differential equation Use x = −1, y = 2 to determine ...
13. (D) ...
14. (A) ...
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