Barrons AP Calculus

(E) Center the ellipse at the origin and let (x, y) be the coordinates of the vertex of the inscribed rectangle in ...

(B) (B) When f ′ is positive, f increases. By the Fundamental Theorem of Calculus, f ′(x) = 1 ...

(B) The volume is composed of elements of the form ΔV = (2x)^2 Δy. If h is the depth, in fe ...

volume to be V π · 8^2 · 25 + π · 6^2 · 25 + π · 4^2 · 25 + π ...

(B) Use areas; then . Thus, f (7) −f (1) = 7. (B) The region x units from the ...

(B) (D) Evaluate . (A) at the point (3, 4). Use, also, the facts that the speed ...

(D) . Note that the series converges by the Alternating Series Test. Since the first term ...

12 Miscellaneous Free-Response Practice Exercises ...

1. 2. 3. Part A (a) (b) It appears that the rate of change of f, while negative, is increasing. This implies ...

(a) Since f ′ is even and f contains (0, 0), f is odd and its graph is symmetri ...

(b) Since . (c) When S is rotated about the x-axis, its volume can be obtained using disks: See the figur ...

(b) f ′ has a relative minimum at x = d, because f ′′ equals 0 at d, is less than 0 on (b, ...

representing the rate at which letters are processed then. (i) Letters began to pile up when they ar ...

x^4 and y = sin x. Solving a^4 = sina with the calculator, we find a = 0.9496. (b) Eleme ...

equation is (a) The volume of the tank, using disks, is , where the ellipse’s symmetry about ...

the trapezoid are 24 − 2x and , and the height is . The volume of the trough (in in.^3 ) is given by Sin ...

The series therefore converges. (b) Since the series converges by the Alternating Series Test, the error in us ...

. (c) means 1 + 4 · 2−t = 1.25, so t = 4. (d) , so the value of y approaches 10. (a) Sin ...

(b) You want to maximize . See signs analysis. The maximum y occurs when t = 1, because y changes from ...

horizontal tangents are at the points where y (not r) is a maximum. You need, therefore, to maximize ...