Download Practice Calculus Questions #4

Practice Calculus Questions #4
(you may use a calculator on 5, 6, 7, and 9)
1) The average value of √3𝑥 on the closed interval [0, 9] is
(A)
2√3
3
(B) 2√3
(C) 6
(D) 6√3
(E) 18√3
2) ∫ 23𝑥 𝑑𝑥 =
23𝑥
23𝑥
(A) 𝑙𝑛2 + 𝐶
(B) 3𝑙𝑛2 + 𝐶
23𝑥+1
(C) 3𝑥+1 + 𝐶
23𝑥
3
+𝐶
(E) (𝑙𝑛2)23𝑥 + 𝐶
(D) II and III only
(E) I, II, and III
(D)
𝑓(𝑥)
3) If lim 𝑥−2 = f ‘(2) = 0, which of the following must be true?
𝑥→2
(A) I only
I.
f(2) = 0
II.
f(x) is continuous at x = 2
III.
f(x) has a horizontal tangent line at x = 2
(B) II only
(C) I and II only
4) The base of a solid is the region enclosed by the ellipse 4x2 + y2 = 1. If all plane cross sections perpendicular to the
x-axis are semicircles, then the volume is
(A) π/3
(B) π/6
(C) π/2
(D) 2π/3
(E) π/4
5) The area enclosed by the polar curve r = 6cosθ + 8sinθ from θ = 0 to θ = π is
(A) 9π
(B) 16π
(C) 25π
(D) 36π
(E) 64π
6) A missile rises vertically from a point on the ground 75,000 feet from a radar station. If the missile is rising at the rate
of 16,500 feet per minute at the instant when it is 38,000 feet high, what is the rate of change, in radians per minute, of
the missile angle of elevation from the radar station at this instant?
(A) 0.175
(B) 0.219
(C) 0.227
(D) 0.469
(E) 0.507
7) The region R in the first quadrant is enclosed by the lines x = 0 and y = 2 and the graph of y = ex. The volume of the
solid generated when R is revolved about the x-axis is given by
2
(B) 𝜋 ∫0 (2 − 𝑒 𝑥 )2 𝑑𝑥
𝑙𝑛2
(E) 2𝜋 ∫0 𝑥(2 − 𝑒 2 )𝑑𝑥
(A) 𝜋 ∫0 (4 − 𝑒 2𝑥 )𝑑𝑥
(D) 𝜋 ∫0 (4 − 𝑒 2𝑥 )𝑑𝑥
𝑙𝑛2
𝑥(2 − 𝑒 𝑥 )𝑑𝑥
2
8) The Maclaurin series for the function f is given by ∑∞
𝑛=2
(−1)𝑛 (2𝑥)𝑛
𝑛−1
convergence for the Maclaurin series of f. Justify your answer.
9)
𝑙𝑛2
(C) 2𝜋 ∫0
on its interval of convergence. Find the interval of