D Question 1 1 pts The base of a solid, S, is the region bounded by the curve y = e , the x-axis, the y-axis, and a line x = 1. Cross sections perpendicular to the x-axis are squares. What is the exact volume of the solid, S? 0 -4(1 -e-1) 0 4 (1 -e-2 ) 0 2(1 -e-1) 0 -(1 -e-2) D Question 2 1 pts The base of a solid, S, is a triangle bounded by the x-axis, y-axis, and the line x + y = 1. Cross sections perpendicular to the -axis are semi-circles. What is the exact volume of the solid, S? O 24 O D Question 3 1 pts A region is enclosed by the x-axis, the y-axis, the line x = 7, and the curve y = sin a. When this region is rotated around the x-axis, what expression represents the volume of the solid? O n fat x sin xda On So sin ydy On So sin? ydy On fo" sin xdaQuestion 4 1 pts A region is enclosed by the x-axis, the line x = 1, the line ax = 3, and the curve y = 2. When this region is rotated around the x-axis, what is the volume of the solid generated? O Question 5 1 pts A region is enclosed by the line x = 2, the line y = -1, and the curve y = x2 - 1. When this region is rotated around the line y = -1, what is the expression that represents the volume of the solid generated O T S2 (x2 - 1)dx O T Sa (202 + 1) da Onfo (24 + 1)da Onfox' da Question 6 1 pts A region is enclosed by the line y = * and the curve y = 2. When this region is rotated around the x-axis, what is the volume of the solid generated? O 75 O1 pts D Question 7 A region is enclosed by the y-axis, the line y = 2 and the curve y = va. When this region is rotated around the x-axis, what is the volume of the solid generated? O 2TT O 4TT O 8TT O 6T 1 pts Question 8 A region is enclosed by the y-axis, the line y = 1 and the curve y = sin a on the interval [0, 2]. When this region is rotated around the y-axis, what is the expression for the volume of the solid generated? O 27 7/2 x(1 + sin x) da O 27 7/2 x(1 - sin x) da O 27 for /2 a(1 - cos x ) da O 27 /2 x(1 + cos x) dx 1 pts Question 9 A region is enclosed by the *-axis, y-axis, and the curve y = etan on the interval [-1, 0]. When this region is rotated around the y-axis, what is the expression for the volume of the solid generated? O -27 4 x2 etan a dx O 27 , 2 2 etan & dac O -27 , Betan a dac O 27 1 retan a daQuestion 10 1 pts A region is enclosed by the x-axis and the graph 4 = x3 + y3 . When this region is rotated around the line a = 8, what is the expression for the volume of the solid generated? T SB (8 - 20) (4 -23) 2 27 8 (8 - 2) (4 - 23) idx 0 -27 8 (8 - x) (4 -x3) 2dx O _7 8 (8 - x) (4 -x3) 2dxD Question 1 1 pts Which of the following is a solution to the equation y' = by? O y(a) = Lebx O y(a) = Aeba O y(x) = 2eba O y(z) = Aerba D Question 2 1 pts If Q = Cekt , what is the value of k that satisfies the differential equation "# = -0.03Q? O -0.06 O -0.3 O -0.03 O -0.09 D Question 3 1 pts Which of the following satisfies the differential equation y" - y = 0? O y = ex2 O y = ex O y = er O y = e2xD Question 4 1 pts Which of the following satisfies the differential equation y" - y = 0? Oy = ex Oy = 22 Oy =ex Oy =23 D Question 5 1 pt Which of the following satisfies the differential equation x?y" + 2xy' - 2y = 0? O y = a-2 Oy= =2 Oy = -x Oy =x D Question 6 1 pts Which of the following satisfies the differential equation x2y" - 6y = 0? Oy= 22 Oy = 23 Oy=x-3 Oy =xD Question 7 1 pts Which of the following satisfies the differential equation x2y" - 6y = 0? O y = ex2 O y = = Oy= -x Oy = x-2 D Question 8 1 pts Which of the following satisfies the differential equation xy' - 3y = 0? O O -225 27 O O D Question 9 1 pts Which of the following satisfies the differential equation xy' - 2y = 0? O x O 2x O 3x O 3x2Question 10 1 pts Which of the following satisfies the differential equation y' + 2y = 0? O e-2x O O e2x O ex