Please answer all 15 questions attached.

Question 1(Multiple Choice Worth 4 points) The base of a solid in the region bounded by the two parabolas y2 = 8x and x2 = 8y. Cross sections of the solid perpendicular to the x-axis are semicircles. What is the volume, in cubic units, of the solid? 0 288x 35 O 5761: 35 0 144K 35 0811 [EU Question 2(Multiple Choice Worth 4 points) Which of the following integrals correctly computes the volume formed when the region bounded by the curves x2 + y2 = 25, x = 4 and y = 0 is rotated around the y-axis? On 25 - yz - 4 )dy Ox 42 - ( 125 - 4 2 ) Jay On 25 - x2 dy 25- yz - 42 dyD Question 3(Multiple Choice Worth 4 points) I The base of a solid in the rst quadrant of the xy plane is a right triangle bounded by the coordinate axes and the line x + y = 4. Cross sections of the solid perpendicular to the base are squares. What is the volume, in cubic units, of the solid? Question 4(Multiple Choice Worth 4 points) Use your calculator to nd the approximate volume in cubic units of the solid created when the region under the curve y = cos(x) on the interval [0, g] is rotated around the x-axis. O 1 O 0.785 O 2.467 03.142 1:: Ti Question 5(Multiple Choice Worth 4 points) Find the volume of the solid formed by revolving the region bounded by the graphs of y = x3, x = 2, and y = 1 about the y-axis. 0% | 0120: 0 None of these 0 "I: ~ U Question 1(Multiple Choice Worth 4 points) Find the average value of f(x) = sin(x) over the interval [0, 11]. 0211 Question 2(Multiple Choice Worth 4 points) Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 312 + cos(t) and v(0) = 2. Ov(t) = 13 + sin(t) + 2 Ov(t) = 13 - sin(t) + 3 Ov(t) = 6t - sin(t) + 2 Ov(t) = 13 - sin(t) + 2a Question 3(Multiple Choice Worth 4 points) | Find the distance, in feet, a particle travels in its rst 4 seconds of travel, if it moves according to the velocity equation v(t)= t2 + 4 (in feet/sec). Question 4(Multiple Choice Worth 4 points) if:3 A girls throws a tennis ball straight into the air with a velocity of 64 feet/sect If acceleration due to gravity is -32 ft/secz, how many seconds after it leaves the girl's hand will it take the ball to reach its highest point? Assume the position at time t = 0 is 0 feet 0 4 secs 0 2 secs 0 1 sec 0 Cannot be determined U Question 5(Multiple Choice Worth 4 points) For an object whose velocity in /sec is given by v(t) = -t2 + 4, what is its displacement, in feet, on the interval t = 0 to t = 3 secs? 0 7.67 O 3.00 O -0.33 Question 1(Multiple Choice Worth 4 points) - - - 91 = L The dlfferentlal equation dx x4' I. will have a slope eld with negative slopes in quadrant I II. will have a slope eld with positive slopes in all quadrants III. will produce a slope eld with columns of parallel tangents O | only 0 I] only 0 III only 0 None of these [E2] Question 2(Multiple Choice Worth 4 points) Choose the appropriate table for the differential equation dy _ x+2 dx X X 0 0.5 2 ay 2 5 dy undefined X 0 0.5 2 ay 5 dx undefined 2 X 0 0.5 2 dy 4 dx undefined 2 O Cannot be found without solving the differential equationQuestion 3(Multiple Choice Worth 4 points) A differential equation that is a function of x only 0 will produce a slope field with parallel tangents along the diagonal Q will produce a slope field that does not have rows or columns of parallel tangents Q will produce a slope field with rows of parallel tangents Q will produce a slope field with columns of parallel tangents [E2] Question 4(Multiple Choice Worth 4 points) The differential equation g = 2x14 yl. I. produces a slope eld with horizontal tangents at y = 4 II. produces a slope eld with horizontal tangents at x = 0 III. produces a slope eld with vertical tangents at x = 0 and y = 4 O | only 0 || only 0 | and || 0 "I only i: Question 5(Multiple Choice Worth 4 points) Which of the following differential equations has the slope field below? HI HO HI O dy = x- y dx O dy = dy - VX dx O dy -xy dx O dy 2x dx