Find the volume of the solid that lies between the planes perpendicular to the x-axis at x = - 3 and x = 3 in cubic units. The cross sections perpendicular to the x-axis are circles whose diameters...

................................................................................................................................................. MAT231 Calculus with Analytic Geometry II Midterm Exam .. 1. Find the volume of the solid that lies between the planes perpendicular to the x-axis at and in cubic units. The cross sections x=- 3 x= 3 perpendicular to the x-axis are circles whose diameters stretch from 6 6 y=- to y= . 2 2 1+ x 1+ x a. 24p b. 96p 2 24p c. 2 d. 96p 2. Find the volume of the solid generated by revolving the region bounded by 2 , y= 0 and x = 3 about the x-axis in cubic units. y=3x a. 27p b. 81p 2187 c. 5 2187p d. 5 3. Use the shell method to find the volume of the solid generated by revolving the region bounded by , y = 9x-8 and x = 0 about the y-axis in cubic y= x units. a. 14p /5 b. 28p /5 c. 14p 2 d. 14p /5 3 y 9 4. Find the length of the curve x= + on 3£ y£5 . 27 4y a. 17477/18000 b. 1061/270 c. 121/30 d. 93812/18000 ..................................................................................................................................................................................................... Midterm Exam 07/07/09 ..5. Use a grapher to find the length of the following curve numerically, rounded 2 to the nearest hundredth: 2y + y= x+4 from (-3,-1) to (17,3) . a. 20.00 b. 23.01 c. 114.16 d. 611.38 dy x-y 6. Solve the differential equation = 4e . dx y x a. e = 4e +C x b. y=4e +C c. y= 4*ln| x|+C y 4x d. e =e +C dy 1 2 7. Solve the differential equation = × y×cos ( y) . dx 5 -1 5cos ( y)= x+C a. b. 5sin( y)×cos( y)= x+C 1 2 c. ×cos ( y)= x+C 5 d. 10×tan( y)= x+C 8. A force of 8N will stretch a rubber band .04 m. Assuming Hooke’s law applies, how much work (in joules) does it take to stretch the rubber band .06 m. ? a. .16 b. .20 c. .36 d. 200 9. A vertical right circular cylindrical tank measures 20 ft. high and 14 ft. in 3 diameter. ...