Midterm 2 Mock Exam. Math 231 BD3. Spring 2015. 3/13/2015.Multiple Choice Questions:1. What number do we get if we approximate the integralZ20x2dx using the trapezoidal methodwith 4 intervals ?(A)134(B)154(C)114(D)94(E)74Determine whether each of these series diverge or converge and if it converges to which value:2.∞Xn=132n+15n22n:(A)2513(B)2315(C)2913(D)2711(E) Diverges3.∞Xn=569n2+ 6n − 8:(A)29208(B)24143(C)2099(D)28187(E) DivergesDetermine whether each of these series diverge or converge:4.∞Xn=21n ln(n) ln(ln(n)):(A) Converges (B) Diverges5.∞Xn=27nn3− 4n2+ 2:(A) Converges (B) Diverges6.∞Xn=01n2− 1:(A) Converges (B) Diverges7. limn→∞n!4n:(A) Converges (B) Diverges8.∞Xn=1sin(1n) :(A) Converges (B) Diverges9. True or False: If∞Xn=1anconverges, then the sequence {sn}∞n=1converges, (sn= a1+ a2+ ... + an)(A) True (B) FalseFree Response:10. Consider the lamina L in the plane of constant density ρ, which is bounded by the curvesx = 5 − y4, x = y2− 1.Find the moments Mxand Myand the center of mass of L.11. We have a triangle shaped swimming pool formed by the lines y = −2x y = 0 and x = 5, whichis completely filled up with water. Draw a picture of the pool and find the hydrolic force of thewater at the bottom.12. Let y =√x − 1 from x = 1 to x = 10. Set up but do not evaluate the following:a) The arc length of the curveb) The surface area when rotated around the x-axis where the intergral has to be in terms of x.c) The surface area when rotated around the x-axis where the intergral has to be in terms of y.d) The surface area when rotated around the y-axis.13. Suppose the sum of the series s =∞Xk=11k3is approximated by its 5th partial sum, s5= 1 +18+ ... +1125.Approximate the maximum possible error in this
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