MATH 152 Fall 2019 Section 06 Prof Dean MIDTERM EXAM 2 Thurs October 31 2019 NAME please print legibly Student ID Number Discussion Section please circle 07 Gerson 9 00 08 Abhishek 9 00 09 Karan 10 00 10 Abhishek 10 00 No calculators or notes are allowed on this exam Please show all your work You may use the backs of pages if necessary You may not receive full credit for a correct answer if there is no work shown Don t cheat QUESTION 1 2 3 4 5 6 TOTAL VALUE 20 20 20 30 10 10 100 SCORE 1 a 8 points Approximate the integral using the Trapezoid Rule with Express your answer as a fraction b 12 points Evaluate the following improper integrals or show they diverge i ii 2 a 10 points Find the length of the curve b 10 points Find the surface area of the surface obtained by revolving the curve about the axis 3 a 12 points Find the limits of the following sequences or show that they diverge i ii iii b 8 points The following series converges Find its sum 4 30 points Determine whether the following series converge or diverge a b c d e 5 10 points Determine whether the following series are absolutely convergent conditionally convergent or divergent a b 6 10 points The alternating series converges Estimate the sum to within 0 001 Write your answer as a fraction