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 VALUE SCORE 1 20 2 20 3 20 4 30 5 10 6 10 TOTAL 1001) (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