MATH 201 Final, Fall 2014

MATH 201: Calculus and Analytic Geometry ii Fall 2014-2015, Final, Duration: 120 min. Exerciseld | 231415 16178 19 aoe Points |15/10|7/8)17|10 He 151 10 Scores Name: AUB 1D Circle your section: Lausey i Section 2 Section 3 a ectiol ua cae ee MWF 3, Kobeissi MWEF 3, Kobeissi MWF 3, ant Recitation F. 11 Recitation F. 4 Recitation F. 5 Recitation F. Section 7 Section 8 Section 5 MWEF 10, Bertrand Recitation T. 11 Section 9 MWF 11, Raji Recitation F. 2 Section 13 MWE 2, Nahlus Recitation M. 9 Section 17 MWEFE 9, Khachadourian Recitation Th. 9:30 Section 21 MWF 1, Nahlus Recitation F. 10 Section 25 MWEFE 10, Yamani Recitation F. 4 Section 29 MWF 11, Egeileh Recitation Th. 5 INSTRUCTIONS: T BE GRADED. Section 6 MWF 10, Bertrand Recitation T. 3:30 Section 10 MWF 11, Raji Recitation F 3 Section 14 MWFE 2, Nahlus Recitation M. 12 Section 18 MWF 9, Khachadourian Recitation Th. 8 Section 22 MWF 1, Nahlus Recitation F. 9 Section 26 MWFE 10, Yamani Recitation F. 2 Section 30 MWF 11, Egeileh Recitation Th. 2 MWEF 10, Bertrand MWEF 10, Bertrand Recitation T. 5 Recitation T. 2 Section 11 Section 12 MWE 11, Raji MWF 11, Raji Recitation F. 4 Recitation F. 5 Section 15 Section 16 MWFE 2, Nahlus MWFE 2, Nahlus Recitation M. 10 Recitation M. 8 Section 19 Section 20 Recitation Th. 3:30 Recitation Th. 5 Section 23 Section 24 MWF 1, Nahlus MWF 1, Nahlus Recitation F. 11 Recitation F. 2 Section 27 Section 28 MWE 10, Yamani MWE 10, Yamani Recitation F 3 Recitation F. 1 Section 31 Section 32 MWF 11, Egeileh MWF 11, Egeileh Recitation Th. 3:30 Recitation Th. 11 (a) Explain your answers precisely and clearly to ensure full credit. ) No book. No notes. Only non-graphical calculators are allowed. S CLEARLY SPECIFIED OTHERWISE, THE BACKSIDE OF THE PAGES WILL MWE 9, Khachadourian MWF 9, Khachadourian 2 Exercise 1. Determine whether or not the following series converge. (Inn)* (a) G points) 9S yD n=l = (b) (5 points) y(-(var — vin) n=1 Exercise 5. Let D be the solid region of the ball x? + y? + 2? <8 where ea ee (a) (5 points) Set up but do not evaluate i i | y dV in cylindrical Coordinates with the order of D integration drdzdé. lo not evaluate / i} il y GV in spherical coordinates with the order of integration D 8) dpdydd Exercise 2. Suppose f(x, y, z) is a differentiable function statisfying F(6,2,0)=1, Vf(6,2,0) =i+j+k (a) (S points) Find the derivative of f at (6,2, 0) in the direction of the vector A = 9} + j+2k (b) (5 points) Estimate (6.2, 2.1, 0.2). erated triple integral using the order of integration be the region in the zy-plane bounded by the lines v, ¢+y=4, 7+y=2andy=0. , y =u—vtorewrite ff 2(¢+y)e*-Y dA as an integral over an lane. Then evaluate the ‘eames over G.