MATH 201 Final, Fall 2016

MATH 201: Calculus and Analytic Geometry II Fall 2016-2017, Final Exam, Duration: 2 hours Problem} 1 2 3 4 5 6 df 8 9 10 11 | Total Points| 16 16 14 16 32° |) 12 24 10 16 24 | 20 200 Scores Name: AUB ID: Please circle your section: Section 1 Section 2 Section 3 Section 4 MWE 3, Nahlus MWE 3, Nahlus MWE 3, Nahlus MWE 3, Nahlus Recitation F. 11 Section 5 MWF 10, Shayya Recitation T. 11 Section 9 MWF 11, Yamani Recitation F. 2 Section 13 MWEF 2, Nahlus Recitation M. 9 Section 17 MWE 9, Makdisi Recitation Th. 9:30 Section 21 MWF 1, Karam Recitation F. 10 Section 25 MWEF 10, AbiKhuzam Recitation F. 4 Section 29 MWEF 11, Aoun Recitation Th. 3:30 INSTRUCTIONS: Recitation F. 10 Section 6 MWEF 10, Shayya Recitation T. 12:30 Section 10 MWF 11, Yamani Recitation F 3 Section 14 MWE 2, Nahlus Recitation M. 1 Section 18 MWE 9, Makdisi Recitation Th. 2 Section 22 MWF 1, Karam Recitation F. 9 Section 26 MWEFE 10, AbiKhuzam’ Recitation F. 2 Section 30 MWF 11; Aoun Recitation Th. 2 Recitation F. 8 Section 7 MWE 10, Shayya Recitation T. 2 Section 11 MWF 11, Yamani Recitation F. 4 Section 15 MWFE 2, Nahlus Recitation M. 10 Section 19 MWE 9, Makdisi Recitation Th. 8 Section 23 MWF 1, Karam Recitation F. 12 Section 27 MWEF 10, AbiKhuzam Recitation F 3 Section 31 MWFE 11, Aoun Recitation Th. 5 (a) Explain your answers precisely and clearly to ensure full credit. (b) Closed book. No notes. No calculators. No cellphones. (c) UNLESS CLEARLY SPECIFIED OTHERWISE, THE BACKSIDE OF THE PAGES WILL NOT BE GRADED, 1 Recitation F. 9 Section 8 MWEF 10, Shayya Recitation T. 5 Section 12 MWF 11, Yamani Recitation F. 5 Section 16 MWE 2, Nahlus Recitation M. 8 Section 20 MVWE 9, Makdisi Recitation Th. 5 Section 24 MWF 1, Karam Recitation F. 8 Section 28 MWEF 10, AbiKhuzam Recitation F. 1 Section 32 MWEFE 11, Aoun Recitation Th. 12:30 Problem 1 2 (16 pts) Find the tangent plane and normal line to the surface x + y —z =6at the point (3,1,2). Problem 2 (16 pts) Consider the region in the xy-plane given by D= {(x, y): x 4+ y < 5} Find the extreme values (maximum and minimum values) of fley)ax ty +2x-y over D. Problem 3 (14 pts) Determine if the following series converges or diverges. nat Problem 4 1 5x+6 x = —2.Then find the largest open interval in which the series converges to the given function. Hint: The resulting series is geometric. (16 pts) Find the Taylor series generated by f (x) = at the point Problem 5 Let R be the region in the first quadrant below the line y =1 and above the parabola 2 x TES Te (a) (6 pts) SET UP BUT DO NOT EVALUATE [{dA(x,y)= [[ dA as an iterated double R R integral(s) in Cartesian coordinates using the order of integration dydx. (b)(6 pts) SET UP BUT DO NOT EVALUATE {/dA(x,y)= [[ dA as an iterated double R R integral(s) in Cartesian coordinates using the order of integration dxdy. (©) (12 pts) SET UP BUT DO NOT EVALUATE [{dA(x, y)= [dA as an iterated double R R integral(s) in polar coordinates using the order of integration drdQ. (d) (8 pts) Evaluate ii} dA(x, y)= [[a4. R R Problem 6 (12 pts) Prove directly from the definition of differentiability that the function f(x, y) =(1+ x\(2 + y)is differentiable at the point (0,0). 10