MATH 201 Exam 1, Fall 2017

MATH 201: Calculus and Analytic Geometry III Fall 2017-2018, Exam 1, Duration: 60 min. . a - : — — oe —- on | Problem| la | 1b | Ie | 2a | 2b | 2¢ | 2d |2e | 3a | 3b | da | 4b Total Ponts) 8 | 8 8 |8 8 |8 8 8 (16 10/5 |5 | 100 | Seores| 7 IQ | ( | a | F _1¢ - LO i ¢i)Fi7 121% [ Name:_ AUB ID:_ Please circle your section: \ Section | Section 2 Section 3 (ak MWE 3, Karam MWE 3, Karam MWEF 3; Karam \ a Recitation F. 11 Section 5 MWEF 10, Shayya Recitation T. 11 Section 9 MWE 11, Yamani Recitation F. 3 Section 12 MWF 2, Nahlus Recitation M. 8 a ————_ Section 16 MWF 9, vitor ei Recitation Th. 9:30 Section 19 MWE 1, Nahlus Recitation F. 10 Section 22 MWEF 10, Abi Khuzam Recitation F. 4 Section 26 MWFE 11, Aoun Recitation Th. 11 INSTRUCTIONS: (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, Recitation F. 8 Section 6 MWFE 10, Shayya Recitation T. 12:30 Section 10 MWEF 11, Yamani Recitation F. 4 Section 13 MWF 2, Nahlus Recitation M. 9 Section 17 MWF 9, Mourtada Recitation Th. 2 Section 20 MWF 1, Nahlus Recitation F. 8 Section 23 MWEF 10, Abi Khuzam Recitation F. 2 Section 27 MWEFE 11, Aoun Recitation Th. 12:30 1 Recitation F. 10 '- Section 8 MWEFE 10, Shayya Recitation T. 5 Section 7 MWF 10, Shayya Recitation T. 2 Notes before solving the exam: 1) You have to solve the recommended problems in the book after understand- ing each chapter from the book and the notes. 2) Please understand that this exam is solved by students, and it may contain some mistakes. 3) If you have any questions or con- cerns, let us know through our mail: in- sightclub@gmail.com. GOOD LUCK:) Section 28 MWF 11, Aoun Recitation Th. 5 Problem 1 (8 pts each) Which of the following sequences converge, and which diverge? Find the limit of each convergent sequence. (a) ay =n(e” 1) — j el me etn ~ | = Yn Lin an = Bim Dim —, & an . =. “we n Pee (y gt = \ a Sie 6 Problem 2 (8 pts each) Which of the following series converge, and which a Find the sum of the series when possible. @> (S. in =] 5 ics (-y* 8 —, 4 MLA Fis po bee | nit Fie ~ Ga rca) f %% ard 2 Gk fx Ln C+) Jeresry esd re) a \ {hen £(x) ly wd - on Lik ce balh lv f («) iP ~ Lip “( dx 2 No of ak - i {hn -~ Lim ( = 7 Ss ge dé wee y Bs oe mi i \ aK \ WN - ff = as , > = ; mes “ 3 eats) 7 W300 (e) x (are tan (n + 1) —aretan (n)) (Note: arctan (n) = tan (n) ) od & wichan (ut) archin (x) ra («We L ~ arctan i). (veka SS | ( sch \ nish a [«cten (1-11) ~archon ) then by telecetin series * (% athe pati ( wun) Sn Spe = arc tan (mit) — arc tan | = arctan Crt) ~ 4 bl Lim 30 x Te n> v4Yn 4 insight el o Ran arc bin (reat) — ay tan(n) Conve 4 wb - U n~\ C4 a nents, aia cum= | L / Peleapeg