MATH 201 Exam 2 with solution, Fall 2017

Pap LEBANESE AMERICAN UNIVERSITY Division of Computer Science and Mathematics Calculus I Exam II Fall 2008 (December 11, 2008) Name: ») © lw ( Circle the name of your instructor: ID: Dr. Habre Dr. Hamdan: Question Number Grade | 1.8 % 2.8% 3.24% 4.24% 5.9% 6.27% Total kad (-1)"2" 1. (8%) Examine convergence of the series > 7 6 = 2 2) Ges. sere, unt ra — ! 3 Irl<| => Gem. Sets can Ul fem bo : _ofrt fem 2 276 1 2h (_v¥ (+ 2/3 B/3 and determine its sum. 1 n(n +2)" oo 2. (8%) Consider the series: > n=1 (a) Find the third and fourth partial sums: 33 and 34. c3 $27 A, +«G +a =- | + / oo —_— 3 { cL 3 \ 3) 26) 3(6) 20 Sy tAt ant Ga thy = S3t | 2 3 + t (b) Find the nth partial sum s,, and then deduce the sum of the series. > 1 p--- Pn 73) 2H * Use Rarkiad Ffrachioe. A. Ae A4S)n + ot A — ‘ z n(n42) 7 N4Z n (m+?) ane hop Be -e DP slr _ if. r {Nn Apo Spe A ae | 4- 5)*(t-t wf Li _ | nz (C 5) t(4- \+t( 3 5) Ae 6) ive) an Ag A3 ae a 3. (24%) Determine the convergence or divergence of the following series: oo nl ‘ 7 @ Sm Roto (cok : hom Anas L Le (ort a (? Cun (mi)! vn] nel) - n aR (5 — fk <( = Sete Cay. by Ratvo Taf. e @ Sar Lan Zo aa / Ca S nr L ~ Ls = Mem — n n by DCI Sue ——— — Se, nvs p zl 4. (24%) Determine whether the following series converge absolutely, conditionally, or diverge: co 1 —~1)? ——___ (@) du Fy Ined Ss l y aL Cn V. by LOT we ve ne . the, suyinl ene, conveys fleshy 2 ! a y _ (b) ser (1-2)" ay = ('- 4) —> (<') = ea wo gt 5. (9%) Find the values of x for which the power series 57> gn converges: Explain. n=1 Ae) 5 [4] yin 3 > | 4] cl > 3 6. (27%) Using Maclaurin series, answer the following questions: * ia 2 el0/a? _ (a) Find ling (e 1) 1\2 3 Le. yt / + ee « (lr) ~ le). toes -') A» eo 3/ + [ l lo? x Oo + {0 ) - Ae [ a( we op xt 1 get ) Uy . . fo) Zz —? 47 WA a ge (b) Represent the function f(x) = as @ power series */ IN. {! bn +lbr) eG) (4 ) Ued Fb 2. to 2 (amr Mare 7 - L Ik [eal <! aa 3 8 bby pe.