MATH 201 Final QUESTIONS, Fall 2006

Math 201 — Fall 2011-12 Calculus and Analytic Geometry III, all sections Final Exam, January 21 — Duration: 2 hours 15 minutes GRADES: NOTES BEFORE SOLVING THE EXAM: 1) You have to solve the recommended exer- cises in the book after understanding each chapter from the book if not from notes. 2) This exam is not a complete one and it needs around 90 minutes to be solved. 3) Please understand that this exam is solved by students, and it may contain some mis- takes. a : Gnane 4) If you have any questions or concerns, U { Cc oN email: insightclub@gmail.com YOUR NAME: Seed) a INSIGNt PLEASE CIRCLE YOUR SECTION: Section 1 Section 2 Section 3 Section 4 MWF 3, Kobeissi MWEF 3, Kobeissi MWF 3, Kobeissi MWF 3, Kobeissi Recitation F 11 Recitation F 5 Recitation F 4 Recitation F 10 Section 5 Section 6 Section 7 Section 8 MWF 10, Abi-Khuzam MWF 10, Abi-Khuzam MWF 10, Abi-Khuzam MWF 10, Abi-Kbuzam Recitation T 11 Recitation T 3:30 Recitation T 5 Recitation T 2 Section 9 Section 10 Section 11 Section 12 MWF 11, Brock MVWF 11, Brock MWF il, Brock MWF 11, Brock Recitation T 12:30 Recitation T 2 Recitation T 11 Recitation T 3:30 Section 13 Section 14 Section 15 Section 16 MWF 2, Nahlus MWF 2, Nahlus MWF 2, Nahlus MWF 2, Nahlus Recitation Th 11 Recitation Th 3:30 Recitation Th 8 Recitation Th 5 Section 17 Section 18 Section 19 Section 20 MWF 8, Makdisi MWF 8, Makdisi MWF 8, Makdisi MWF 8, Makdisi Recitation F 2 Recitation Th 8 Recitation Th 2 Recitation Th 3:30 Section 23 Section 22 Section 23 MWF 1, Raji MWF 1, Raji MWF 1, Raji ; a Recitation M 8 Recitation M 9 Recitation M 4 ae ee ) bd e Section 24 Section 25 Section 26 MWF 10, Egeileh MWF 10, Egeileh MWF 10, Egeileh ) S | Recitation F 11 Recitation F 2 Recitation F 3 e be sb ee ca CS ie GES a higee cali RI Kieth RIES 1. (5 pts each part,15 pts total) (a) Use the Sandwich theorem to find the following limit Le they Shee he < nwo «8lnyn ° ee Asight CSU nt x n ss oo Sas dn(wt). =eeSne < | t4an Antntl) ¢ Sn Ann lat So HA n (nd) 3 fain Sintn 4 Leen > 3 dan ho Sian BS neo the lower anol upper boumel — 2. ie » AS TR YD SAhetem (b) (UNRELATED) Find, with justification, all values of p for which the following series is convergent :. by LCT ae suits behave alice, (c) (UNRELATED) Compute the n partial sum S, of the following eS ee oo othe Se L eres (f+ ae eels 2. (5 pts each part, 15 pts total) (a) Consider the function 3 feu) = a if (e.u) # (0,0) Prove that f(0,0) may be defined in such a way that f becomes continuous at (0, 0). O¢ Suny -3 aes Bs ina “ hin ‘7 7 i ae a —— ee . by Corrolaty +0 canewich ton et swe \xI—a©& (b) If in part (a) (0,0) has been defined correctly, prove that f is not differentiable at (0,0). For this part, you may use without proof that f2(0, 0) = fy(0, 0) =0. insight ety (c) (UNRELATED) By about how much will h(z,y) = In(z? + y? +2”) change if the point P(z, y,z) moves from fo(1,1,—1) a distance of ds = 0.1 unit in the direction of the vector 3i +6) — 2k? oa Q eS = Ie 3. (5 pts each part, 15 pts total) (a) Sketch the region of integration and evaluate the double integra! weal (b) Evaluate the double integral leit lve Clearly cd] Know how 0 a this ome, So, we Flip the ofdeC af tel stetchig the ceo | eee INSIGNt = £ (c) Evaluate the integral Le [eten. o> 2 So Liege J e~odx, o insight | « Cre U o = J ery xl ° Chane. to polar, (roe ye =) 5 ek ae 6 (2) 6 sa Be : 7 en Ax. f one ae ier iso duovny i, Vag sable) cst wet x '€all ;¢ J INS a e C. (4a ght