MATH 201 Final, Fall 1999

January 27 , 2000 FINAL EXAMINATION VERSION I MATHEMATICS 201 FALL 1999- 2000 Time : 2 Hours Circle out your instructor’s name and your section number Prof. H.Abu-Khuzam Section: 6 and 12 Prof. A. Lyzzaik Section: 5 and 7 NOTE: Make sure that you have 6 pages and twenty questions /100 Circle the correct answer in each of the following problems (5 points for each correct answer, and 0 for no or more than one answer) My 3)" 1. The interval of convergence of the following series »y 23) is n=l n 2 5 7 5 7 A) =< x<- B) —sxs<- C) ls x s5 (A) 5 *S 5 (B) 7 SESS (C) Is x (D) l<x<5 (E) none of the above 2. The surface x _y Le is a 36 «6 (A) elliptic paraboloid (B) elliptic cone (C) circular paraboloid (D) hyperbolic paraboloid (E) none of the above 3. The sum of the series }n(1/2)"" is n=l (A) 6 (B) e? (C) 4 (D) 25/4 (E) none of the above 4. Which one of the following series converges: co eo n 3 co (A) S lvaal - Vil (B) ¥2 (nt) © ¥Wn n=} ml (3n)! n=) (D) ¥ cosa (E) y+ n=l 5. Anestimate of the magnitude of the error obtained by taking the first four terms of (0.01)" 3 the series »y (-1)"" n=] nf to approximate its value is (A) 1.56 x 10°? (B) 8x 1077 (C) 8x 108 (D) 1.56 x 107° (E) none of the above 6. The sequence whose n-th term is a, = (1- 2) on nA (A) Converges to e” (B) Diverges (C) Converges to e* (D) Converges to er (E) none of the above .. ~ COSNT 7. The series nmi Naf lon (A) is not alternating (B) diverges (C) converges conditionally (D) converges absolutely (E) none of the above 8. The spherical coordinate equation for the sphere x? + y? + (z-4)?=16 is (A) p=4cos 6 (B) p=4coso (C)p=8cos > (D) p=8cos@ (E) none of the above 1 9, The value of the double integral Evaluate j } eo” dydx is 0 x/2 (A) 1 - Le (B) 1+ Le (C) 1 (Dye (E) none of the above 10. If f(x,y) = In xy +In yz +In xz, then the derivative of fat P(1,1,!) in the direction where f increases Most rapidly is (A) ¥3 (B) 2V3 (C)0 (E) none of the above (D) 33 4 11. Using the Maclaurin series for u =» the Maclaurin series of 5x =< is I+x (+x)° (A) Sn" (By) YCD"Snx”™ Yep Snax n=l n=l n=l (D) >y -5nx"" n=} (E) none of the above 44, XY for(x,y) # 0) 12. Consider the function f(xy) = 4x ty k for(x. y) = (0,0) . Then (A) fis discontinuous at (0,0) for all values of k. (B) f is continuous at (0,0) provided that k=0 (C) f is continuous at (0,0), provided that k=1 (D) f is continuous at (0,0) , provided that k=-l. (E) fis continuous at (0,0) for all values ofk. 13. The function f(x, y)=-x'-y? —5xy~—1 has (A) saddle point at (0,0) and local maximum at -3,-3 . (B) saddle point at (0,0) and local minimum at 3 2) . 5 5 a (C) saddle point at a 3 and local minimum at (0,0). (D) saddle point at C3-D and local maximum at (0,0). . oe) (E) local maximum at Co =). 3 14. The function f(x,y) =3xy-6x—3y+7 defined on the triangular plate R with vertices (0,0), (3,0), and (0,5) has 9 a (A) an absolute maximum 3 and absolute minimum -8. 9 (B) an absolute maximum = and absolute minimum -11. (C) an absolute maximum 7 and absolute minimum 1. (D) an absolute maximum 8 and absolute minimum -11. (E) none of the above. 15. The area of the region that is inside the cardioid r= 4+ 4 cos 6 and outside the circle r = 6 is (A) 1843 +22 (B) 183 - 4x (C) 5x (D) 5 V3 +10 {E) none of the above 16. Using triple integration in cylindrical coordinates, the volume of the solid bounded above by the hemisphere z= /25-—.x? — y” , below by the xy-plane, and laterally by the cylinder x? + y? =9 is (A) 402/3 (B) 35/3 (C) 122n/3 (D) 46n/3 (E) none of the above