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Final_Fall-1999-2000_Abu-Khuzam_Lyzzaik

# Final_Fall-1999-2000_Abu-Khuzam_Lyzzaik - January 27 2000...

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Unformatted text preview: January 27 , 2000 FINAL EXAMINATION VERSION II 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 Circle the correct answer in each of the followin roblems 5 oints for each correct answer, and 0 f0!“ no 01' more than one answer! I 1 no 2" . _ 3 H . 1. The interval of convergence of the followmg series 2 —-—92—) IS nil H 5 7 5 7 a A —<~<—— B —S.S-— C ls SS ( ) 2 x 2 ( ) 2 x 2 ( ) x (D) 1< x < 5 (E) none of the above 2. The surface £- y_‘ = 5 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 2nd I 2)”1 is "=1 (A) 6 (B) .32 (C) 4 (D) 25/4 (E) noncofthe above 4. Which one of the following series converges: (A) ELM - JR] (B) i W” (C) in ”=1 ":1 (3”)! ”=1 (D) icosmr (E) ii n=l rr=l n S. An estimate of the magnitude of the error obtained by taking the ﬁrst four terms of co . 1 H the series 2 (—1)"+1 (0 0 ) 3 "=1 ['1 to appmximate its value is (A) 1.56 x 10‘12 (B) s x 10‘” (C) s x 10'” (D) 1.56 x 10'”J (E) none of the above . _ 7r ,1 6. The sequence whose n-th term 18 an = (1 ~ ——)2 n (A) Converges to e"r (B) Diverges (C) Converges to 62” (D) Converges to e‘?”r (E) none of the above 7. The series GOSH” ”:1 n Inn (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 x2 + y2 + (z — 4) 3 = 16 is (A)p=4cosB (B) p=4cos¢ ,(C)p=8cos<|) (D) p = 8 cos 8 (E) none of the above l 9. The value of the double integral Evaluate j Jay: dydx is 0.1:]? (A) l - lie (B) l + l/e (C) l (D) e (E) none ofthe above 10. If f(x,y) = ln xy +ln yz +1n x2, then the derivative of f at P(1,l,l) in the direction where f increases most rapidly is (A) J3 (B) 2% (C) 0 (D) 3J3— (E) none of the above — 4 11. Using the Maclaurin series for , the Maclaurin series of ——:£3—7 is 1+ x (1 + x )' (A) 25HXSH U3) :‘(--1)"5rtt5"_1 (C) 2(— 1) "+1 Sims"—1 “:1 ”:1 ”:1 (D) Z — SHXS’H rt=l (E) none of the above 4-4] A )" fbr(x,_v)¢(0,0) Then 12. Consider the function f(x,y) = x6 + y" k for(x, y) = (0,0) (A) f is discontinuous at (0,0) [or all values of k. (B) f is continuous at (0,0) provided that k:() (C) f is continuous at (0,0), provided that k=l (D) f is continuous at (0,0) , provided that kz—l. (E) f is continuous at (0,0) for all values of k. 13. The function f(x, y) =—.):3 — y3 —5xy “1. has (A) saddle point at (0,0) and local maximum at (—§,— §) . (B) saddle point at (0,0) and local minimum at (—§,-— %) . (C) saddle point at (—%,— g) and local minimum at (0,0). (D) saddle point at (—§,—%) and local maximum at (0,0). . 5 5 (E) local maxrmum at (—§,—- :) . J 14. The function f (x, y) =3xy — 6.x—3y+7 deﬁned on the triangular plate R with vertices (0,0), (3,0), and (0,5) has 9 . . (A) an absolute maximum g and absolute mmlmum e8. . 9 . . (B) an absolute maxrmum g and absolute minimum —1 l. (C) an absolute maximum 7 and absolute minimum 1. (D) an absolute maximum 8 and absolute minimum —l l. (E) none of the above. 15. The area of the region that is inside the cardioid r = 4 + 4 cos 0 and outside the circle r = 6 is (A) 18J§ +2n (B) 18J§ — 411 (C) 51: (D) 5 45 +10 (E) none of the above 16. Using triple integration in cylindrical coordinates, the volume of the solid bounded above by the hemisphere z = 1125 --x2 - y2 , below by the xy—plane, and laterally by the cylinder x2 + yz :9 is (A) 401t/3 (B) 351113 (C) 1221:13 (D) 4611/3 (E) none of the above ...
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Final_Fall-1999-2000_Abu-Khuzam_Lyzzaik - January 27 2000...

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