Final_Fall-2003-2004_Jurdak_Lyzzaik

Final_Fall-2003-2004_Jurdak_Lyzzaik - FINAL EXAM.-, MATH...

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Unformatted text preview: FINAL EXAM.-, MATH 201 “w...” .m- January 28., 2004 EJHIAA i.\!\'£1i. Zkli I I. i B l: A 3: 't'" (If: HHHH"! Name: Signature: Student number: Section number (Encircle): 17 (Miss Jaafar) 18 (Miss Jaafar) 19 (Mrs. Jurdak) 20 (Mr. Lyzzaik) Instructor: Prof. Abdallah Lyzzaik 1. Instructions: 0 Calculators are allowed: — There are two types of questions: PART I consists of six subjective questions, and PART II consists of seven multiple-choice questions of which each has exactly one correct answer. 0 GIVE DETAILED SOLUTIONS FOR THE PROBLEMS OF PART I IN THE PROVIDED SPACE AND CIRCLE THE-{APPROPRIATE AN- SWER FOR EACH PROBLEM OF PART II. 2. Grading policy: 0 12 points for each problem of PART I. - 4 points for each problem of PART II: 0mm. for no answer, -1 for a. wrong answer or more than one answer of PART II: GRADE OF PART I,/?2: GRADE OF PART 11,08: TOTAL GRADE/100: —— l f a l l Part I Find the absolute maximum and minimum values attained by the function fix, 3;) 2 :53; —~ 3: — y + 3 on the triangular region R in the icy—plane with vertices (O: 0): (2,0), and (0:4). Enema“. rmvzgnsr'r ' Il.f{?"'l‘\‘7 ,_..—..—-—......_._._.__._._,_, UF HEHHI‘I LiBiL-Hl‘a' ; l IQ Part I (2). Evaluate the integral 2 1 3 / yes: dandy. 0 W? r:me MIN-:an LIBRA “Y? “F "EH-.3": “‘me Part I Set up a triple integral (Without evaluating it) in cylindrical coordinates for the volume of the solid bounded by the my—pkme, the cylinder 7‘2 = cos 29,, and the sphere I2 + y2 + 22 = l. Part I Evaluate the integral f/Rsin dzdyh where R is the trapezoid in the :cy-plane with vertices (1.1), (2,2), (4,0), and (23 U), by making the change of variables: u = y — :5; w z y + 3:. J." b" I if!“ t. " : 11 Q1 Part I Evaluate the line integral jig 3ng (13:5 + 2&2 dy: where C is the boundary of the region R bounded above by the line y = a: and below by the parabola y = $2 — 22f. Interpret this integral in terms of vector fields. Part I Find the interva] of convergence of the power series fax—1)” “:2 inn ‘ State where the series converges absoiutely and conditionally. if ,i Part II 1. If flay? 2 2323/,‘(334 ~‘~ then (a) limizlyifimgm flan; y) = 0. (b) h111(1,y)_.(910) f(.IT.J y) = 1. (C) imam—«om fife/i = 2- (d) limmypmam Hz, 3;) does not exist. (6) None of the above 2. An estimate of the integral '1 1 —oos:c / _2._dx o x Wit-h an error less than 1/(615) is (a)1/2!+l/(4T3). (b)1i/21—1/(4!3)+1/(6!5). (c) ~1/2!+1/(4!3)-1/(615i (d) 1/2!—1/(4!3). (6} None of the above, 3. The function defined by (a) is continuous at (O, G) (b) has no limit at; (0,0). (c) has a limit a: (O, 0) but is discontinuous at. (0, 0). (d) is bounded in the my—piane. (e) None of the above. 'w 2 flat, y) where 1“. x 6" cos 6 and y = 8r sin 6’. then (a) w” —r new = w,”r + wr/T + wag/TE. (b) w“ —~'r wyy = kw” + wrfr + wag/7'2. (@1113; + wyy = 11;” + w,/r — wag/T2. (d) mm + wyy = w”, — wr/r —; wag/T2_ (e) None of the above. 5. An equation of the tangent plane to the surface with equation 33+zz—y2 = 1 at the point (1,3,2) is (a) 2:5 +’6y +132 :10. (b) 2x + By — 13.2 2 10. (c) 2.x — 63; +132: = —10. (d) 2.1r — 61; +132 =10. (e) None of the above. .. v 6. The volume of the solid bounded by the cylinder y 2 x2 and the planes 3; + 2 = 4 and z = 0 is given by the triple integral (a) j; 5"!” [3% dz dy dz. (b) 2 I; f$ f0“? dz dz dy‘ (c) I32 I52 I51”? dz dy dz. r _2 V;— ‘xdifcffo ffijgdrdydz. (e) .None‘oi the above. T. The function flair: y) = I3 + 32y -— ya admits (a) a saddle point. and a. local minimum value (b) no saddle point and no local minimum value. a local minimum value and no saddle point (all a saddle point and no local minimum value (e) None of the above. ...
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Final_Fall-2003-2004_Jurdak_Lyzzaik - FINAL EXAM.-, MATH...

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