MultiFinalExam04

MultiFinalExam04 - Math 2224 Instructions: Form A Common...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 2224 Instructions: Form A Common Part of Final Exam May 6, 2002 Please enter your NAME, ID NUMBER, Form designation, and INDEX NUMBER on your op—scan sheet. The index number should be written in the upper right—hand box labeled 77Course.77 Do not include the course number. In the box labeled 77Form77 write the appropriate test form letter A. Darken the appropriate circles below your ID number and Form designation. Use a #2 pencil; machine grading may ignore faintly marked circles. Mark your answers to the test questions in rows 1713 of the op—scan sheet. You have 1 hour to complete this part of the final exam. Your score on this part of the final exam will be the number of correct answers. Please turn in your op—scan sheet and the guestion sheet at the end of this part of the final exam. 1. The value of fol fox y — :1: dy d1: is (a) 0 a 2. The partial derivative — {fly sin :1: (a) 2:1:y cos 5—2 (b) 2:1:y sin 5—2 —|— ny cos 5—2 (c) 2:1:y sin acyZ — :—:cos 5—2 (d) 2:1:y sin 5—2 —|— Z—ZCOS 5—2 3. Given A : 2:021 3—: and B = true? (a) Both series converge. (b) Both series diverge. (c) A converges but B diverges ( d) A diverges but B converges. (c) g 1} y_2 22:. [ equals 1 1 __|__ 2" n , which of the following statements is 4. A thin plate is modeled by the plane region bounded by the curve y = :12, the line :1: = 2, and the :1:—axis. The density of the plate at the point (:1:,y) is ,0(:1:,y) : :1: and the total mass of the plate is 4. Then the y—coordinate of the plate’s center of mass is given by 1 1 x2 (a) if: fairy d3: dy (b) f0 my dy d1: 1 1 (c) 1 f: fofi :1:y d:1: dy (d) if; féydy d:1: 5. The rate of change of the function f(:1:,y) : 3:1:2y3 at the point (2,1) in the direction of the vector V = —i —|— Zj is 60 12 (a) 60 (b) E (c) E (d) 12 6. Suppose lirnn_,OO : i and is given by the power series Hm) = Z2nbn<w — 1)" Then the open interval of convergence for this power series is (a) 67%) (b) (—173) (C) (—00700) (d) No interval: diverges except for :1: = 1 7. The integral fOZ fagg—fi :1: dy d:1: can also be expressed as (a) f: fi” 16—y2 :1:d:1: dy ME (b) f: r(cos (9)7“ dr d6 (c) f: r(cos (9)7“ dr d6 (d) f0% f04 r(cos (9)7“ dr d6 8. For the function flaky) = 1'2 +y2 —wy+2w+2y7 which one of the following statements is true: (a) (—2, 0) is a local maximum (b) (0, —2) is a local minimum (c) (—2, —2) is a local minimum (d) none of (a)7 (b) or (c) is correct. (_1)n+1 9. Consider the series 2:021 . Which of the following statements is true? n2 (a) The series converges to 0. (b) The series converges to a number 5 7E 07 and an economical way to estimate S with an accuracy of 0.01 is to use the sum of the first 99 terms of the series. (c) The series converges to a number 5 7E 07 and an economical way to estimate S with an accuracy of 0.01 is to use the sum of the first 5 terms of the series. (d) The series converges to a number 5 7E 07 and an economical way to estimate S with an accuracy of 0.01 is to use the sum of the first 9 terms of the series. 10. The volume of the solid in the first octant bounded by y = 07 z = 07 :1: = 1 y = 91:, and y2 —|—z2 : 1 is given by (a) fol 0V 1—y2f 1—ydx dz dy (b) fol fol fyl d1: dz dy 1 y (c) f1 x V 1—y2 dz dy d1: (d) fol fol fox dy dz d1: 2—:ry—y2ataczl, y=1 is 11. The equation of the plane tangent to the surface z = :1: (a) z—:1:—|—3y=1 (b) z—|—:1:—|—3y:1 (c) z—3:1:—|—y=—3 (d) z—|—:1:—3y:1 12. The first 4 terms of the Taylor series for : VJ} —|— 1 centered at a = 0 are 1—— §$—Z$2+§$3 1 1 1 (c) 1:201: i 1) 8<x:1>2: 16(2: : 1>3 1 12 1 3 (d) 1+2x—8x +1691: 13. The volume in the first quadrant7 under the surface 22 = 91:2 —|— y2 and inside 91:2 —|— y2 = 4 may be computed by (a) fog fOZ ff dz rdr d6 (b) ff f0? fordzrdrdfi (c) ff ff fom p2singbdp d¢ d6 (d) ff fom {)2 sin a dp d¢ d6 ...
View Full Document

This note was uploaded on 04/02/2008 for the course MATH 2224 taught by Professor Mecothren during the Fall '03 term at Virginia Tech.

Page1 / 4

MultiFinalExam04 - Math 2224 Instructions: Form A Common...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online