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Satisfies - Multivariate Calculus - Exam, Exams of Calculus

English and Foreign Languages UniversityCalculus

This is the Exam of Multivariate Calculus and its key important points are: Satisfies, Function, Minimum, Maximum Values, Function, Evaluate the Integral, Order of Integration, Portion, Paraboloid, Surface Area

Typology: Exams

2012/2013

Uploaded on 02/14/2013

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MA 261 Exam 2 Spring 2000 Page 1/8
NAME
STUDENT ID #
RECITATION INSTRUCTOR
RECITATION TIME
DIRECTIONS
1) Fill in the above information. Also write your name at the top of each page of the
exam.
2) The test has 8 pages, including this one.
3) Problems 1 through 5 are multiple choice; circle the correct answer.
4) Problems 6 through 9 are problems to be worked out. Write your answer in the
box provided. YOU MUST SHOW SUFFICIENT WORK TO JUSTIFY YOUR
ANSWERS. CORRECT ANSWERS WITH INCONSISTENT WORK MAY NOT
RECEIVE CREDIT.
5) Points for each problem are given in parenthesis in the left margin.
6) No books, notes, or calculators may be used on this test.
Page 2 /20
Page 3 /20
Page 4 /12
Page 5 /12
Page 6 /12
Page 7 /14
Page 8 /10
TOTAL /100
pf3
pf4
pf5
pf8

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MA 261 Exam 2 Spring 2000 Page 1/

NAME STUDENT ID # RECITATION INSTRUCTOR RECITATION TIME

DIRECTIONS

  1. Fill in the above information. Also write your name at the top of each page of the exam.
  2. The test has 8 pages, including this one.
  3. Problems 1 through 5 are multiple choice; circle the correct answer.
  4. Problems 6 through 9 are problems to be worked out. Write your answer in the box provided.ANSWERS. CORRECT ANSWERS WITH INCONSISTENT WORK MAY NOT YOU MUST SHOW SUFFICIENT WORK TO JUSTIFY YOUR RECEIVE CREDIT.
  5. Points for each problem are given in parenthesis in the left margin.
  6. No books, notes, or calculators may be used on this test.

Page 2 / Page 3 / Page 4 / Page 5 / Page 6 / Page 7 / Page 8 / TOTAL /

(8) 1) The function,imate value of f f ( (0x, y. 002 ) satisfies, − 0 .001): f (0, 0) = 4, fx(0, 0) = 3, fy (0, 0) = 2. Find an approx-

(12) 2) Find the minimum and maximum values of the function f (x, y) = x^2 − 4 x + y^2 − 2 y

  • A.
  • B.
  • C.
  • D.
  • E.
  • A. 0 and on the disk x^2 + y^2 ≤ 20:
  • B. 0 and
  • C. −5 and
  • D. −5 and
  • E. 32 and

(12) 5) The surface area of the portion of the paraboloid z = 2 − x^2 − y^2 that lies inside the cone z = √x^2 + y^2 is: A. π 6 (5 32 − 1) B. π 6 (17 32 − 1) C. π 6 · 5 32 D. π 6 · 173 /^2 E. 156 π

(12) 6) Find and classify the critical points of f (x, y) = x^3 + 3xy +^32 y^2 :

Answer to 6)

  1. A solid occupies that part of the sphere of radius 5 about the origin which lies in thesecond octant (x < 0 , y > 0 , z > 0). Its mass density at (x, y, z) is δ(x, y, z) = z. Set up (do not evaluate) triple integrals which give the mass of the solid: (7) 8.a) in rectangular coordinates.

Answer to 8.a)

(7) 8.b) in cylindrical coordinates.

Answer to 8.b)

(10) 9.) Set up (do not evaluate) a triple integral which gives the volume of a solid boundedby the coordinate planes and the plane 2x + y + z = 6.

Answer to 9.)