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Vectors - Multivariate Calculus - Exam, Exams of Calculus

This is the Exam of Multivariate Calculus and its key important points are: Vectors, Angle, Symmetric Equations, Parallel, Equation, Domain, Speed, Length, Curve, Intersection

Typology: Exams

2012/2013

Uploaded on 02/14/2013

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MA 261 EXAM I Spring 1998 Page 1/6
NAME
STUDENT ID #
INSTRUCTOR
INSTRUCTIONS
1. There are 6 different test pages (including this cover page). Make sure you have a
complete test.
2. Fill in the above items in print. I.D.# is your 9 digit ID (probably your social security
number). Also write your name at the top of pages 2โ€“6.
3. Do any necessary work for each problem on the space provided or on the back of the
pages of this test booklet. Circle your answers in this test booklet. No partial credit
will be given but the work on the test booklet may be used in borderline cases.
4. No books, notes or calculators may be used on this exam.
5. Each problem is worth 10 points. The maximum possible score is 100 points.
6. Usinga#2pencil
, fill in each of the following items on your answer sheet:
(a) On the top left side, write your name (last name, first name), and fill in the little
circles.
(b) On the bottom left side, under SECTION, write in your division and section
number and fill in the little circles. (For example, for division 9 section 1, write
0901. For example, for division 38 section 2, write 3802).
(c) On the bottom, under STUDENT IDENTIFICATION NUMBER, write in your
student ID number, and fill in the little circles.
(d) Using a #2 pencil, put your answers to questions 1โ€“10 on your answer sheet by
filling in the circle of the letter of your response. Double check that you have filled
in the circles you intended. If more than one circle is filled in for any question,
your response will be considered incorrect. Use a #2 pencil.
(e) Sign your answer sheet.
7. After you have finished the exam, hand in your answer sheet and your test booklet to
your instructor.
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pf5

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MA 261 EXAM I Spring 1998 Page 1/

NAME

STUDENT ID # INSTRUCTOR

INSTRUCTIONS

  1. There are 6 different test pages (including this cover page). Make sure you have a complete test.
  2. Fill in the above items in print. I.D.# is your 9 digit ID (probably your social security number). Also write your name at the top of pages 2โ€“6.
  3. Do any necessary work for each problem on the space provided or on the back of the pages of this test booklet. Circle your answers in this test booklet. No partial credit will be given but the work on the test booklet may be used in borderline cases.
  4. No books, notes or calculators may be used on this exam.
  5. Each problem is worth 10 points. The maximum possible score is 100 points.
  6. Using a #2 pencil, fill in each of the following items on your answer sheet: (a) On the top left side, write your name (last name, first name), and fill in the little circles. (b) On the bottom left side, under SECTION, write in your division and section number and fill in the little circles. (For example, for division 9 section 1, write
  7. For example, for division 38 section 2, write 3802). (c) On the bottom, under STUDENT IDENTIFICATION NUMBER, write in your student ID number, and fill in the little circles. (d) Using a #2 pencil, put your answers to questions 1โ€“10 on your answer sheet by filling in the circle of the letter of your response. Double check that you have filled in the circles you intended. If more than one circle is filled in for any question, your response will be considered incorrect. Use a #2 pencil. (e) Sign your answer sheet.
  8. After you have finished the exam, hand in your answer sheet and your test booklet to your instructor.

1. The angle between the vectors ~i + ~j and (โˆš 3 โˆ’ 1)~i + (โˆš3 + 1)~j is:

  1. The symmetric equations for a line containing the point (2, โˆ’ 1 , 4) and parallel to the

5. Find the speed โ€–v(2)โ€– where ~a(t) = โˆ’ 10 ~k and v(1) = ~i โˆ’ ~j + ~k.

  • A.
  • B. ฯ€
  • C. ฯ€
  • D. ฯ€
  • E. ฯ€
  • A. x โˆ’โˆ’ 3 2 = y^12 + 1 = z โˆ’ line x = 1 โˆ’ 3 t, y = 2 + 12t, z = 5 are:
  • B. x โˆ’ โˆ’ 3 2 = y^12 + 1 , z =
  • C. x + 3 2 = y โˆ’ โˆ’^112 = z โˆ’
  • D. x + 3 2 = y โˆ’ โˆ’^112 = z โˆ’
  • E. x โˆ’ โˆ’ 3 1 = y^12 โˆ’^2 , z =
  • A. โˆš
  • B. โˆš
  • C. โˆš
  • D.
  • E. โˆš
  • A. e 6. Find the length of the curve ~r(t) = t^2 ~i + 2t~j + ln t~k, 1 โ‰ค t โ‰ค e.
  • B. 2 e +
  • C. 2 e โˆ’
  • D. 2 e +
  • E. e^2 โˆ’
  1. The intersection of the surface โˆ’ 10 x^2 + x + 2y^2 + z^2 = 4 with a plane parallel to the yz-plane is A. a circle B. a parabola C. a hyperbola D. a ellipse E. two lines
  2. Let z =

x^2 + y^2 , x = uv, y = u^2 โˆ’ v^2. Find z zuv.

A. xvxu^ + 2+ 2yuyv

B. u

(^2) v + 2v 3 โˆš x^2 + y^2 C. 2 v

(^3) + u (^2) v 2 u^3 + uv^2 D. (^) u 2 uvโˆ’ v 2

E. 2 u

(^3) โˆ’ uv 2 2 v^3 โˆ’ u^2 v