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Notes for Exam 1 | Vector Calculus | MATH 223, Exams of Calculus

University of Arizona (UA)Calculus
Prof. L. Dawson

Material Type: Exam; Professor: Dawson; Class: Vector Calculus; Subject: Mathematics Main; University: University of Arizona; Term: Spring 2008;

Typology: Exams

Pre 2010

Uploaded on 08/31/2009

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Math 223
Spring 2008
Dawson
Notes for Exam #1
The exam covers sections 13.1-13.4 & 12.1-12.5.
Extra Problems
The best review for your exam is to go over the previously assigned homework problems. If you would
like some extra problems to work on, take a look at those listed below. Also going over the Check Your
Understanding section of each chapter review is highly suggested.
Review Exercises from Chapter 13 - pg 679-682: #1, 7, 9, 11, 13, 16, 17, 19, 22, 23, 27
Review Exercises from Chapter 12 - pg 643-647: #6, 8, 11, 12, 13, 14, 17, 20, 27
Section 12.3 - pg 625-628: #12-15
Section 12.5 - pg 637-638: #21, 26, 28
Solutions to above review problems
.
Please let me know if you find any mistakes.
Review Exercises from Chapter 13
1. 4
~
i+~
j+ 3~
k
7. โˆ’6
~
iโˆ’9~
j+ 3~
k
9. 0
11. (a) 4
(b) โˆ’4
~
iโˆ’11~
jโˆ’17~
k
(c) 15
โˆš17~
i+10
โˆš17~
jโˆ’10
โˆš17~
k
(d) โ‰ˆ79.03โ—ฆ
(e) .784
(f) ~
j+~
k
(g) โˆ’4
~
iโˆ’11~
jโˆ’17~
k
13. โˆ’1
โˆš6~
i+1
โˆš6~
j+โˆ’2
โˆš6~
k
16. (a) t= 1
(b) No values of t
pf2

Partial preview of the text

Download Notes for Exam 1 | Vector Calculus | MATH 223 and more Exams Calculus in PDF only on Docsity!

Math 223 Spring 2008 Dawson Notes for Exam #

The exam covers sections 13.1-13.4 & 12.1-12.5. Extra Problems

The best review for your exam is to go over the previously assigned homework problems. If you would like some extra problems to work on, take a look at those listed below. Also going over the Check Your Understanding section of each chapter review is highly suggested. Review Exercises from Chapter 13 - pg 679-682: #1, 7, 9, 11, 13, 16, 17, 19, 22, 23, 27 Review Exercises from Chapter 12 - pg 643-647: #6, 8, 11, 12, 13, 14, 17, 20, 27 Section 12.3 - pg 625-628: #12- Section 12.5 - pg 637-638: #21, 26, 28

Solutions to above review problems . Please let me know if you find any mistakes.

Review Exercises from Chapter 13

  1. 4~i + ~j + 3~k
  2. โˆ’ 6 ~i โˆ’ 9 ~j + 3~k
  3. 0
  4. (a) 4 (b) โˆ’ 4 ~i โˆ’ 11 ~j โˆ’ 17 ~k (c) โˆš^1517 ~i + โˆš^1017 ~j โˆ’ โˆš^1017 ~k (d) โ‰ˆ 79. 03 โ—ฆ (e). (f) ~j + ~k (g) โˆ’ 4 ~i โˆ’ 11 ~j โˆ’ 17 ~k
  5. โˆšโˆ’^16 ~i + โˆš^16 ~j + โˆ’โˆš^26 ~k
  6. (a) t = 1 (b) No values of t

(c) Any value of t

  1. (a) 13/ (b) 58. 39 โ—ฆ
  2. 4~i + 0~j + 6~k
  3. (a) โˆ’ ABโˆ’โ†’ = โˆ’ 2 ~i + 0~j + 3~k, โˆ’ ACโ†’ = โˆ’ 1 ~i โˆ’ 1 ~j + 1~k (b) 3~i โˆ’ 1 ~j + 2~k (c) 3x โˆ’ y + 2z = 5
  4. (a) โˆ’ 1312 ~i + 134 ~j + 133 ~k (b) โ‰ˆ 49. 76 โ—ฆ (c) 13/2(d) 13/โˆš 29
  5. (a) 53. 13 โ—ฆ^ east of south (b) According to calculations, he should travel 37. 88 โ—ฆ^ west of south. However if he travels at this angle, he will not move across the river (the wind will be too strong). Review Exercises from Chapter 12
  6. See other page
  7. See other page
  8. z = 2x โˆ’ y + 4
  9. (a) = II, (b) = I
  10. This is a line in 3-space, parallel to the z-axis, through the point (2, 1, 0).
  11. z = โˆ’ 52 x + โˆ’ 32 y + 2
  12. z = 2x โˆ’ y + 2
  13. (a) = II, (b) = IV, (c) = VI, (d) = I, (e) = V, (f) = III
  14. See other page Section 12. 12 - 15. See other page Section 12.
  15. The level surface is a cylinder of elliptical cross-sections centered along the y-axis
  16. The level surfaces are spheres centered at the origin.
  17. (a) Squaring we arrive at the equation z^2 + y^2 = 1, which is a circular cylinder of radius 1 along the x-axis. However the square root, restricts us to only the positive z values, so we get the upper half. (b) It is the level surface g(x, y, z) = 0, where g(x, y, z) = โˆš 1 โˆ’ y^2 โˆ’ z