The Calculus of Functions of Several Variables

Section 4.4

cssp — Sun, 01 Jul 2007 18:46:46 +0000

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1. (a)

2. (a)
(c)

Section 4.3

cssp — Sun, 01 Jul 2007 17:54:44 +0000

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1. (a)
(c)

2. (a)

3. (a)

4. (a)

6. (a)

Section 4.2

cssp — Sun, 01 Jul 2007 15:55:08 +0000

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1. (a)

(c)

2. (a) , ,

(c)

(e)

4. (a)

(c)

8. (a) ,

(b) The level curves of are circles.

Section 4.1

cssp — Fri, 29 Jun 2007 18:34:55 +0000

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2. The surface is the graph of .

Section 3.7

cssp — Fri, 29 Jun 2007 18:26:57 +0000

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5. (a)

(c)

6. (a)

(c)

10.

13.

15.

17.

19.

21. (b)

23.

25.

Section 3.6

cssp — Fri, 29 Jun 2007 13:40:15 +0000

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1. (a)

(c)

2. (a)

(c)

3. (a)

(c)

11. (a)

(c)

12.

14. (a) Mass: ; center of mass:

(b) Mass: ; center of mass:

16. (a)

(b)

Section 3.5

cssp — Fri, 29 Jun 2007 00:39:08 +0000

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1. Maximum value of at and ; minimum value of at and

3. Maximum value of at and ; minimum value of at and

5. Local minimum of at all points of the form , ; local maximum of at and

7. Local maximum of at and ; saddle point at

9. Local minimum of at

11.

12.

13. Maximum value of at ; minimum value of at

15. Minimum distance of at

17. Hottest point: at ; coldest point: at

20. Local minimum of at all points of the form ,

24.

Section 3.4

cssp — Thu, 28 Jun 2007 18:38:03 +0000

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1. (a)

(c)

(e)

(g)

2. (a)

(c)

(e)

3. (a)

(b)

4. (a)

(c)

5. (a) Positive definite

(e) Positive definite

Section 3.3

cssp — Thu, 28 Jun 2007 13:11:45 +0000

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1. (a)

(c)

(e)

2. (a)

(c)

4. (a)

(b)

5. ; ;

9. (a)

(c)

10. (a)

(c)

Section 3.2

cssp — Wed, 27 Jun 2007 19:02:36 +0000

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2. (a) ;

(c)

(e)

3. (a)

(c)

4. (a)

(c)

5. (a) , where

6. (a)

(b) Direction:

Rate of change:

9. (b) 0}' title='\displaystyle{\frac{\partial}{\partial y}d_A(x,y) > 0}' class='latex' />, 0}' title='\displaystyle{\frac{\partial}{\partial x}d_B(x,y) > 0}' class='latex' />

11. (a)

(b) No