Thomas Calculus 13th [Solutions]

CHAPTER 14 PARTIAL DERIVATIVES
14.1 FUNCTIONS OF SEVERAL VARIABLES
1. (a) f (0, 0) 0
(b) f ( 1, 1) 0
(c) f (2, 3) 58
(d) f ( 3, 2) 33
2. (a)
(d)
3
f 2,
(b) f 3, 1
(c) f , 1 1
2 2
12 2
4 2
f 2 , 7 1
3. (a) f (3, 1, 2) 4
5
(b) f 1, 1 , 1 8
(c) f 0, 1 , 0 3
2 4 5
3
(d) f (2, 2, 100) 0
4. (a) f (0, 0, 0) 7
(b) f (2, 3, 6) 0
(c) f ( 1, 2, 3) 35
(d) f 4 , 5 , 6 21
2 2 2
2
5. Domain: all points ( x, y ) on or above the line
y x 2
6. Domain: all points ( x, y ) outside the circle
2 2
x y 4
7. Domain: all points ( x, y ) not lying on the graph of
3
y x or y x
8. Domain: all points ( x, y ) not lying on the graph
2 2
of x y 25
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