Thomas Calculus 13th [Solutions]

1060 Chapter 14 Partial Derivatives
6. Domain: All points ( x, y, z ) in space
Range: Nonnegative real numbers
Level surfaces are ellipsoids with center (0, 0, 0).
7. Domain: All ( x, y, z ) such that ( x, y, z) (0, 0, 0)
Range: Positive real numbers
Level surfaces are spheres with center (0, 0, 0) and
radius r 0.
8. Domain: All points ( x, y, z ) in space
Range: (0, 1]
Level surfaces are spheres with center (0, 0, 0) and
radius r 0.
9.
10.
ln 2
lim e y cos x e cos (2)( 1) 2
( x, y) ( , In 2)
lim 2 y 2 0
( , ) (0, 0)
x cos y 0 cos 0
2
x y
x y
x y
11. lim lim lim 1 1 1
2 2
( x, y) (1,1) x y ( x, y) (1,1)
( x y)( x y) ( x, y) (1,1)
x y 1 1 2
x y x y
12.
2 2
lim 3 3
x y 1 lim ( xy 1) x y xy 1
2 2 2 2
( , ) (1,1) ( , ) (1,1)
1
lim x y xy 1 1 1 1 1 1 3
x y
xy y
x y
xy
( x, y) (1,1)
13.
P
lim ln x y z ln 1 ( 1) e ln e 1
(1, 1, e)
14.
P
lim
1
tan ( x y z)
tan
1
1 ( 1) ( 1) tan
1
( 1)
(1, 1, 1)
4
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