Exercicios resolvidos James Stewart vol. 2 7ª ed - ingles

SECTION 14.1 FUNCTIONS OF SEVERAL VARIABLES 0 185
21 . We need 1 - x 2 - y 2 - z 2 ~ 0 or x 2 + y 2 + z 2 ~ 1,
soD= { (x, y, z) I x 2 + y 2 + z 2 ~ 1} (the points inside
or on the sphere of radius 1, center the origin).
23. z = 1 + y, a plane which intersects the yz-plane in the
line z = 1 + y, x = 0. The portion of this plane for
x ~ 0, z ~ 0 is shown.
X
y
25. z = 10 - 4x - Sy or 4x + Sy + z = 10, a plane with
intercepts 2.5, 2, and 10.
27. z = y 2 + 1, a parabolic cylinder
(0, 0, 10)
X
29. z = 9 - x 2 - 9y 2 , an ell iptic paraboloid opening
downward with vertex at (0, 0, 9) .
31. z = )4- 4x 2 - y 2 so 4x 2 + y 2 + z 2 = 4 or
y2
z2
x 2 + 4
+ 4
= 1 and z ~ 0, the top half of an
ellipsoid .
.r
33. The point (- 3, 3) lies between the level curves with z-values 50 and 60. Since the point is a little closer to the level curve with
z = 60, we estimate that f( -3, 3) ~56. The point (3, -2) appears to be just about halfway between the level curves with
z-values 30 and 40, so we estimate !(3, - 2) ~ 35. The graph rises as we approach the origin, gradually from above, steeply
from below.
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