CALCULUS,EARLY TRANS LCPO
9th Edition
ISBN: 9780357771105
Author: Stewart
Publisher: CENGAGE L
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The Cartesian coordinates of a point are given.
(a) (4,-4)
(i) Find polar coordinates (r, e) of the point, where r > 0 and 0 0 and 0 < 0 < 2π.
(r, 6) =
X
7
(ii) Find polar coordinates (r, 8) of the point, where r < 0 and 0 0 < 2π.
(r, 0) =
X
r>0
(r, 0) =
T 0 and one with r 0
2
(c) (9,-17)
3
(r, 8)
(r, 8)
r> 0
r<0
(r, 0) =
(r, 8) =
X
X
X
x x
W
74. Geometry of implicit differentiation Suppose x and y are related
0. Interpret the solution of this equa-
by the equation F(x, y)
=
tion as the set of points (x, y) that lie on the intersection of the
F(x, y) with the xy-plane (z = 0).
surface
Z
=
a. Make a sketch of a surface and its intersection with the
xy-plane. Give a geometric interpretation of the result that
dy
dx
=
Fx
F
χ
y
b. Explain geometrically what happens at points where F = 0.
y
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