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Math 215
Homework Set 10:
§§
17.5 – 17.7
Fall 2007
Most of the following problems are modiﬁed versions of the recommended homework problems from
your text book
Multivariable Calculus
by James Stewart.
17.5a. The role of curl and divergence in multivariable Calculus is similar to the role of words in a com
position; in order for the ﬁnal product to make sense, you need to know in which order things may
be placed. To this end, please do Problems 12, 19, 20, 23–29 of
§
17.5 in Stewart’s
Multivariable
Calculus
.
17.6a. Find the area of the ﬁnite part of the paraboloid of revolution
z
= 2
x
2
+ 2
y
2
cut off by the plane
z
= 50
.
17.6b. Find the area of the surface that lies on the sphere
x
2
+
y
2
+
z
2
= 4
x
and inside the paraboloid of
revolution
x
=
y
2
+
z
2
. Hint: Sketch the surface.
17.6c. Find an equation for the tangent plane to the surface parameterized by
r
(
u, v
) =
±
u
2
, v
2
, uv
²
at the point
(1
,
1
,

1)
. Sketch a graph of the surface and the tangent plane. Use MAPLE if you
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This homework help was uploaded on 04/02/2008 for the course MATH 215 taught by Professor Fish during the Fall '08 term at University of Michigan.
 Fall '08
 Fish
 Multivariable Calculus

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