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APPM 2350
HOMEWORK 05
FALL 2010
Due Thursday, September 30, 2010 at the start of your recitation
1. You know the routine for the Frst problem.
2. If you have not Fnished problem 1, go back and Fnish it.
3. Consider the surface,
S
,descr
ibedby
z
=
f
(
x, y
)
.
(1)
Hence, if
P
0
is a point on
S
, then its coordinates, (
x
0
,y
0
,z
0
), must satisfy (1). Using the basic
concept of partial derivatives, we have the ability to determine the equation of the tangent plane to
S
at
P
0
. To do so, consider the following basic calculations.
(a) At
P
0
, build two vectors,
v
1
and
v
2
, with the following properties:
v
1
should be parallel to the
x

z
plane with slope
f
x
(
P
0
);
v
2
should be parallel to the
y

z
plane with slope
f
y
(
P
0
).
(b) One can use the vectors
v
1
and
v
2
at point
P
0
on
S
to create the tangent plane,
T
. Calculate a
normal
n
to
T
. (Note that your
n
is not necessarily the unit normal vector, ˆ
n
, but it is at least
pointed in the correct direction.)
(c) Now, using the coordinates of
P
0
and the normal
n
, determine the equation of the tangent plane
T
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This note was uploaded on 02/10/2011 for the course APPM 2350 taught by Professor Adamnorris during the Fall '07 term at Colorado.
 Fall '07
 ADAMNORRIS

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