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MTH203
Review Problems(EXAM#2)
Q1. Consider the plane x
+
y
+
z
=
0.
a)Give three distinct points with integer coordinates that lie on this plane.
b) Find the area of the triangle formed by the three points.
Q2. Suppose
u
=<
1,0
>
,
v
=<
1
2
,
1
2
>
,
D
u
f
a
,
b
±±
=
3
and
D
v
f
a
,
b
±±
=
2
a) Find
4
f
a
,
b
±
b) What is the maximum possible value of
D
w
f
a
,
b
±±
=
3
for any
w
c) Find a unit vector
w
=<
w
1
,
w
2
>
such that
D
w
f
a
,
b
±±
=
0.
Q3. Find an equation of the tangent plane to the hyperboloid given by
z
2
?
2
x
2
?
2
y
2
?
12
=
0
at the point
1,
?
1, 4
±
.
Q4. Find symmetric equations for the tangent line to the curve of intersection of the ellipsoid
given by
x
2
+
4
y
2
+
2
z
2
=
27
and the hyperboloid given by
x
2
+
y
2
?
2
z
2
=
11
at the point
(3,2,1).
5) Let R be the region in the plane bounded by the curves
y
2
=
2
x
and
y
2
=
8
?
2
x
. Set up the
R
XX
f
x
,
y
±
dA
in
both orders dxdy and dydx. Find the area of R.
6) Evaluate the iterated integral by converting to polar coordinates
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This note was uploaded on 10/20/2008 for the course MATHS MTH 203 taught by Professor None during the Spring '08 term at American University of Sharjah.
 Spring '08
 none
 Calculus

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