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M 408C
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Gary, Berg
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Mathematics

M 408C

Gary, Berg

Fall

Description

taboada (lat2278) – HW07 – berg – (56260) 1
This print-out should have 21 questions.
Multiple-choice questions may continue on 1 −4
1. area = 4 (1 − e )
the next column or page – ﬁnd all choices
before answering. 1 −2
2. area = (1 − e )
4
001 10.0 points 1
3. area = (1 − e4)
2
The shaded region in
4. area = 1 (1 − e2)
2
1 −2
5. area = 8 (1 − e )
1 −4
6. area = (1 − e )
8
003 10.0 points
Find the area of one loop of the graph of
the polar function
r = 4cos2θ .
1. area = 2π
lies inside the polar curve r = 3cosθ and
outside the polar curve r = 2cosθ. Determine 29
the area of this region? 2. area = π
16
π 31
1. area = 5 2 + 1 3. area = π
16
2. area = 5π 4. area = 33 π
16
3. area = 5 π + 1 15
4 2 5. area = 8 π
5 π
4. area = + 1 004 10.0 points
2 2 Find the area of the shaded region shown
5
5. area = π in
2
5
6. area = 4 π
002 10.0 points
Find the area of the region bounded by the
polar curve
−2θ
r = e
as well as the rays θ = 0 and θ = 1. taboada (lat2278) – HW07 – berg – (56260) 2
between the graphs of the spiral r = 4θ and
the circle r = sinθ. 1 π
6. area = 2 4 + 1
1 8
1. area = π π − 1 006 10.0 points
8 3
2. area = 1π 8 π + 1 Find the arc length of the portion of the
8 3
graph shown as a solid curve in
1 16 3
3. area = π + 1
16 3
1 16
4. area = π − 1
16 3
1 16 3
5. area = 8 3π − 1
1 8 2
6. area = π π + 1
16 3
005 10.0 points of the polar curve
r = 1 + cosθ .
Find the area of the shaded region in
1. arc length = 2
2. arc length = √2
√
3. arc length = 2 − 2
√
4. arc length = 2(2 − 2)
5. arc length = 4
√
6. arc length = 2 2
speciﬁed by the graphs of the circles
007 10.0 points
r = cosθ , r = sinθ .
A triangle ∆PQR has vertices
1 π
1. area = + 1
4 2 P(−2, −1, −1), Q(−3, 0, −4), R(−1, −2, −4).
1
2. area = π Use the distance formula to decide which one
4 of the following properties the triangle has.
1
3. area = 2π
1. isoceles with |RP|= |RQ|
1 π
4. area = 4 2 − 1 2. not isoceles
5. area = 1
4 3. isoceles with |QP|= |QR| taboada (lat2278) – HW07 – berg – (56260) 3
2 2 2
4. isoceles with |PQ|= |PR| 5. x + y + z + 6x − 2y − 4z + 10 = 0
2 2 2
008 10.0 points 6. x + y + z − 6x + 2y + 4z + 5 = 0
Find an equation for the sphere centered at
(2, 2, −1) and passing through (2, 2, 3). 011 10.0 points
Find the vector v having a representation
2 2 2 −−→
1. x + y + z + 4x + 4y − 2z = 7 by the directed line segment AB with respect
to points
2 2 2
2. x + y + z − 4x − 4y + 2z = 7
A(−2, −5, 4), B(−1, −3, −5).
3. x + y + z − 4x − 4y + 2z + 7 = 0
1. v = ▯−1, 2, 9▯
4. x + y + z + 4x + 4y − 2z + 7 = 0
2 2 2 2. v = ▯−3, −8, −1▯
5. 2x + 2y − z = 7
2 2 2 3. v = ▯3, −8, 1▯
6. 2x + 2y − z + 7 = 0

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