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Lecture

Calc Hw7 .pdf

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Department
Mathematics
Course
M 408C
Professor
Gary, Berg
Semester
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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