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3.3 Use the differential volume dv to determine the volumes of the following regions: (a) 0

3.3 Use the differential volume dv to determine the volumes of the following regions: (a) 0

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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O F ZU:38 chapter 03.pdf -> Figure 3.27 For Review Question 3.8. Answers: 3.la-(vi), b-(vii), c-(v), d-(i), e-(ii), f-(iv), g-(iii), 3.2a-(vi), b-(v), c-(vii), d-(ii), e-(i), f-(iv), g-(ii), 3.3a-(v), b-(vi), c-(iv), d-(iii), e-(i), f-(ii), 3.4b, 3.5c, 3.6c, 3.7e, 3.8a, 3.9a, 3.10b. 3.1 Using the differential length dl, find the length of each of the following curves: AS (a) p = 3, w/4 <0< T/2, z = constant (b) r = 1,0 = 30°, 0 < ¢ < 60° (c) r = 4, 30° << < 90°, ¢ = constant 3.2 Calculate the areas of the following surfaces using the differential surface area dS: (a) p = 2,0 < z< 5, n/3 < ¢ < x/2 (b) z = 1, 1< p< 3,0< 6< T/4 (c) r= 10, x/4 <0< 2a/3, 0 <o< 27 (d) 0<r<4, 60° <0 < 90°, o = constant 3.3 Use the differential volume dv to determine the volumes of the following regions: (a) 0<x<1,1<y< 2, -3 <z< 3 (b) 2 <p< 5, /3 < < x, -1<?< 4 (c) 1<r< 3, x/2 <0< 2x/3, x/6 < 6< 1/2 3.4 Given that p, = x + xy, calculate fseds over the region y sx,0 <x< !. 3.5 Given that H = x°a, + y'a,, evaluate H dl, where L is along the curve y = x from (0, 0) to (1, 1). 3.6 Find the volume cut from the sphere radius r= a by the cone e = a. Calculate the volume when a = T/3 and a = r/2. Vector Calculus 3.7 icle from A to B, on a particle that travels from A(0, 0, 0) to B(2, 1, 3) along (a) Die segment (0, 0, 0) → (0, 1, 0) -→ (2, 1, 0) → (2, 1, 3) (b) The straight line (0, 0, 0) to (2, 1, 3) II
Transcribed Image Text:O F ZU:38 chapter 03.pdf -> Figure 3.27 For Review Question 3.8. Answers: 3.la-(vi), b-(vii), c-(v), d-(i), e-(ii), f-(iv), g-(iii), 3.2a-(vi), b-(v), c-(vii), d-(ii), e-(i), f-(iv), g-(ii), 3.3a-(v), b-(vi), c-(iv), d-(iii), e-(i), f-(ii), 3.4b, 3.5c, 3.6c, 3.7e, 3.8a, 3.9a, 3.10b. 3.1 Using the differential length dl, find the length of each of the following curves: AS (a) p = 3, w/4 <0< T/2, z = constant (b) r = 1,0 = 30°, 0 < ¢ < 60° (c) r = 4, 30° << < 90°, ¢ = constant 3.2 Calculate the areas of the following surfaces using the differential surface area dS: (a) p = 2,0 < z< 5, n/3 < ¢ < x/2 (b) z = 1, 1< p< 3,0< 6< T/4 (c) r= 10, x/4 <0< 2a/3, 0 <o< 27 (d) 0<r<4, 60° <0 < 90°, o = constant 3.3 Use the differential volume dv to determine the volumes of the following regions: (a) 0<x<1,1<y< 2, -3 <z< 3 (b) 2 <p< 5, /3 < < x, -1<?< 4 (c) 1<r< 3, x/2 <0< 2x/3, x/6 < 6< 1/2 3.4 Given that p, = x + xy, calculate fseds over the region y sx,0 <x< !. 3.5 Given that H = x°a, + y'a,, evaluate H dl, where L is along the curve y = x from (0, 0) to (1, 1). 3.6 Find the volume cut from the sphere radius r= a by the cone e = a. Calculate the volume when a = T/3 and a = r/2. Vector Calculus 3.7 icle from A to B, on a particle that travels from A(0, 0, 0) to B(2, 1, 3) along (a) Die segment (0, 0, 0) → (0, 1, 0) -→ (2, 1, 0) → (2, 1, 3) (b) The straight line (0, 0, 0) to (2, 1, 3) II
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