21.
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Chapter 13 Solutions
Calculus: Early Transcendentals (2nd Edition)
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University Calculus: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
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Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus & Its Applications (14th Edition)
- Converting from Rectangular Coordinates to Spherical Coordinates Convert the following integral into spherical coordinates: y=3 x=√√9-y²z=√√/18-x²-y² , , x=0 y=0 [ (x² + y² + z²) dz dx dy. z=√√/x² + y²arrow_forwardDescribe the motion of a particle with position (x, y) as t varies in the given interval. (For each answer, enter an ordered pair of the form x, y.) x = 4 + sin(t), y = 6 + 3 cos(t), π/2 ≤ t ≤ 2π The motion of the particle takes place on an ellipse centered at (x, y) = › = ( [ (x, y) = As t goes from 1/2 to 2π, the particle starts at the point (x, y) = and moves clockwise three-fourths of the way around the ellipse toarrow_forwardV4 - x2 8- x2 – y 2 Convert the integral dz dy dx into an integral in spherical coordinates and evaluate it. x2 Vx2 + y2 dp dp de Derarrow_forward
- Triple integral in cylindrical coordinates is given by 2π 2 Υ r?dz dr de 0 0 (i) Evaluate the triple integral. (ii) Convert the integral to spherical coordinates. (Do not evaluate).arrow_forwardr5 •/25–z² (c) The integral p2 sind dr dz d0 is given in cylindrical coordinates. (i) Express the triple integral as an iterated integral in spherical coordinates. Do not evaluate.arrow_forwardEvaluate the integral by changing to cylindrical coordinates. V4 - y2 xz dz dx dy V4 - y2'Vx? + y2arrow_forward
- Calc 3 Evaluate the integral, where E is the solid that lies within the cylinder x2 + y2 = 9, above the plane z = 0, and below the cone z2 = x2 + y2. Use cylindrical coordinates.arrow_forwardChange the integral into cylindrical coordinates. 4-a2 8-22-y2 (22 ²+y²) dzdydaarrow_forwardDescribe the motion of a particle with position (x, y) as t varies in the given interval. (For each answer, enter an ordered pair of the form x, y.) x = 5 + sin(t), y = 2 + 4 cos(t), π/2 ≤ t ≤ 2л The motion of the particle takes place on an ellipse centered at at the point As t goes from л/2 to 2л, the particle starts and moves clockwise three-fourths of the way around the ellipse toarrow_forward
- Q1 Use the parametric equations to calculate the line integral . in the graph ху ds over the path c which is given y (0 ,2p) c2 a circular segment C3 is line segment C1 is line segment (0,-2p)arrow_forwardChanging an Integral from Rectangular to Spherical Coordinates 2 O So S" Só (p² sinp)dpdpd0 O F S2 So (p² sinp)dpdpd® 2x O fr S S ? (6² sinp)dpdpd0 O " So2 S (p² sinp)dpdpdOarrow_forwardWHite the veD secsand orde equation as is equivalent svstem of hirst order equations. u" +7.5z - 3.5u = -4 sin(3t), u(1) = -8, u'(1) -6.5 Use v to represent the "velocity fumerion", ie.v =(). Use o and u for the rwo functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) +7.5v+3.5u-4 sin 3t Now write the system using matrices: dt 3.5 7.5 4 sin(3t) and the initial value for the vector valued function is: u(1) v(1) 3.5arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning