2. The function f(x,y,z) = xyz has gradient Vf(x,y, z) = (yz, cz, ry). Let C be the path from (1, 1, 1) to (2,2,2) consisting of the line segment from (1, 1,1) to (10,9,8), followed by the line segment from (10,9,8) to (–4,3,7), followed by the line segment from (–4, 3, 7) to (2, 2, 2). Compute ſc yz dx + xz dy + ry dz. Explain.
2. The function f(x,y,z) = xyz has gradient Vf(x,y, z) = (yz, cz, ry). Let C be the path from (1, 1, 1) to (2,2,2) consisting of the line segment from (1, 1,1) to (10,9,8), followed by the line segment from (10,9,8) to (–4,3,7), followed by the line segment from (–4, 3, 7) to (2, 2, 2). Compute ſc yz dx + xz dy + ry dz. Explain.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 78E: Let S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from...
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Transcribed Image Text:2. The function f(x,y,z) = xyz has gradient
V f(x, y, z) = (yz, rz, ry).
Let C be the path from (1, 1, 1) to (2, 2,2) consisting of the line segment from (1, 1,1)
to (10,9,8), followed by the line segment from (10,9, 8) to (–4, 3, 7), followed by the line
segment from (-4,3,7) to (2,2, 2). Compute fC yz dx + cz dy + xy dz. Explain.
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