Let h be the vector field h(x, y, z) = (2xy + ²)i + (x² − 2yz)j + (2x= − y²) k. (a) Show that h is a gradient field. (b) What is the value of [((2xy + 2²) dx + (x² − 2yz) dy + (2x= − y²) dz for every piecewise-smooth curve C (i) from (1, 0, 1) to (3, 2, -1)? (ii) from (3, 2, -1) to (1, 0, 1)?

Let h be the vector field h(x, y, z) = (2xy + ²)i + (x² − 2yz)j + (2x= − y²) k. (a) Show that h is a gradient field. (b) What is the value of [((2xy + 2²) dx + (x² − 2yz) dy + (2x= − y²) dz for every piecewise-smooth curve C (i) from (1, 0, 1) to (3, 2, -1)? (ii) from (3, 2, -1) to (1, 0, 1)?

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 11P

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