please dont use chat gpt 2. Verify the Stokes' theorem for the vector fieldF(x, y, z) = (2z − y)i + (x + z)j + (3x - 2y)kwhere the outward oriented surface S is given by z = 9 - x² - y² for z > 0, and the curveC = {(x, y, z)| x² + y² = 9, z = 0}which is oriented consistently with S; use the right-hand direction to determine the orientation ofC. Support your answer with a sketch of the surface S along with the curve C. Remark. Here,you are asked to show that the total (or net) infinitesimal rotation of F over the entire surface Sis equal to the circulation of F "just" along C.

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Answered: 2. Verify the Stokes' theorem for the…

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

Section9.6: Equations Of Lines And Planes

Problem 2E

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