Section 17.7) Verify Stokes' Theorem for F(x, y, z) =< y, −z, 2x > if C' is the intersection of z = 4 + y and x² + y² = 4counterclockwise when viewed from above.

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Answered: Section 17.7) Verify Stokes' Theorem…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Example 3 Determine the equation of a plane tangent to the surface defined by f(x, y) = √√x² + y2 at the point (3,4,5). x2 (a) Find a parameterization for the x = 3 trace of f. What is a direction vector for the line tangent to this trace at the point (3, 4, 5)? (b) Find a parameterization for the y = 4 trace of f. What is a direction vector for the line tangent to this trace at the point (3,4,5)? (c) The direction vectors in parts (a) and (b) form a plane containing the point (3,4,5). What is a normal vector for this plane? (d) Use your work in parts (a), (b), and (c) to determine an equation for the tangent plane.
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Section 17.7) Verify Stokes' Theorem for F(x, y, z) =< y, -z, 2x > if C is the intersection of z = 4 + y and x² + y² = 4 counterclockwise when viewed from above.