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3. Verify Stokes' Theorem for the vector field F= 2zi +3xj+5yk, taking S to be a portion of the paraboloid z=4-x² - y² for which z≥0 with an upward orientation, and C to be positively oriented circle x² + y² = 4 that forms the boundary of S in the xy-plane.

3. Verify Stokes' Theorem for the vector field F= 2zi +3xj+5yk, taking S to be a portion of the paraboloid z=4-x² - y² for which z≥0 with an upward orientation, and C to be positively oriented circle x² + y² = 4 that forms the boundary of S in the xy-plane.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.2: Inner Product Spaces
Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...
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3. Verify Stokes' Theorem for the vector field F= 2zi +3xj+5yk, taking S to be a portion of the paraboloid z=4-x² - y² for which z≥0 with an upward orientation, and C to be positively oriented circle x² + y² = 4 that forms the boundary of S in the xy-plane.
Transcribed Image Text:3. Verify Stokes' Theorem for the vector field F= 2zi +3xj+5yk, taking S to be a portion of the paraboloid z=4-x² - y² for which z≥0 with an upward orientation, and C to be positively oriented circle x² + y² = 4 that forms the boundary of S in the xy-plane.
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