Show that the curl of is zero but that is not zero if C is the circle

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Show that the curl ofimage


is zero but thatimage


is not zero if C is the circle x2 + y2 = 1 in the xy-plane. (Theorem 7 does not apply here because the domain of F is not simply connected. The field F is not defined along the z-axis so there is no way to contract C to a point without leaving the domain of F.)image

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Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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