3. A) www Find the circulation of F = -yi + x²j + zk around the oriented boundary of the part of the paraboloid z = 9 - x² - y² lying above the xy-plane and having the normal vector pointing upward. B) Let C be a piecewise, smooth, simple, closed plane curve in R³, which lies in a plane with unit normal N = ai + bj + ck and has orientation inherited from that of the plane. Prove that the plane area enclosed by C is 1 √(bz 2 C (bz - cy)dx + (cx - az)dy + (ay - bx)dz.

3. A) www Find the circulation of F = -yi + x²j + zk around the oriented boundary of the part of the paraboloid z = 9 - x² - y² lying above the xy-plane and having the normal vector pointing upward. B) Let C be a piecewise, smooth, simple, closed plane curve in R³, which lies in a plane with unit normal N = ai + bj + ck and has orientation inherited from that of the plane. Prove that the plane area enclosed by C is 1 √(bz 2 C (bz - cy)dx + (cx - az)dy + (ay - bx)dz.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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