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d) Use Green's Theorem to evaluate the integral In(1+y) dx-dy, where Cis y the triangle with vertices (0,0), (2,0) and (0,4).

d) Use Green's Theorem to evaluate the integral In(1+y) dx-dy, where Cis y the triangle with vertices (0,0), (2,0) and (0,4).

Calculus: Early Transcendentals
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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d)

a) b) c) d) If A=xz³ i-2x²yz j+2yz4 k, find VxA (curl A) at the point (1,-1,1). Find the directional derivative of = x²yz + 4xz² at (1,-2,-1) in the direction 2i-j-2k. Suppose that a particle travels once around the units circle in the counterclockwise direction and that at the point (x, y) it is subject to the force F(x, y) = (ex-³)i + (x+cos y)j. Use Green's theorem to find the work done by the force. Use Green's Theorem to evaluate the integral In(1+y) dx-dy, where Cis 1+ the triangle with vertices (0,0), (2,0) and (0,4).
Transcribed Image Text:a) b) c) d) If A=xz³ i-2x²yz j+2yz4 k, find VxA (curl A) at the point (1,-1,1). Find the directional derivative of = x²yz + 4xz² at (1,-2,-1) in the direction 2i-j-2k. Suppose that a particle travels once around the units circle in the counterclockwise direction and that at the point (x, y) it is subject to the force F(x, y) = (ex-³)i + (x+cos y)j. Use Green's theorem to find the work done by the force. Use Green's Theorem to evaluate the integral In(1+y) dx-dy, where Cis 1+ the triangle with vertices (0,0), (2,0) and (0,4).
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