a) Prove that if E is a Jordan region whose topological boundary is a piecewise smooth curve

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a) Prove that if E is a Jordan region whose topological boundary is a piecewise smooth curve oriented in the counterclockwise direction, then

b) Find the area enclosed by the loop in the Folium of Descartes; that is, by

c) Find an analogue of part a) for the volume of a Jordan region E in R3.
d) Compute the volume of the torus with radii a > b (see Example 13.32).

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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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Question Posted: Mar 29, 2016 04:28 AM

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a) Prove that if E is a Jordan region whose topological boundary is a piecewise smooth curve

Question:

Area (E)dy y dx. 31 312 ф(t) =

Step by Step Answer:

a Let P y and Q x Then Q x P y 2 and we have by Greens Theorem that b If x 3t1 t 3 and y 3t 2 1 ...View the full answer

An Introduction to Analysis

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