Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 17 - Line and Surface Integrals - 17.4 Parametrized Surfaces and Surface Integrals - Exercises - Page 957: 1

Answer

(a) Figure 16 (v) (b) Figure 16 (iii) (c) Figure 16 (i) (d) Figure 16 (iv) (e) Figure 16 (ii)

Work Step by Step

We plot the parametrizations and compare with those in Figure 16. Please see figure attached. (a) The parametrization $\left( {u,\cos v,\sin v} \right)$ corresponds to Figure 16 (v). (b) The parametrization $\left( {u,u + v,v} \right)$ corresponds to Figure 16 (iii). (c) The parametrization $\left( {u,{v^3},v} \right)$ corresponds to Figure 16 (i). (d) The parametrization $\left( {\cos u\sin v,3\cos u\sin v,\cos v} \right)$ corresponds to Figure 16 (iv). (e) The parametrization $\left( {u,u\left( {2 + \cos v} \right),u\left( {2 + \sin v} \right)} \right)$ corresponds to Figure 16 (ii).
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