Explanation For funding the tangent vector we have to use the partial derivatives and normal is the vector product of two tangent vectors as well as for surface integral we have to write the surface integral as iterated double integral by using surface integral formula. Given: Surface is bounded by the following equations. G ( u , v ) = ( 2 u sin ( v 2 ) , 2 u cos ( v 2 ) , 3 v ) 0 ≤ u ≤ 1 and 0 ≤ v ≤ 2 π Calculation:(a ) G ( u , v ) = ( 2 u sin ( v 2 ) , 2 u cos ( v 2 ) , 3 v ) Then find the derivative of function G u ( u , v ) = ( 2 sin ( v 2 ) , 2 cos ( v 2 ) , 0 ) and G v ( u , v ) = ( u cos ( v 2 ) , − u s i n ( v 2 ) , 3 ) at given point p = G ( 1 , π 3 ) G u ( 1 , π 3 ) = ( 2 sin ( π 6 ) , 2 cos ( π 6 ) , 0 ) and G v ( u , v ) = ( cos ( π 6 ) , − s i n ( π 6 ) , 3 ) G u ( 1 , π 3 ) = ( 1 , 3 , 0 ) and G v ( 1 , π 3 ) = ( 3 2 , − 1 2 , 3 ) t h e n T u = G u ( 1 , π 3 ) | G u ( 1 , π 3 ) | = ( 1 , 3 , 0 ) 2 = ( 1 2 , 3 2 , 0 ) T v = G v ( 1 , π 3 ) | G v ( 1 ,

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 17, Problem 44CRE

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To calculate: (a) The tangent vectors and normal vector at given point as well as normal vector at same point (b) equation of tangent plane (c) surface integral .

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Chapter 17, Problem 43CRE

Chapter 17, Problem 45CRE

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Chapter 17 Solutions

Calculus - Standalone book

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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(a) The tangent vectors and normal vector at given point as well as normal vector at same point (b) equation of tangent plane (c) surface integral .

Solution Summary: The author explains how to calculate the tangent vector and normal vector at a given point, and the surface integral.

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To calculate: (a) The tangent vectors and normal vector at given point as well as normal vector at same point (b) equation of tangent plane (c) surface integral .

Want to see the full answer?

Chapter 17 Solutions