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 ,

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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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 4E (LL) W/ ACHIEVE ACCESS

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

Ch. 17.1 - Prob. 7E Ch. 17.1 - Prob. 8E Ch. 17.1 - Prob. 9E Ch. 17.1 - Prob. 10E Ch. 17.1 - Prob. 11E Ch. 17.1 - Prob. 12E Ch. 17.1 - Prob. 13E Ch. 17.1 - Prob. 14E Ch. 17.1 - Prob. 15E Ch. 17.1 - Prob. 16E Ch. 17.1 - Prob. 17E Ch. 17.1 - Prob. 18E Ch. 17.1 - Prob. 19E Ch. 17.1 - Prob. 20E Ch. 17.1 - Prob. 21E Ch. 17.1 - Prob. 22E Ch. 17.1 - Prob. 23E Ch. 17.1 - Prob. 24E Ch. 17.1 - Prob. 25E Ch. 17.1 - Prob. 26E Ch. 17.1 - Prob. 27E Ch. 17.1 - Prob. 28E Ch. 17.1 - Prob. 29E Ch. 17.1 - Prob. 30E Ch. 17.1 - Prob. 31E Ch. 17.1 - Prob. 32E Ch. 17.1 - Prob. 33E Ch. 17.1 - Prob. 34E Ch. 17.1 - Prob. 35E Ch. 17.1 - Prob. 36E Ch. 17.1 - Prob. 37E Ch. 17.1 - Prob. 38E Ch. 17.1 - Prob. 39E Ch. 17.1 - Prob. 40E Ch. 17.1 - Prob. 41E Ch. 17.1 - Prob. 42E Ch. 17.1 - Prob. 43E Ch. 17.1 - Prob. 44E Ch. 17.1 - Prob. 45E Ch. 17.1 - Prob. 46E Ch. 17.1 - Prob. 47E Ch. 17.1 - Prob. 48E Ch. 17.1 - Prob. 49E Ch. 17.1 - Prob. 50E Ch. 17.1 - Prob. 51E Ch. 17.1 - Prob. 52E Ch. 17.1 - Prob. 53E Ch. 17.1 - Prob. 54E Ch. 17.1 - 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Prob. 12E Ch. 17.5 - Prob. 13E Ch. 17.5 - Prob. 14E Ch. 17.5 - Prob. 15E Ch. 17.5 - Prob. 16E Ch. 17.5 - Prob. 17E Ch. 17.5 - Prob. 18E Ch. 17.5 - Prob. 19E Ch. 17.5 - Prob. 20E Ch. 17.5 - Prob. 21E Ch. 17.5 - Prob. 22E Ch. 17.5 - Prob. 23E Ch. 17.5 - Prob. 24E Ch. 17.5 - Prob. 25E Ch. 17.5 - Prob. 26E Ch. 17.5 - Prob. 27E Ch. 17.5 - Prob. 28E Ch. 17.5 - Prob. 29E Ch. 17.5 - Prob. 30E Ch. 17.5 - Prob. 31E Ch. 17.5 - Prob. 32E Ch. 17.5 - Prob. 33E Ch. 17.5 - Prob. 34E Ch. 17.5 - Prob. 35E Ch. 17.5 - Prob. 36E Ch. 17.5 - Prob. 37E Ch. 17.5 - Prob. 38E Ch. 17 - Prob. 1CRE Ch. 17 - Prob. 2CRE Ch. 17 - Prob. 3CRE Ch. 17 - Prob. 4CRE Ch. 17 - Prob. 5CRE Ch. 17 - Prob. 6CRE Ch. 17 - Prob. 7CRE Ch. 17 - Prob. 8CRE Ch. 17 - Prob. 9CRE Ch. 17 - Prob. 10CRE Ch. 17 - Prob. 11CRE Ch. 17 - Prob. 12CRE Ch. 17 - Prob. 13CRE Ch. 17 - Prob. 14CRE Ch. 17 - Prob. 15CRE Ch. 17 - Prob. 16CRE Ch. 17 - Prob. 17CRE Ch. 17 - Prob. 18CRE Ch. 17 - Prob. 19CRE Ch. 17 - Prob. 20CRE Ch. 17 - Prob. 21CRE Ch. 17 - Prob. 22CRE Ch. 17 - 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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 .

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Chapter 17 Solutions