Explanation Given: The upper half of the sphere x 2 + y 2 + z 2 = 9 has parametrization G ( r , θ ) = ( r cos θ , r sin θ , 9 − r 2 ) and R is the small domain defined by 2 ≤ r ≤ 2.1 , π 3 ≤ θ ≤ π 3 + 0.05 . Formula used: Area ( S i j ) ≈ ‖ N ( u i j , v i j ) ‖ A r e a ( R i j ) Calculation: a. T r ( r , θ ) = ( cos θ , sin θ , − r 9 − r 2 ) T θ ( r , θ ) = ( − r sin θ , r cos θ , 0 ) Therefore, T r ( 2 , π 3 ) = ( cos π 3 , sin π 3 , − 2 9 − 2 2 ) = ( 1 2 , 3 2 , − 2 5 ) T θ ( 2 , π 3 ) = ( − 2 sin π 3 , 2 cos π 3 , 0 ) = ( − 3 , 1 , 0 ) Thus, N=T r ×T θ = | i j k 1 2 3 2 −

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Chapter 17, Problem 51CRE

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The normal vector and estimate the surface area of G(R).

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Chapter 17, Problem 50CRE

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Chapter 17 Solutions

CALCULUS (CLOTH)

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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The normal vector and estimate the surface area of G ( R ).

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The normal vector and estimate the surface area of G(R).

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Chapter 17 Solutions