That G ( u , v ) = ( 2 u + 1 , u − v , 3 u + v ) parametrizes the plane 2 x − y − z = 2 . And to determine the following a) Calculate T u , T v and n ( u , v ) b) Find the area of S = G ( D ) , where D = { ( u , v ) : 0 ≤ u ≤ 2 , 0 ≤ v ≤ 1 } c) Express f ( x , y , z ) = y z in terms of u and v , and evaluate ∬ S f ( x , y , z ) d S

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Answer 1

Question

Chapter 17.4, Problem 3E

To determine

To show: That $G (u, v) = (2 u + 1, u - v, 3 u + v)$ parametrizes the plane $2 x - y - z = 2$ . And to determine the following

a) Calculate $T_{u}$ , $T_{v}$ and $n (u, v)$

b) Find the area of $S = G (D)$ , where $D = {(u, v) : 0 \leq u \leq 2, 0 \leq v \leq 1}$

c) Express $f (x, y, z) = y z$ in terms of u and v, and evaluate $\iint_{S} f (x, y, z) d S$

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Answer 2

Question

Chapter 17.4, Problem 3E

To determine

To show: That $G (u, v) = (2 u + 1, u - v, 3 u + v)$ parametrizes the plane $2 x - y - z = 2$ . And to determine the following

a) Calculate $T_{u}$ , $T_{v}$ and $n (u, v)$

b) Find the area of $S = G (D)$ , where $D = {(u, v) : 0 \leq u \leq 2, 0 \leq v \leq 1}$

c) Express $f (x, y, z) = y z$ in terms of u and v, and evaluate $\iint_{S} f (x, y, z) d S$

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Answer 3

Question

Chapter 17.4, Problem 3E

To determine

To show: That $G (u, v) = (2 u + 1, u - v, 3 u + v)$ parametrizes the plane $2 x - y - z = 2$ . And to determine the following

a) Calculate $T_{u}$ , $T_{v}$ and $n (u, v)$

b) Find the area of $S = G (D)$ , where $D = {(u, v) : 0 \leq u \leq 2, 0 \leq v \leq 1}$

c) Express $f (x, y, z) = y z$ in terms of u and v, and evaluate $\iint_{S} f (x, y, z) d S$

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Answer 4

Question

Chapter 17.4, Problem 3E

To determine

To show: That $G (u, v) = (2 u + 1, u - v, 3 u + v)$ parametrizes the plane $2 x - y - z = 2$ . And to determine the following

a) Calculate $T_{u}$ , $T_{v}$ and $n (u, v)$

b) Find the area of $S = G (D)$ , where $D = {(u, v) : 0 \leq u \leq 2, 0 \leq v \leq 1}$

c) Express $f (x, y, z) = y z$ in terms of u and v, and evaluate $\iint_{S} f (x, y, z) d S$

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Answer 5

Chapter 17.4, Problem 3E

To determine

To show: That $G (u, v) = (2 u + 1, u - v, 3 u + v)$ parametrizes the plane $2 x - y - z = 2$ . And to determine the following

a) Calculate $T_{u}$ , $T_{v}$ and $n (u, v)$

b) Find the area of $S = G (D)$ , where $D = {(u, v) : 0 \leq u \leq 2, 0 \leq v \leq 1}$

c) Express $f (x, y, z) = y z$ in terms of u and v, and evaluate $\iint_{S} f (x, y, z) d S$

Answer 6

Chapter 17.4, Problem 3E

To determine

To show: That $G (u, v) = (2 u + 1, u - v, 3 u + v)$ parametrizes the plane $2 x - y - z = 2$ . And to determine the following

a) Calculate $T_{u}$ , $T_{v}$ and $n (u, v)$

b) Find the area of $S = G (D)$ , where $D = {(u, v) : 0 \leq u \leq 2, 0 \leq v \leq 1}$

c) Express $f (x, y, z) = y z$ in terms of u and v, and evaluate $\iint_{S} f (x, y, z) d S$

Answer 7

Chapter 17.4, Problem 3E

To determine

To show: That $G (u, v) = (2 u + 1, u - v, 3 u + v)$ parametrizes the plane $2 x - y - z = 2$ . And to determine the following

a) Calculate $T_{u}$ , $T_{v}$ and $n (u, v)$

b) Find the area of $S = G (D)$ , where $D = {(u, v) : 0 \leq u \leq 2, 0 \leq v \leq 1}$

c) Express $f (x, y, z) = y z$ in terms of u and v, and evaluate $\iint_{S} f (x, y, z) d S$

Answer 8

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Answer 9

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Answer 10

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Answer 11

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

Solution Summary: The author explains that G ( u, v ) parametrizes the plane 2 x y

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Solution Summary: The author explains that G ( u, v ) parametrizes the plane 2 x y

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To show: That G(u,v)=(2u+1,u−v,3u+v) parametrizes the plane 2x−y−z=2. And to determine the following a) Calculate Tu,Tv and n(u,v) b) Find the area of S=G(D), where D={(u,v):0≤u≤2,0≤v≤1} c) Express f(x,y,z)=yz in terms of u and v, and evaluate ∬Sf(x,y,z)dS

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Chapter 17 Solutions