A conservative vector field of the form F = ( g ( y ) , h ( x ) ) such that F ( 0 , 0 ) = 〈 1 , 1 〉 , where g(y) and h(x) are differentiable functions. And also to determine all such vector fields.

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Answer 1

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Chapter 17, Problem 27CRE

To determine

To find: A conservative vector field of the form $F = (g (y), h (x))$ such that $F (0, 0) = 〈 1, 1 〉$ , where g(y) and h(x) are differentiable functions. And also to determine all such vector fields.

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(12 points) Let E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}. (a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such that (x, y, z) (psin cos 0, psin sin 0, p cos) € E. (b) (8 points) Calculate the integral E xyz dV using spherical coordinates.

(10 points) Let f(x, y, z) = ze²²+y². Let E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z < 3}. Calculate the integral y, f(x, y, z) dV.

(14 points) Let f: R3 R and T: R3. →R³ be defined by f(x, y, z) = ln(x²+ y²+2²), T(p, 0,4)=(psin cos 0, psin sin, pcos). (a) (4 points) Write out the composition g(p, 0, 4) = (foT)(p,, ) explicitly. Then calculate the gradient Vg directly, i.e. without using the chain rule. (b) (4 points) Calculate the gradient Vf(x, y, z) where (x, y, z) = T(p, 0,4). (c) (6 points) Calculate the derivative matrix DT(p, 0, p). Then use the Chain Rule to calculate Vg(r,0,4).

Answer 2

Question

Chapter 17, Problem 27CRE

To determine

To find: A conservative vector field of the form $F = (g (y), h (x))$ such that $F (0, 0) = 〈 1, 1 〉$ , where g(y) and h(x) are differentiable functions. And also to determine all such vector fields.

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Answer 3

Question

Chapter 17, Problem 27CRE

To determine

To find: A conservative vector field of the form $F = (g (y), h (x))$ such that $F (0, 0) = 〈 1, 1 〉$ , where g(y) and h(x) are differentiable functions. And also to determine all such vector fields.

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Answer 4

Question

Chapter 17, Problem 27CRE

To determine

To find: A conservative vector field of the form $F = (g (y), h (x))$ such that $F (0, 0) = 〈 1, 1 〉$ , where g(y) and h(x) are differentiable functions. And also to determine all such vector fields.

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Answer 5

Chapter 17, Problem 27CRE

To determine

To find: A conservative vector field of the form $F = (g (y), h (x))$ such that $F (0, 0) = 〈 1, 1 〉$ , where g(y) and h(x) are differentiable functions. And also to determine all such vector fields.

Answer 6

Chapter 17, Problem 27CRE

To determine

To find: A conservative vector field of the form $F = (g (y), h (x))$ such that $F (0, 0) = 〈 1, 1 〉$ , where g(y) and h(x) are differentiable functions. And also to determine all such vector fields.

Answer 7

Chapter 17, Problem 27CRE

To determine

To find: A conservative vector field of the form $F = (g (y), h (x))$ such that $F (0, 0) = 〈 1, 1 〉$ , where g(y) and h(x) are differentiable functions. And also to determine all such vector fields.

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

A conservative vector field of the form F = ( g ( y ) , h ( x ) ) such that F ( 0 , 0 ) = 〈 1 , 1 〉 , where g(y) and h(x) are differentiable functions. And also to determine all such vector fields.

Solution Summary: The author explains that a conservative vector field must satisfy the following conditions: g(y) and h(x) are differentiable functions.

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To find: A conservative vector field of the form $F = (g (y), h (x))$ such that $F (0, 0) = 〈 1, 1 〉$ , where g(y) and h(x) are differentiable functions. And also to determine all such vector fields.

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Chapter 17 Solutions

A conservative vector field of the form F = ( g ( y ) , h ( x ) ) such that F ( 0 , 0 ) = 〈 1 , 1 〉 , where g(y) and h(x) are differentiable functions. And also to determine all such vector fields.

Solution Summary: The author explains that a conservative vector field must satisfy the following conditions: g(y) and h(x) are differentiable functions.

Videos

To find: A conservative vector field of the form F=(g(y),h(x)) such that F(0,0)=〈1,1〉, where g(y) and h(x) are differentiable functions. And also to determine all such vector fields.

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Chapter 17 Solutions

To find: A conservative vector field of the form $F = (g (y), h (x))$ such that $F (0, 0) = 〈 1, 1 〉$ , where g(y) and h(x) are differentiable functions. And also to determine all such vector fields.