F = ∇ f , where f ( x , y , z ) = x y e z and compute ∫ C F ⋅ d r (a) C is any curve from ( 1 , 1 , 0 ) to ( 3 , e , − 1 ) (b) C is the boundary of the square 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 oriented counterclockwise.

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Answer 1

Question

Chapter 17, Problem 33CRE

To determine

To calculate: $F = \nabla f$ , where $f (x, y, z) = x y e^{z}$ and compute $\int_{C} F \cdot d r$

(a) C is any curve from $(1, 1, 0) to (3, e, - 1)$

(b) C is the boundary of the square $0 \leq x \leq 1, 0 \leq y \leq 1$ oriented counterclockwise.

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Answer 2

Question

Chapter 17, Problem 33CRE

To determine

To calculate: $F = \nabla f$ , where $f (x, y, z) = x y e^{z}$ and compute $\int_{C} F \cdot d r$

(a) C is any curve from $(1, 1, 0) to (3, e, - 1)$

(b) C is the boundary of the square $0 \leq x \leq 1, 0 \leq y \leq 1$ oriented counterclockwise.

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Answer 3

Question

Chapter 17, Problem 33CRE

To determine

To calculate: $F = \nabla f$ , where $f (x, y, z) = x y e^{z}$ and compute $\int_{C} F \cdot d r$

(a) C is any curve from $(1, 1, 0) to (3, e, - 1)$

(b) C is the boundary of the square $0 \leq x \leq 1, 0 \leq y \leq 1$ oriented counterclockwise.

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Answer 4

Question

Chapter 17, Problem 33CRE

To determine

To calculate: $F = \nabla f$ , where $f (x, y, z) = x y e^{z}$ and compute $\int_{C} F \cdot d r$

(a) C is any curve from $(1, 1, 0) to (3, e, - 1)$

(b) C is the boundary of the square $0 \leq x \leq 1, 0 \leq y \leq 1$ oriented counterclockwise.

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Answer 5

Chapter 17, Problem 33CRE

To determine

To calculate: $F = \nabla f$ , where $f (x, y, z) = x y e^{z}$ and compute $\int_{C} F \cdot d r$

(a) C is any curve from $(1, 1, 0) to (3, e, - 1)$

(b) C is the boundary of the square $0 \leq x \leq 1, 0 \leq y \leq 1$ oriented counterclockwise.

Answer 6

Chapter 17, Problem 33CRE

To determine

To calculate: $F = \nabla f$ , where $f (x, y, z) = x y e^{z}$ and compute $\int_{C} F \cdot d r$

(a) C is any curve from $(1, 1, 0) to (3, e, - 1)$

(b) C is the boundary of the square $0 \leq x \leq 1, 0 \leq y \leq 1$ oriented counterclockwise.

Answer 7

Chapter 17, Problem 33CRE

To determine

To calculate: $F = \nabla f$ , where $f (x, y, z) = x y e^{z}$ and compute $\int_{C} F \cdot d r$

(a) C is any curve from $(1, 1, 0) to (3, e, - 1)$

(b) C is the boundary of the square $0 \leq x \leq 1, 0 \leq y \leq 1$ oriented counterclockwise.

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

F = ∇ f , where f ( x , y , z ) = x y e z and compute ∫ C F ⋅ d r (a) C is any curve from ( 1 , 1 , 0 ) to ( 3 , e , − 1 ) (b) C is the boundary of the square 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 oriented counterclockwise.

Solution Summary: The author explains the formula used to calculate F = f, where x, y, and z are equal. C is the boundary of a square oriented counterclockwise.

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To calculate: $F = \nabla f$ , where $f (x, y, z) = x y e^{z}$ and compute $\int_{C} F \cdot d r$

(a) C is any curve from $(1, 1, 0) to (3, e, - 1)$

(b) C is the boundary of the square $0 \leq x \leq 1, 0 \leq y \leq 1$ oriented counterclockwise.

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Chapter 17 Solutions

F = ∇ f , where f ( x , y , z ) = x y e z and compute ∫ C F ⋅ d r (a) C is any curve from ( 1 , 1 , 0 ) to ( 3 , e , − 1 ) (b) C is the boundary of the square 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 oriented counterclockwise.

Solution Summary: The author explains the formula used to calculate F = f, where x, y, and z are equal. C is the boundary of a square oriented counterclockwise.

Concept explainers

Videos

To calculate:F=∇f, where f(x,y,z)=xyez and compute ∫CF⋅dr (a) C is any curve from (1,1,0) to (3,e,−1) (b) C is the boundary of the square 0≤x≤1,0≤y≤1 oriented counterclockwise.

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Chapter 17 Solutions

To calculate: $F = \nabla f$ , where $f (x, y, z) = x y e^{z}$ and compute $\int_{C} F \cdot d r$

(a) C is any curve from $(1, 1, 0) to (3, e, - 1)$

(b) C is the boundary of the square $0 \leq x \leq 1, 0 \leq y \leq 1$ oriented counterclockwise.