(a) To show: F 3 ( x , y , z ) k ⋅ d r = F 3 ( x ( t ) , y ( t ) , f ( x ( t ) , y ( t ) ) ) ( f x ( x ( t ) , y ( t ) ) x ' ( t ) + f y ( x ( t ) , y ( t ) ) y ' ( t ) ) d t And ∮ C F 3 ( x , y , z ) k ⋅ d r = ∮ C F 3 ( x ( t ) , y ( t ) , f ( x ( t ) , y ( t ) ) ) ( f x ( x ( t ) , y ( t ) ) x ' ( t ) + f y ( x ( t ) , y ( t ) ) y ' ( t ) ) d t

Question

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Answer 1

Question

Chapter 18.2, Problem 37E

To determine

(a)

To show:

$F_{3} (x, y, z) k \cdot d r = F_{3} (x (t), y (t), f (x (t), y (t))) (f_{x} (x (t), y (t)) x' (t) + f_{y} (x (t), y (t)) y' (t)) d t$

And

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \oint_{C} F_{3} (x (t), y (t), f (x (t), y (t))) (f_{x} (x (t), y (t)) x' (t) + f_{y} (x (t), y (t)) y' (t)) d t$

To determine

(b)

To show:

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \iint_{S} c u r l (F_{3} (x, y, z) k) \cdot d S$

Using Green’s Theorem.

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Answer 2

Question

Chapter 18.2, Problem 37E

To determine

(a)

To show:

$F_{3} (x, y, z) k \cdot d r = F_{3} (x (t), y (t), f (x (t), y (t))) (f_{x} (x (t), y (t)) x' (t) + f_{y} (x (t), y (t)) y' (t)) d t$

And

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \oint_{C} F_{3} (x (t), y (t), f (x (t), y (t))) (f_{x} (x (t), y (t)) x' (t) + f_{y} (x (t), y (t)) y' (t)) d t$

To determine

(b)

To show:

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \iint_{S} c u r l (F_{3} (x, y, z) k) \cdot d S$

Using Green’s Theorem.

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Answer 3

Question

Chapter 18.2, Problem 37E

To determine

(a)

To show:

$F_{3} (x, y, z) k \cdot d r = F_{3} (x (t), y (t), f (x (t), y (t))) (f_{x} (x (t), y (t)) x' (t) + f_{y} (x (t), y (t)) y' (t)) d t$

And

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \oint_{C} F_{3} (x (t), y (t), f (x (t), y (t))) (f_{x} (x (t), y (t)) x' (t) + f_{y} (x (t), y (t)) y' (t)) d t$

To determine

(b)

To show:

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \iint_{S} c u r l (F_{3} (x, y, z) k) \cdot d S$

Using Green’s Theorem.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 18.2, Problem 37E

To determine

(a)

To show:

$F_{3} (x, y, z) k \cdot d r = F_{3} (x (t), y (t), f (x (t), y (t))) (f_{x} (x (t), y (t)) x' (t) + f_{y} (x (t), y (t)) y' (t)) d t$

And

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \oint_{C} F_{3} (x (t), y (t), f (x (t), y (t))) (f_{x} (x (t), y (t)) x' (t) + f_{y} (x (t), y (t)) y' (t)) d t$

To determine

(b)

To show:

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \iint_{S} c u r l (F_{3} (x, y, z) k) \cdot d S$

Using Green’s Theorem.

Expert Solution & Answer

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Answer 5

Chapter 18.2, Problem 37E

To determine

(a)

To show:

$F_{3} (x, y, z) k \cdot d r = F_{3} (x (t), y (t), f (x (t), y (t))) (f_{x} (x (t), y (t)) x' (t) + f_{y} (x (t), y (t)) y' (t)) d t$

And

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \oint_{C} F_{3} (x (t), y (t), f (x (t), y (t))) (f_{x} (x (t), y (t)) x' (t) + f_{y} (x (t), y (t)) y' (t)) d t$

To determine

(b)

To show:

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \iint_{S} c u r l (F_{3} (x, y, z) k) \cdot d S$

Using Green’s Theorem.

Answer 6

Chapter 18.2, Problem 37E

To determine

(a)

To show:

$F_{3} (x, y, z) k \cdot d r = F_{3} (x (t), y (t), f (x (t), y (t))) (f_{x} (x (t), y (t)) x' (t) + f_{y} (x (t), y (t)) y' (t)) d t$

And

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \oint_{C} F_{3} (x (t), y (t), f (x (t), y (t))) (f_{x} (x (t), y (t)) x' (t) + f_{y} (x (t), y (t)) y' (t)) d t$

Answer 7

Chapter 18.2, Problem 37E

To determine

(a)

To show:

$F_{3} (x, y, z) k \cdot d r = F_{3} (x (t), y (t), f (x (t), y (t))) (f_{x} (x (t), y (t)) x' (t) + f_{y} (x (t), y (t)) y' (t)) d t$

And

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \oint_{C} F_{3} (x (t), y (t), f (x (t), y (t))) (f_{x} (x (t), y (t)) x' (t) + f_{y} (x (t), y (t)) y' (t)) d t$

Answer 8

To determine

(b)

To show:

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \iint_{S} c u r l (F_{3} (x, y, z) k) \cdot d S$

Using Green’s Theorem.

Answer 9

To determine

(b)

To show:

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \iint_{S} c u r l (F_{3} (x, y, z) k) \cdot d S$

Using Green’s Theorem.

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 18.1 - Prob. 1PQ Ch. 18.1 - Prob. 2PQ Ch. 18.1 - Prob. 3PQ Ch. 18.1 - Prob. 4PQ Ch. 18.1 - Prob. 5PQ Ch. 18.1 - Prob. 1E Ch. 18.1 - Prob. 2E Ch. 18.1 - Prob. 3E Ch. 18.1 - Prob. 4E Ch. 18.1 - Prob. 5E

Solution Summary: The author explains that S is the graph of z = f ( x, y) over a domain D, and C the boundary S with parametrization.

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(b)

To show:

$\oint_{C} F_{3} (x, y, z) k \cdot d r = \iint_{S} c u r l (F_{3} (x, y, z) k) \cdot d S$

Using Green’s Theorem.

Want to see the full answer?

Chapter 18 Solutions

Solution Summary: The author explains that S is the graph of z = f ( x, y) over a domain D, and C the boundary S with parametrization.

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