To prove: m ( r ) ≤ I φ ( r ) ≤ M ( r ) and use the continuity of φ to prove that lim r → 0 I φ ( r ) = φ ( P ) .

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Answer 1

Question

Chapter 18.1, Problem 49E

To determine

To prove:

$m (r) \leq I_{φ} (r) \leq M (r)$ and use the continuity of $φ$ to prove that $\lim_{r \to 0} I_{φ} (r) = φ (P)$ .

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Explain why Green’s Theorem proves that if gx = ƒy,then the vector field B = ⟨ƒ, g⟩ is conservative.

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Show that F = (3, 1, 2) is conservative. Then prove more generally that any constant vector field F = (a, b, c) is conservative.

Answer 2

Question

Chapter 18.1, Problem 49E

To determine

To prove:

$m (r) \leq I_{φ} (r) \leq M (r)$ and use the continuity of $φ$ to prove that $\lim_{r \to 0} I_{φ} (r) = φ (P)$ .

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 18.1, Problem 49E

To determine

To prove:

$m (r) \leq I_{φ} (r) \leq M (r)$ and use the continuity of $φ$ to prove that $\lim_{r \to 0} I_{φ} (r) = φ (P)$ .

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 18.1, Problem 49E

To determine

To prove:

$m (r) \leq I_{φ} (r) \leq M (r)$ and use the continuity of $φ$ to prove that $\lim_{r \to 0} I_{φ} (r) = φ (P)$ .

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 18.1, Problem 49E

To determine

To prove:

$m (r) \leq I_{φ} (r) \leq M (r)$ and use the continuity of $φ$ to prove that $\lim_{r \to 0} I_{φ} (r) = φ (P)$ .

Answer 6

Chapter 18.1, Problem 49E

To determine

To prove:

$m (r) \leq I_{φ} (r) \leq M (r)$ and use the continuity of $φ$ to prove that $\lim_{r \to 0} I_{φ} (r) = φ (P)$ .

Answer 7

Chapter 18.1, Problem 49E

To determine

To prove:

$m (r) \leq I_{φ} (r) \leq M (r)$ and use the continuity of $φ$ to prove that $\lim_{r \to 0} I_{φ} (r) = φ (P)$ .

Answer 8

Expert Solution & Answer

Answer 9

Expert Solution & Answer

Answer 10

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Answer 11

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

To prove: m ( r ) ≤ I φ ( r ) ≤ M ( r ) and use the continuity of φ to prove that lim r → 0 I φ ( r ) = φ ( P ) .

Solution Summary: The author explains that the average value of a continuous function on C r is defined as the integral I

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To prove:

$m (r) \leq I_{φ} (r) \leq M (r)$ and use the continuity of $φ$ to prove that $\lim_{r \to 0} I_{φ} (r) = φ (P)$ .

Want to see the full answer?

Chapter 18 Solutions

To prove: m ( r ) ≤ I φ ( r ) ≤ M ( r ) and use the continuity of φ to prove that lim r → 0 I φ ( r ) = φ ( P ) .

Solution Summary: The author explains that the average value of a continuous function on C r is defined as the integral I

Concept explainers

Videos