To prove: (a) F is path independent, that is, for any two paths C 1 and C 2 in D with the same initial and terminal points ∫ C 1 F . d r = ∫ C 2 F . d r (d) F is conservative.

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Answer 1

Question

Chapter 17.3, Problem 31E

To determine

To prove:

(a) $F$ is path independent, that is, for any two paths $C_{1}$ and $C_{2}$ in $D$ with the same initial and terminal points $\int_{C_{1}} F . d r = \int_{C_{2}} F . d r$

(d) $F$ is conservative.

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Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. 8+x f(x) = x(x-1) (Use a comma to separate answers as needed.) OA. The function f is discontinuous at the single value x = OB. The function f is discontinuous at the single value x = OC. The function f is discontinuous at the two values x = OD. The function f is discontinuous at the two values x = not oo or -0. OE. The function f is discontinuous at the two values x = The limit is The limit does not exist and is not oo or - co. The limits for both values do not exist and are not co or - co. The limit for the smaller value is The limit for the larger value does not exist and is The limit for the smaller value does not exist and is not co or - co. The limit for the larger

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Answer 2

Question

Chapter 17.3, Problem 31E

To determine

To prove:

(a) $F$ is path independent, that is, for any two paths $C_{1}$ and $C_{2}$ in $D$ with the same initial and terminal points $\int_{C_{1}} F . d r = \int_{C_{2}} F . d r$

(d) $F$ is conservative.

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Answer 3

Question

Chapter 17.3, Problem 31E

To determine

To prove:

(a) $F$ is path independent, that is, for any two paths $C_{1}$ and $C_{2}$ in $D$ with the same initial and terminal points $\int_{C_{1}} F . d r = \int_{C_{2}} F . d r$

(d) $F$ is conservative.

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Answer 4

Question

Chapter 17.3, Problem 31E

To determine

To prove:

(a) $F$ is path independent, that is, for any two paths $C_{1}$ and $C_{2}$ in $D$ with the same initial and terminal points $\int_{C_{1}} F . d r = \int_{C_{2}} F . d r$

(d) $F$ is conservative.

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Answer 5

Chapter 17.3, Problem 31E

To determine

To prove:

(a) $F$ is path independent, that is, for any two paths $C_{1}$ and $C_{2}$ in $D$ with the same initial and terminal points $\int_{C_{1}} F . d r = \int_{C_{2}} F . d r$

(d) $F$ is conservative.

Answer 6

Chapter 17.3, Problem 31E

To determine

To prove:

(a) $F$ is path independent, that is, for any two paths $C_{1}$ and $C_{2}$ in $D$ with the same initial and terminal points $\int_{C_{1}} F . d r = \int_{C_{2}} F . d r$

(d) $F$ is conservative.

Answer 7

Chapter 17.3, Problem 31E

To determine

To prove:

(a) $F$ is path independent, that is, for any two paths $C_{1}$ and $C_{2}$ in $D$ with the same initial and terminal points $\int_{C_{1}} F . d r = \int_{C_{2}} F . d r$

(d) $F$ is conservative.

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

To prove: (a) F is path independent, that is, for any two paths C 1 and C 2 in D with the same initial and terminal points ∫ C 1 F . d r = ∫ C 2 F . d r (d) F is conservative.

Solution Summary: The author proves that F is path independent for any two paths C 1 and C 2 in D with the same initial and terminal points.

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To prove:

(a) $F$ is path independent, that is, for any two paths $C_{1}$ and $C_{2}$ in $D$ with the same initial and terminal points $\int_{C_{1}} F . d r = \int_{C_{2}} F . d r$

(d) $F$ is conservative.

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Chapter 17 Solutions

To prove: (a) F is path independent, that is, for any two paths C 1 and C 2 in D with the same initial and terminal points ∫ C 1 F . d r = ∫ C 2 F . d r (d) F is conservative.

Solution Summary: The author proves that F is path independent for any two paths C 1 and C 2 in D with the same initial and terminal points.

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