Show that if the vector field F = Pi + Qj + Rk is conservative and P, Q, R have continuous first-order partial derivatives, then the following is true. ∂P ∂y = ∂Q ∂x ∂P ∂z = ∂R ∂x ∂Q ∂z = ∂R ∂y . Since F is conservative, there exists a function f such that F = ∇f, that is, P, Q, and R are defined as follows. (Enter your answers in the form fx, fy, fz.) P = Q = R = Since P, Q, and R have continuous first order partial derivatives, says that ∂P/∂y = fxy = fyx = ∂Q/∂x, ∂P/∂z = fxz = fyx = ∂ARE/∂x,

1 answer
Question:

Show that if the vector field F = Pi + Qj + Rk is conservative and P, Q, R have continuous first-order partial derivatives, then the following is true. ∂P ∂y = ∂Q ∂x ∂P ∂z = ∂R ∂x ∂Q ∂z = ∂R ∂y . Since F is conservative, there exists a function f such that F = ∇f, that is, P, Q, and R are defined as follows. (Enter your answers in the form fx, fy, fz.) P = Q = R = Since P, Q, and R have continuous first order partial derivatives, says that ∂P/∂y = fxy = fyx = ∂Q/∂x, ∂P/∂z = fxz = fyx = ∂ARE/∂x, and ∂Q/∂z = fyx = fxy = ∂R/∂y.

Answers

Answer:Answer with steps is in the following attachmentsStep-by-step explanation:

Similar Solved Questions

1 answer

What came first in romes conquest of the Italian peninsula

What came first in romes conquest of the Italian peninsula...
1 answer

Find the first , fourth , and eighth terms of the sequence A(n) = -3 •2 ^x - 1

Find the first , fourth , and eighth terms of the sequence A(n) = -3 •2 ^x - 1...
2 answers

Which government agency monitors air quality?

Which government agency monitors air quality?...
2 answers

Patel bought a model rocket kit from a catalog. The price of the kit was $125. A $10 charge for shipping will be added. Patel received an allowance of $20 per week. How many weeks will it take him to purchase the kit?

Patel bought a model rocket kit from a catalog. The price of the kit was $125. A $10 charge for shipping will be added. Patel received an allowance of $20 per week. How many weeks will it take him to purchase the kit?...
1 answer

Jared earns $455.00 per week as manager of the Save-Mart. What will be his income over 12 weeks

Jared earns $455.00 per week as manager of the Save-Mart. What will be his income over 12 weeks...
1 answer

What is true about economic resources? A. Economic resources include only money. B. Economic resources are limited. C. Economic resources exist only at the individual level. D. Economic resources are always controlled by the government.

What is true about economic resources? A. Economic resources include only money. B. Economic resources are limited. C. Economic resources exist only at the individual level. D. Economic resources are always controlled by the government....
2 answers

Où le magicien emmène-ta-il Aladin

Où le magicien emmène-ta-il Aladin...
2 answers

What are the overall powers of the legislative branch

What are the overall powers of the legislative branch...
2 answers

Who was Othello's wife?​

Who was Othello's wife?​...
1 answer

Any help would be greatly appreciated

Any help would be greatly appreciated...
2 answers

Bbbbbbbbbbbbbbbbbbbbbbbbbbb

bbbbbbbbbbbbbbbbbbbbbbbbbbb...
1 answer

Divide 36087 by 56 and verify the result by division algorithm.​

Divide 36087 by 56 and verify the result by division algorithm.​...
2 answers

Select the correct answer. Which theme is highlighted in this excerpt from “The Tell-Tale Heart” by Edgar Allan Poe? A. murder leads to justifying the act B. murder leads to deceiving authorities C. murder causes an all-encompassing guilt D. murder creates a feeling of extreme power

Select the correct answer. Which theme is highlighted in this excerpt from “The Tell-Tale Heart” by Edgar Allan Poe? A. murder leads to justifying the act B. murder leads to deceiving authorities C. murder causes an all-encompassing guilt D. murder creates a feeling of extreme power...
2 answers

I need to show the work for 48÷1,261

I need to show the work for 48÷1,261...
1 answer

2. Which investment would earn the most money by retirement at age 65? I. investing $5,000 in stocks at 6% return at age 25 II. investing $10,000 in bonds at 3% interest at age 35 III. investing $10,000 in stocks at 8% return at age 45 Explain the reasoning behind your answer.

2. Which investment would earn the most money by retirement at age 65? I. investing $5,000 in stocks at 6% return at age 25 II. investing $10,000 in bonds at 3% interest at age 35 III. investing $10,000 in stocks at 8% return at age 45 Explain the reasoning behind your answer....
1 answer

What is the exponent form of -6•6•6

What is the exponent form of -6•6•6...
1 answer

What were the two main areas of dispute between Russia and Japan during the Russo-Japanese War? a. Korea b. Manchuria c. China d. Siberia

What were the two main areas of dispute between Russia and Japan during the Russo-Japanese War? a. Korea b. Manchuria c. China d. Siberia...
1 answer

Describe the main points of the Great Compromise?

Describe the main points of the Great Compromise?...

-- 0.010505--