Question: In problem 1-4 determine whether the given field F is conservative. Is so, find f so that F = f; if not, state that F

In problem 1-4 determine whether the given field F is conservative. Is so, find f so that F = ∇f; if not, state that F is not conservative.
1. F(x, y) = (10x - 7y) i - (7x - 2y)j
2. F(x, y) = (12x2 + 3y2 + 5y)i + (6xy - 3y2 + 5x)j
3. F(x, y) = (45x4y2 - 6y6 + 3)i + (18x5y - 12xy5 + 7)j
4. F(x, y) = (35x4 - 3x2y4 + y9)i + (4x3y3 - 9xy8)j

Step by Step Solution

★★★★★

3.31 Rating (177 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

1 M y 7 Nx so F is conservative f x y 5x 2 7xy y 2 C 2 M y ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

955-M-C-D-E (3442).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

In Exercise determine whether the given graph is planar. If so, draw it so that no edges cross. b d

In each case, determine whether the given matrix is hermitian, unitary, or normal. (a) (b) (c) (d) (e) (f) (g) (h) 2 3 -i 2

In Exercises 1-3, determine whether the given matrix is orthogonal. If it is, find its inverse. 1. 2. 3. 0 01 1/V2 1/V2 1 2 15 15 25 1212 0 13-3-3

Chapter 7 (Section 7.1) from the textbook is the following: Textbook is Blitzer, thinking mathematically, Eight Edition. Section 7.1 (Page 424, Textbook): 5,11,15,21,23,25,27,29,31,33,35,37,39,41,43...

4. Find a potential function for F (x.y,z) = , and use it to find F - dr, where the oriented curve C is parametrizationt),t2 +2t + 17, for Osts 1, where g(t) is a differentiable function such that...

1) A researcher examines the records of all the registered voters in one city and finds that 43% are registered Democrats. A) Parameter B) Statistic C) Population D) Variable Find the indicated...

(1 point) Determine whether the vector field is conservative and, if so, find a potential function f. F(x, y, z) = (cos z, 2yl, -x sin z) f (x, y, z) = Note: if the vector field is not conservative,...

Let o(t) = 0 and use the method of successive approximations to solve the initial value problem y' = ty - 5t, y(0) = 0. a) Determine (t) for an arbitrary value of n. on(t) = b) Use a graphing utility...

What's the mechanism of action of trizepatide, the new diabetes 2 drug? and how does it differ from GLP-1 agonists?

Which of the follow is not a problem with the repricing model? Group of answer choices It ignores runoffs and prepayments. It is overaggregative. It ignores cash flows from off - balance - sheet...

Margaret pays a local income tax of 2 percent, regardless of the size of her income. This tax is a. proportional. b. regressive. c. progressive. d. a mix of a. and b.

Based on the estimates of the U.S. daily oil demand function in Equation 9.3 and supply function in Equation 9.4, use calculus to determine the change in deadweight loss from a marginal increase in a...

The U.S. government claimed that China and Vietnam were dumping shrimp in the United States at a price below cost, and proposed duties as high as 112%. Suppose that China and Vietnam were subsidizing...

Show that if the importing country faces an upward-sloping foreign supply curve (excess supply curve), a tariff may raise welfare in the importing country?

If an investor in a common stock expects a return of 6% a year on his investment, he is expecting the yield plus the price appreciation to equal 6% a year. True False You won the lotteryl , You are...

What is the probability that a number passwordless than 10,000 created from the digits 0,1,2,3,4,5,6,7,8,9, using each digit at most once, contains 6 or 8 or both? (using the slot method with cases)...

Need help in this homework please Homework: Week 10 SCOPE: 0 0f 1 pt 4 10 of 14 (9 complete) V ) HW Score: 61.9%, 8.67 of 14 pts 16.3.33 Question Help V g Consider the sample space S = {01, 02, 03,...