Question: Show that F is a conservative vector field. Then find a function f such that F = f. F(x, y, z) = sin y i

Show that F is a conservative vector field. Then find a function f such that F = ∇f.

F(x, y, z) = sin y i + x cos y j - sin z k

Step by Step Solution

★★★★★

3.41 Rating (173 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

F is defined on all of R its components have continuous partial derivatives and curl F 0 0 i ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

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

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

Show that f is continuous on (- , ). x2 if x

Q:

Show that f is continuous on ( ∞, ∞). x? if x 7/4 36. f(x) =

Q:

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = f. F(x, y) = (xy + y2) i + (x 2 + 2xy) j

Q:

Page (a) Show that F is a conservative vector field (b) Find a potential function p (x, y) whose gradient is FPage 3 of 8 - ZOOM + K (c) Evaluate the line integral S F . dr where C is the curve from...

Q:

Let F (111:) = hyi + (I2 + i- a. Show that F is a conservative vector field. b. Find the potential function [:,y). c. Use the potential function obtained above to evaluate the integral lial] My 6'1 +...

Q:

I am having some trouble with this question. Thank you so much in advance for your help Let F(x,y) = 1)...

Q:

1 1 - 1 2 Show that F is a conservative vector field. Then find a function f such that F = gradf. 1 1 . F ( x , y ) = ( 1 + x y ) e x y i + ( e y + z 2 e 0 y ) j

Q:

Consider the force field F(x, y, z) = 8ryzi+12xyzj+4xy k, and the Helix C: r(t) = 2 costi + 2 sintj + tk from A(2,0,0) to B(0,2,5). (a) Show that F is a conservative vector field. (b) Find the work...

Q:

I am having some trouble with these questions thank you in advance for your help Let F(x,y) = a) Show...

Q:

Show that the integral is independent of the path, and use fundamental theorem of line integral to find its value. - 1 0 , 1 , 1 , 2 ( 3 x - y + 1 ) d x - ( x + 4 y + 2 ) d y a ) State and show why F...

Q:

List five sources of data for a country's national statistical office as guided by International Labor Organization(5 mks) b) Describe the factors that affect manpower planning. (10 mks) c)List two...

Q:

All the compounds in Problem 9.19 are isomers except one. Which one?

Q:

Which of the following is CORRECT about the effective annual rate (EFF%)? a. If compounding occurs more than once per year, the effective rate will be higher than the nominal rate. b. If compounding...

Q:

Do you think contingent valuation should be widely used as a tool for developing environmental policy recommendations? What do you think is the main strength of CV? What do you think is its main...

Q:

Suppose the first trial has probability of success 0.5, and the second is successful with probability 0.8 if the first is and succeeds with probability 0.2 if the first fails. Show that the second...

Q:

Suppose the first trial has probability of success 0.2, and the second is successful with probability 0 if the first is and succeeds with probability 0.25 if the first fails. Show that the second...

Q:

Show that Explain why this must be true. The values have many beautiful mathematical properties. Here are just a few. (i)-.)

Q:

On april 30, 1990, Jack purchased a $1,000 10% par-value seven-year bond having semiannual coupons; these were payable at the end of each October as well as on the anniversaries of the purchase. Jack...

Q:

Pacific Healthcare is an investor-owned hospital chain that owns and operates nine hospitals in Washington, Oregon, and northern California. Marcia Long, a recent graduate of a prominent health...

Q:

In the WACC Sensitivity tab on the accompanying spreadsheet, alter the cells as described below to see how changes to WACC s inputs impact the WACC. Write a few sentences describing each change. FED...