3. Let F(x, y, z) ellipsoid x? (0, 2xz? cos(x2), 4.x(x2 + y?) 2ye+y), and...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
3. Let F(x, y, z) ellipsoid x? (0, –2xz? cos(x2), 4.x(x2 + y?) – 2ye+y"), and let S be the top half of the + y? + 4z2 = 1, oriented upward. %3D (a) Verify that div(F) = 0. %3D (b) Check that F curl(G), where G = (e+u", (22 + y²)², z² sin(x²)). , (2² + y²)², z² sin(r²)). 1 (c) Use Stokes' Theorem to evaluate the flux integral F. dS by considering a line integral of G along the boundary of S (don't forget orientation!). Note: This integral would be very hard if we only considered changing surfaces. 3. Let F(x, y, z) ellipsoid x? (0, –2xz? cos(x2), 4.x(x2 + y?) – 2ye+y"), and let S be the top half of the + y? + 4z2 = 1, oriented upward. %3D (a) Verify that div(F) = 0. %3D (b) Check that F curl(G), where G = (e+u", (22 + y²)², z² sin(x²)). , (2² + y²)², z² sin(r²)). 1 (c) Use Stokes' Theorem to evaluate the flux integral F. dS by considering a line integral of G along the boundary of S (don't forget orientation!). Note: This integral would be very hard if we only considered changing surfaces.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mechanical engineering questions
-
Use Stokes Theorem to evaluate C F dr. In each case C is oriented counterclockwise as viewed from above. F(x, y, z) = (x + y 2 ) i + (y + z 2 ) j + (z + x 2 ) k, C is the triangle with vertices (1,...
-
Use Stokes Theorem to evaluate C F dr. In each case C is oriented counterclockwise as viewed from above. F(x, y, z) = i + (x + yz) j + (xy - z) k, C is the boundary of the part of the plane 3x + 2y...
-
Use Stokes Theorem to evaluate C F dr. In each case C is oriented counterclockwise as viewed from above. F(x, y, z) = xy i + yz j + zx k, C is the boundary of the part of the paraboloid z = 1 - x 2...
-
Show that = E[(m(X) - X'p)] B = argmind (b) = (E[XX']) E[Xm(X)] = [E[XX'])E[XY]. berk Hint: To show E[Xm(X)] = E[XY] use the law of iterated expectations. then
-
Based on what you learned in Chapter 4, complete a Barringer/Ireland Business Model template for DrawQuest. Is there anything that is noticeable in the business model template that may have forecast...
-
A body of mass m is suspended from a spring fixed to the ceiling of an elevator car. The stiffness of the spring is . At the moment t = 0 the car starts going up with an acceleration w. Neglecting...
-
Record the following transactions in the journal of Bingham Phone Accessories. Explanations are not required 2009 31 Dec 19 Received a $3,000, 60-day, 12% note on account from Arnold Collins. Made an...
-
You have just been hired by EduRom Company, which was organized on January 2 of the current year. The company manufactures and sells a variety of educational DVDs for personal computers. It is your...
-
What restrictions apply to the use of the aggregate functions within the SELECT statement? How do nulls affect the aggregate functions? What is the difference between a subquery and a join? Under...
-
Ricky Bobby is divorced with two dependent children, ages 9 and 11. During 2022, Ricky had the following gross receipts: Salary income Passive loss from Alpha Partnership (Ricky is a limited partner...
-
Stereo Warehouse is a US retailer that offers employees a defined benefit pension plan as part of its compensation package. Stereo Warehouse prepares its financial statements in accordance with US...
-
During 20--, Rachael Lopez, president of Mathieson Company, was paid a semimonthly salary of $9,000. Compute the amount of FICA taxes that shoul withheld from her. Note: Rachael's tax return status...
-
144. Given below is the diagramatic sketch of a transverse section of young anther, Identify the parts labelled A, B, C and D :- A 10101 B (1) Epidermis middle layer (2) Epidermis Endothecium (3)...
-
On December 3 1 , Cullumber Ltd . had a cash balance of $ 1 8 , 9 9 0 in its general ledger. The bank statement from the National Bank on that date showed a balance of $ 1 5 , 5 3 0 . A comparison of...
-
Produce a complete list of everyone involved in, affected by or responsible for each initiative. In your answer: use an appropriate business analysis technique (e.g. affinity diagrams) to identify...
-
Net Sales $ 1 7 5 , 0 Net Income 3 5 , 0 0 0 Cash provided by Operating Activities 4 0 , 0 0 0 Expenditures on Property, Plant and Equipment 1 5 , 0 0 0 Current Assets 4 7 , 2 5 0 Current Liabilities...
-
A block lies on a smooth inclined plane tilted at an angle of 34 to the horizontal. If the block started from rest 9.0 m up the incline from its base, determine the block's speed (in m/s) when it...
-
Explain how the graph of each function can be obtained from the graph of y = 1/x or y = 1/x 2 . Then graph f and give the (a) Domain (b) Range. Determine the largest open intervals of the domain over...
-
If the curve z = x2 in the xz-plane is revolved about the z-axis the resulting surface has equation z = x2 + y2, obtained as a result of replacing x by x2 + y2. If y = 2x2 in the xy-plane is revolved...
-
Show that the error used in approximating S by Sn satisfies Where the notation is the same as in the discussion preceding Example 5? En2 f(x) dx n+1
-
In problems, use the table of integrals on the inside back cover, perhaps combined with a substitution, to evaluate the given integrals. 1. (a) x 3x + 1 dx (b) ex (3ex + 1 ex) dx 2. (a) 2t 3-4t dt...
-
Describe one occasion where you have been influenced to buy a product or engage in an activity as a direct result of an item of corporate communication, eg social media update; and explain what that...
-
What are the elements of a master budget?
-
Discuss the potential conflict between using a budget as a motivational device and as a means of control.
Study smarter with the SolutionInn App