Question: Assuming that the required partial derivatives exist and are continuous, show that (a) Div (curl F) = 0; (b) Curl (grad f) = 0; (c)

Assuming that the required partial derivatives exist and are continuous, show that
(a) Div (curl F) = 0;
(b) Curl (grad f) = 0;
(c) Div (fF) = (f) (div F) + (grad f) ∙ F;
(d) Curl (fF) = (f) (curl F) + (grad f) × F.

Step by Step Solution

★★★★★

3.42 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Div curl F div P y N z M z P x N x M y P yx N zx ... 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 (3419).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Prove the identity, assuming that the appropriate partial derivatives exist and are continuous. If f is a scalar field and F, G are vector fields, then f F, F G, and F x G are defined by (f F)(x, y,...

Calculus 3 (Math-UA-123) Fall 2016 Homework 10 Due: Thursday, December 8 at the start of class Please give complete, well-written solutions to the following exercises. 1. For each of the following...

77. Proof In parts (a), (b), (c), (d), (e), (f), (9), and (h), prove the property for vector fields F and G and scalar function f. (Assume that the required partial derivatives are continuous.) a....

In parts (a)(h), prove the property for vector fields F and G and scalar function f. (Assume that the required partial derivatives are continuous.) (a) curl(F + G) = curl F + curl G (b) curl(vf) = V ...

\f\f3. a) potential function = x2 +y 2 +z 2 ; magnetic force M = y 2 zi+z 2 xj+x2 yk i) Grad = i+ j+ k x y z Note that : = 2x = 2y = 2z x y z Hence, Grad = 2xi + 2yj + 2zk M M M ii) Div M = + + x y z...

Prove (a) - (d) vector differential identities Vector differential identities. Let f and g be scalar valued functions from R' to R and F and G be vector fields from R' to RS. Assuming that all...

Find curl v for v given with respect to right-handed Cartesian coordinates. Show the details of your work. 4. v = [2y,5x, 0] 5. v = xyz(x, y, z) 6. v = (x+ +22)-3/2[x. y. 2] 7. v=0.0. e sin yl 8. v =...

We have seen that all vector fields of the form F = g satisfy the equation curl F = 0 and that all vector fields of the form F = curl G satisfy the equation div F = 0 (assuming continuity of the...

How does seeing oneself as responsible for a perceived gain or loss affect the value of that gain or loss? Why is perceived responsibility an important factor in the consumers response to a discount?

Use forward selection stepwise regression to develop the multiple regression model. The variable x2, family income, was brought into the model. Discuss why this happened. The J. J. McCracken Company...

the diffrence of two numbers is 1 0 . what two numbers will miniize the product

The federal government finances a budget deficit by a. taxing businesses and households. b. selling Treasury securities. c. printing more money. d. reducing its purchases of goods and services.

Replace the production function in Solved Problem 7.4 with a Cobb-Douglas q = ALaKb, and use calculus to find the cost minimizing capital-labor ratio?

Derive the long-run cost function for the constant elasticity of substitution production function q = (L( + K()1/(?

A U-shaped long-run average cost curve is the envelope of U-shaped short-run average cost curves. On what part of the curve (downward sloping, flat, or upward sloping) does a short-run curve touch...

On January 1, 2014, Wooden Company issued 16,000 shares of $2 par value common stock for $120,000. On March 1, 2014, the company purchased 2,000 shares of its common stock for $15 per share for the...

Data table (Click on the following icon in order to copy its contents into a spreadsheet.) Year 0 1-9 Revenues Manufacturing Expenses (other than depreciation) Marketing Expenses Depreciation EBIT...

Conch Republic Electronics, Part 1 Conch Republic Electronics is a midsized electronics manufacturer located in Key West, Florida. The company president is Shelley Couts, who inherited the company....