Prove the following Product Rule: curl(f F) = f curl(F)+f F
Question:
curl(f F) = f curl(F)+∇f × F
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 80% (5 reviews)
We evaluate the curl of f F Since f using the Product Rule for scalar functions ...View the full answer
Answered By
Muhammad Rehan
Enjoy testing and can find bugs easily and help improve the product quality.
4.70+
10+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Calculus questions
-
Let F, G: R3 R3 and f : R3 R be differentiable. Prove the following analogues of the Sum and Product Rules for the "derivatives" curl and divergence. a) (F + G) = ( F) + ( G) b) (fF) = f( F)...
-
Let f be a scalar field and F a vector field. Indicate which of the following are scalar fields, vector fields, or meaningless. (a) Div f (b) Grad f (c) Curl F (d) Div (grad f) (e) Curl (grad f) (f)...
-
Suppose that f is differentiable at a and f(a) 0. a) Show that for h sufficiently small, f(a + h) 0). b) [RECIPROCAL RULE] Using Definition 4.1 directly, prove that 1/f(x) is differentiable at x =...
-
Sung Corporation, a clothing retailer, engaged in the transactions listed in the first column of the table below. Opposite each transaction is a ratio and space to mark the effect of each transaction...
-
In Chapters 9 and 10, we used cost allocations to estimate the cost of capacity resources, and to measure the long-term profitability of investing in resources and products. In what ways does this...
-
Our discussion in the text stresses that multinationals succeed by using their firm-specific advantages throughout their global operations. We have also noted that most foreign direct investments are...
-
Compare some of the ways the societies provide care for their elderly members and critique the elder care practices of your society.
-
Busch Corporation has an existing loan in the amount of $4.5 million with an annual interest rate of 5.5%. The company provides an internal company-prepared financial statement to the bank under the...
-
Sell at Split-Off or Process Further Decision, Alternatives, Relevant Costs Vihaan Chemicals Company processes a number of chemical compounds used in disinfecting health club fitness equipment. One...
-
When a country has a comparative advantage in the production of a good, it means that it can produce this good at a lower opportunity cost than its trading partner. Then the country will specialize...
-
Prove that curl(fa) = f a, where f is a differentiable function and a is a constant vector?
-
Verify that B = curl(A) for r > R in the setting of Example 6?
-
A sample of a bright blue mineral was weighed in air, then weighed again while suspended in water. An object is buoyed up by the mass of the fluid displaced by the object. In air, the mineral weighed...
-
2 Anne-Marie and Yancy calculate their current living expenditures to be $50,000 a year. During retirement they plan to take one cruise a year that will cost $5,000 in today's dollars. Anne-Marie...
-
Instructions: I Complete the 5 steps of computations for the process costing system, using FIFO for Department A and weighted average for Department B; and journalize the transfers from Department A...
-
Following table contains information related to the major activities of a research project: Task a b C To d e f 9 h Immediate predecesso r a a b b c, e d, e 1.9 Duration (days) h 5 18 13 3 10 11 4 9...
-
Hugh George is a 40% partner in the Hammond & George Partnership. During 2022, the partnership reported the total items below (100%) on its Form 1065: View the items on the Form 1065. View more...
-
The company has a target of 98.5% deliveries being made ON TIME (or a max of 1.5% being late). The data is provided below the questions. Use it to analyze whether the company is reaching this...
-
Describe the role of the encounter pair in the cage effect.
-
2.) Find the Laplace transform of f(t) 7e-St cos 2t +9 sinh2 2t. Use Laplace Table. %3D
-
Many equations can also be solved by repeatedly applying a discrete-time dynamical system. Compare the following discrete-time dynamical systems with the Newton's method discrete-time dynamical...
-
The logistic dynamical system xt+1 = rxt(1 - xt). Start from x0 = 0.75. Find the value of the parameter r for which the given discrete-time dynamical system will converge most rapidly to its positive...
-
The Ricker dynamical system xt+1 = rxte-xt. Start from x0 = 0.75. Find the value of the parameter r for which the given discrete-time dynamical system will converge most rapidly to its positive...
-
American Blossom management is planning to make a $3.7 million loan to a French firm. Currently, LIBOR is at 0.55 percent. American management considers a default risk premium of 1.10 percent, a...
-
The following account balances are for Ping Chung, Certified Public Accountant, as of April 30, 20X1. Cash Accounts receivable $120,000 48,000 Maintenance expense 21,400 Advertising expense 17,060...
-
Abbott Equipment leased a protein analyzer to Werner Chemical, Inc., on September 30, 2021. Abbott purchased the machine from NutraLabs, Inc., at a cost of $5 million. The five-year lease agreement...
Study smarter with the SolutionInn App