a If f is a differentiable vector field on M C Rn, show that there is an open set A 1069 M and a differentiable vector field F on A with F(x) F (x) for x 1028 M b If M is closed, show that we can choose A Rn ...

b In the construction of part a one can assume that the are open rectangles with sides ...

a. If f is a differentiable vector field on M C Rn, show that there is an

Question:

a. If f is a differentiable vector field on M C Rn, show that there is an open set AЭM and a differentiable vector field F on A with F(x) = F (x) for xЄM.
b. If M is closed, show that we can choose A = Rn.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus Early Transcendentals

ISBN: 978-1285741550

8th edition

Authors: James Stewart

See More Books

Question Posted: Jan 12, 2010 12:39 AM

See More Questions

If f is a differentiable function and g(x) = xf(x), use the definition of a derivative to show that g(x) = xf(x) + f(x).
Suppose that u < e(r)h. Show that there is an arbitrage opportunity. Now suppose that d >e(r)h. Show again that there is an arbitrage opportunity. Many (but not all) of these questions can be...
Suppose that u < e(r)h. Show that there is an arbitrage opportunity. Now suppose that d > e(r)h. Show again that there is an arbitrage opportunity.
A company has the following data: net sales, $405,000; cost of goods sold, $220,000; selling expenses, $90,000; general and administrative expenses, $60,000; interest expense, $4,000; and interest...
What are the risks of foreign ownership of U.S. government debt? Could the United States possibly default on the debt owed to foreigners?
What is information overload?
Find the probability that a tumor is malignant, given the following: a. The values for all predictors are at the minimum (1). b. The values for all predictors are at a moderate level (5). c. The...
Methanol is to be delivered to a process unit at a rate of 15.0k mol/h by a stream that is 30.0 mole% methanol and 70.0mole% propane. Estimate the volumetric flow rate of this stream at 10.0 atm and...
Customer Angela Sosa purchased $144,789 worth of car parts with her Standard credit card. The cost to Cars Plus for the sale is $83,301. Standard credit card charges Cars Plus a fee of 5% of the...
Soo Office Equipment manufactures and sells metal shelving. It began operations on January 1, 2013. Costs incurred for 2013 are as follows (V stands for variable; F stands for fixed): Direct...
If M is an -dimensional manifold-with-boundary in Rn, define as the usual orientation of M x = Rnx (the orientation so defined is the usual orientation of M. If xЄM, show that the two...
Let f: A Rp be as in Theorem 5-1. a. If x Є M = g-1(0), let h: U Rn be the essentially unique diffeomorphism such that goh (y) = (y n p + 1 . yn) and h (0) = x. Define f: Rn- p f: Rn-p Rn by f...
Tom Adams has received a job offer from a large investment bank as a clerk to an associate banker. His base salary will be $ 55,000. He will receive his first annual salary payment one year from the...
How do I record these entries? January 1: Purchased a fleet of vehicles for $350,000 via a loan from the bank. The trucks have a useful life of six years. The loan is for six years with an interest...
How do feedback mechanisms and performance evaluation systems contribute to individual and team development within a corporate context ?
How do ideological frameworks underpin political movements, and what is their role in legitimizing or challenging power structures?
According to the 8-step communication model, what should one do once the crisis has passed?
Who is PGR and what do they do? How much premium did the company (consolidated) write in the most recent complete fiscal year? Was it a good, average, or bad year for them? Comment on the premium...
(Postretirement Benefit Expense Computation) Marvelous Marvin Co. provides the following information about its postretirement benefit plan for the year 2011. Service cost $ 90,000 Prior service cost...
In order to get an idea on current buying trends, a real estate agent collects data on 10 recent house sales in the area. Specifically, she notes the number of bedrooms in each house as follows: a....
Consider the system water(1) + methylethylketone(MEK)(2) + propanoic acid(PA)(3). Use UNIFAC to predict the compositions for the coexisting phases at x 3 = 0.01, 0.05, and 0.10 at 298.15 K. Let be...
There are three basic approaches to CVP analysis - equation approach, contribution margin approach, and the contribution ratio margin approach. How are these approaches similar and how do they...
There are six farmers in Great Britain with access to government land to graze their cows for free. They all must share the land. Each farmer has an individual incentive to put as many of his cows on...
Describe several common sources of yardstick data that you can use as bases for developing forecast assumptions

a. If f is a differentiable vector field on M C Rn, show that there is an

Question:

Step by Step Answer:

b In the construction of part a one can assume that the are open rectangles with sides ...View the full answer

Calculus Early Transcendentals

Students also viewed these Basic questions