Question: If f : Rn R is differentiable and f (0) = 0, prove that there exist gi: Rn R such that f (x) =

If f : Rn → R is differentiable and f (0) = 0, prove that there exist gi: Rn → R such that f (x) =

Step by Step Solution

★★★★★

3.47 Rating (154 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Following the hint le... 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

Document Format (1 attachment)

M-C-34.docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

Prove that there exist functions u(x, y), v(x, y), and w(X, y), and an r > 0 such that M.V.W are continuously differentiable and satisfy the equations u + xv? - y + w = 0 v5 + yu? - x+ w = 0 w* + y -...

Q:

Suppose that f: R R is differentiable and periodic and that f' is integrable on [-Ï, Ï]. Prove that a(f') = kb;(f) and b(f)= -kar(f), ke N.

Q:

Suppose that g : R R is differentiable and that g'(x) > 1 for all x R. Prove that if g(l) = 0 and f(x, y) = (x - l)2(y + l)/(yg(x)), then there is an L R such that f(x, y) L as (x, y) (1, b) for...

Q:

Holt Company purchased a computer for $8,000 on January 1, 2009. Straight-line depreciation is used, based on a 5-year life and a $1,000 salvage value . In 2011, the estimates are revised. Holt now...

Q:

Write a paper, Find Scholar Academic Journal Article Review about non-verbal communication class, the topic about "Vocalic" - What did you looking for? - How did you go for looking? - What did you...

Q:

According to Investment Digest ("Diversification and the Risk/Reward Relationship", Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 15.4%, and the standard...

Q:

Personal influences: What influences did personal characteristics or circumstances, such as social class, gender, race and ethnicity, language, disability, or sexual orientation, have in shaping...

Q:

Park and Go, near an airport, incurred the following costs to acquire land, make land improvements, and construct and furnish a small building: Park and Go depreciates land improvements over 20...

Q:

Determine the indices for the plane shown in the cubic unit cell

Q:

Sunshine Sushi, a Japanese restaurant, has the following adjusted trial balance with accounts listed in alphabetical order. Using the template provided, prepare a classified balance sheet for the...

Q:

Dale Crosby's Gift Shop had overhead expenses totaling $2,732 during the month of August. The business recorded departmental sales for the month of August as follows: china, $3,923; silver, $8,923;...

Q:

A water storage tank has a cylindrical shape. The diameter of the base of the tank is 0.568 m. The height of the tank is 0.855 m. This is shown in the following diagram. -0.568 m 0.855 m (a) Write...

Q:

A company is studying the effectiveness of their text message advertisements by counting the number of visits to their website that originate from a link in one of the texts. The function A(r) gives...

Q:

This is a circuit design i made in TinkerCAD. I am trying to use the green LED with variable brightness as a function of the Ultrasonic sensor reading. The three Red LEDs are a warning indicator if...

Q:

Question 3 (10 points) Listen What is corporate personhood, and how does it relate to corporate social responsibility? Relate this to our discussion on Exxon Mobile (the largest Oil and Gas...

Q:

Problem 4. PREVIEW ONLY -- ANSWERS NOT RECORDED (2 points) Assume you are to select digits from the set {2, 3, 4, 5, 6, 7, 9} to form a number between 20 and 900. 60 (1) HOW MANY such numbers can be...

Q:

The calculation of average which is calculated by pooling the data together from different data sets is classified as A. geometric mean B. harmonic mean C. deviation square mean D. paired mean

Q:

Suppose the market is semistrong form efficient. Can you expect to earn excess returns if you make trades based on? a. Your brokers information about record earnings for a stock? b. Rumors about a...

Q:

Imagine that an auditor finds an error in the clients financial statements, and that correcting the error in the clients financial records would result in EPS declining by one penny. Why might the...

Q:

You want to borrow $10,000. You figure that you can make the following payments. If the interest rate on the loan is 8.7% per year, will your payments be enough to pay off the $10,000 loan? (Select...

Q:

Ineed to do a retirement future savings. Please help me to answer the questions 5,6,7, (Show all work here.) on 7 9,11,12,13, *******answer the blanks I need to put this on excel I will my self...

Q:

Match each of the following definitions to the appropriate terms: Terms (1- independence theory with corporate taxes,2- independence theory- no taxes, 3- saucer-shaped cost of capital curve),...

Related Book

An Introduction to Analysis 4th edition by William R. Wade