Prove that there exist functions u(x, y), v(x, y), and w(X, y), and an r > 0

Question:

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 - x* = 1

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

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 04:22 AM

See More Questions

Given nonzero numbers x0, y0, u0, v0, s0, t0 which satisfy the simultaneous equations prove that there exist functions u(x, y), v(x, y), s(x, y), t(x, y), and an open ball containing (x0, y0), such...
Define the sequence (cn) and (sn) inductively by c1(x) := 1, s1(x):= x, and for all n N, x R. Reason as in the proof of Theorem 8.4.1 to conclude that there exist functions c : R R and s : R R such...
Suppose that a R, that is a nonempty subset of R, and that f, g : E R are uniformly continuous on E. a) Prove that f + g and f are uniformly continuous on E. b) Suppose that f, g are bounded on E....
(a) Decide whether each of the following expressions are true or not. Answer yes or no. In any case where it is not true, provide the actual O-complexity. (i) log n = O(n!) (ii) 10! = O(log n) (iii)...
At the end of January, Higgins Data Systems had an inventory of 650 units, which cost $16 per unit to produce. During February, the company produced 950 units at a cost of $19 per unit. If the firm...
What are some possible negative signals when the product of the accounts receivable turnover ratio is lower (i.e., fewer times)?
Explain why communication is key to fostering effective relationships.(pp. 132134)
The intangible assets section of Willingham Company at December 31, 2014, is presented below. Patents ($100,000 cost less $10,000 amortization) ...... $ 90,000 Copyrights ($60,000 cost less $24,000...
How much money should a person donate today in order for equal annual scholarships of $850 to be awarded forever if the first scholarship is awarded at the end of 14 years? The scholarship fund earns...
The donkey driver Donkey King is using a donkey to carry goods from Harbor City to a village up in the mountains. The people living in the village are willing to buy gold, silk, salt, and sponge....
For each of the following functions, find out whether the given expression can be solved for z in a nonempty, open set V containing (0, 0, 0). Is the solution differentiable near (0, 0)? a) xyz +...
Find conditions on a point (x0, y0, u0, v0) such that there exist real-valued functions u(x, y) and v(x, y) which are continuously differentiable near (x0, y0) and satisfy the simultaneous equations...
In the United States, most fishing streams are public property, with access available to all. In Britain, most fishing streams are privately owned, with access restricted to those who are willing to...
Kelly Corporation received an advanced payment of $\$ 30,000$ in 2018 from Rufus Company for consulting services. Kelly performed half of the consulting in 2018 and the remainder in 2019. Kelly...
Rosa Dominguez, the owner of Elegant Dining in San Jose, California, is pondering whether to buy electronic menu technology and tablets for her five-star restaurant. Prices for a typical four course...
Dura Corporation makes metal frames for several world brands of portable home generators. They sell the frames to a wide variety of portable generator manufacturers such as DeWalt, DuroMax, Generac,...
Rocker Industries (RI) produces recreational in-line skates (see Exhibit 14.36). Demand is seasonal, peaking in the summer months, with a smaller peak demand during December. For one of their more...
The BOM, current inventory, and lead time (in months) for the in-line skates in Rocker Industries (A) case is shown in Exhibit 14.37. Using the chase demand strategy, you developed in Rocker...
Timothy Saueressig typed his will, which left his property to his friends, Scott Smith, Harry Ernst, and Cliff Thomas, and named Smith as his executor. Saueressig had no brothers or sisters, and his...
The Higher the time period of the financial security the higher the. ............... risk. O a. Maturity O b. Default and Maturity Oc. Default O d. Liquidity
(a) Sketch the graph of the tax rate R as a function of the income I. (b) How much tax is assessed on an income of $14,000 On $26,000? (c) Sketch the graph of the total assessed tax T as a function...
The functions in Example 10 and Exercises 54 and 55 (a) Are called step functions because their graphs look like stairs. Give two other examples of step functions that arise in everyday life.
Graphs of f and are shown. Decide whether each function is even, odd, or neither. Explain your reasoning. 57. 58.
An 8%, 30-year semi-annual corporate bond was recently being priced to yield 10%. The Macaulay duration for this bond is 10.2 years. What is the bonds modified duration? How much will the price of...
Question 7 of 7 0/14 W PIERDERY Current Attempt in Progress Your answer is incorrect Buffalo Corporation adopted the dollar value LIFO retail inventory method on January 1, 2019. At that time the...
Cost of debt with fees . Kenny Enterprises will issue a bond with a par value of $1,000, a maturity of twenty years, and a coupon rate of 9.9% with semiannual payments, and will use an investment...

Prove that there exist functions u(x, y), v(x, y), and w(X, y), and an r > 0

Question:

u + xv? - y + w = 0 v5 + yu? - x+ w = 0 w* + y - x* = 1

Step by Step Answer:

Let Fx y u vw u 5 xv 2 y w v 5 yu 2 x ww 4 y 5 x 4 1 and observe ...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions