Suppose that V is open in Rn and that f: V R is continuous. Prove that if

Question:

Suppose that V is open in Rn and that f: V †’ R is continuous. Prove that if

for all nonempty Jordan regions E Š‚ V, then f = 0 on V.

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 04:24 AM

See More Questions

Suppose that V is open in Rn, that f, g: V R3, and that a V. If f and g are differentiable at a, prove that f g is differentiable at a and D(f g)(a)(y) = f(a) (Dg(a)(y)) - g(a) (Df(a)(y)) for...
Suppose that V is open in Rn, that f: V R is C2 on V, and that fxj(a) = 0 for some a H and all j = I, ...,n. Prove that if H is a compact convex subset of V, then there is a constant M such that for...
Suppose that V is open in Rn, that a V, and that F : V R is C1 on V. If F(a) = 0 Fxj(a) and u(j): = (x1 . . . . .. . . .-xj-1, xj+1,. . . . . . . . ., xn) for j = 1,2, ...,n, prove that there exist...
Calculate the dollar proceeds from the FIs loan portfolio at the end of the year, the return on the FIs loan portfolio, and the net interest margin for the FI if the spot foreign exchange rate has...
Lenows Drug Stores and Halls Pharmaceuticals are competitors in the discount drug chain store business. The separate capital structures for Lenow and Hall are presented next. a. Compute earnings per...
Joe purchased a van on February 1, 20X4 for use in his business, Crew Airport Transport. The van was purchased for $30,000, has an estimated useful life of 10 years, and a salvage value of $2,000. No...
State the form of the Laplace equation in axisymmetric spherical coordinates. Verify that the following functions satisfy this equation: \[r \cos \theta ; \quad \cos \theta / r^{2}\] A linear...
On January 1, 2007 the Stimpson Company sells land to Barker Company for $2.5 million, then immediately leases it back. The relevant information is as follows: 1. The land was carried on Stimpsons...
MARKET RESEARCH PROBLEM: To determine the best location in North America to launch a chocolate bar. (CHOCOLATE COMPANY WE ARE LAUNCHING - HEAVEN BAR) Question 1: State the market research problem...
Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The...
Suppose that E is a Jordan region in Rn and that f, g: E R is integrable on E. a) Modifying the proof of Corollary 5.23, prove that fg is integrable on E. b) Prove that f g and f g are integrable...
Evaluate each of the following iterated integrals. a) «10 «10 (x + y) dx dy b) c) 6y cos(y) dy dx
Consider the following 2 x 3 (i.e., r = 2 and c = 3) contingency table: a. Specify the null and alternative hypotheses that should be used in testing the independence of the row and column...
The dataset ToyotaCorolla.csv contains data on used cars on sale during the late summer of 2004 in the Netherlands. It has 1436 records containing details on 38 attributes, including Price, Age,...
An Italian food company that operates several restaurants across seven European countries plans to open a second outlet in Paris. As part of the planning phase, the management would like to see how...
David and Doris Kelley were divorced on February 3, 2018. They lived apart during 2018. The divorce decree required David to make the following payments: a. Transfer full title to their jointly owned...
Xeno Corporation purchased supplies from Kimbo Company in 2019. The total invoice was for $20,000, but Xeno claimed that only one-halfo f the order was received and paid only $10,000 in 2019. Both...
Network Density and Size. Imagine that two new nodes are added to the undirected network in the previous exercise. a. By what percent has the number of nodes increased? b. By what percent has the...
Use Eulers method to approximate the indicated function value to 3 decimal places, using h = 0.1. dy dx = e +e; y(1) = 1; find y(1.5)
Listed below are several terms and phrases associated with basic assumptions, broad accounting principles, and constraints. Pair each item from List A (by letter) with the item from List B that is...
Find an explicit formula for f 1and use it to graph f 1, f and the line y = x on the same screen. To check your work, see whether the graphs of f and f 1 are reflections about the line. 29. f(x) = 1...
Use the given graph of f to sketch the graph of f-1. 1.
Use the given graph of f to sketch the graphs of f-1 and 1/f. y. 1+
A company's 2022 net sales are $80,187. The previous fiscal year, net sales were $76,118. What would the sales be for a 24 month pro forma projection? Show your work and explain how you arrived at...
ABC's stock price is $90. The stock price will either increase 10% or decrease 8% in the first month. If the price increases in the first month, it will go up by $12 or down by $15 in the second...
MyCarCorp produces car parts and is considering opening a new factory in Russia (assume now is beginning of 2002 and the factory would open in 2003). Factory will re- quire an initial investment of...

Suppose that V is open in Rn and that f: V R is continuous. Prove that if

Question:

L sav f dV = 0

Step by Step Answer:

Let x 0 V Then B r x 0 is a ...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions