Prove that if f is uniformly continuous on a bounded subset A of R, then f is

Question:

Prove that if f is uniformly continuous on a bounded subset A of R, then f is bounded on A.

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

Step by Step Answer:

Related Book For book-img-for-question

Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

See More Books

Question Posted: Apr 07, 2016 11:01 AM

See More Questions

Decide which of the following statements are true and which are false. Prove the true ones and provide counterexamples for the false ones. a) If f is uniformly continuous on (0, ) and g is positive...
Suppose that E X and that f : E Y. (a) If f is uniformly continuous on E and xn E is Cauchy in X, prove that f(xn) is Cauchy in Y. (b) Suppose that D is a dense subspace of X (i.e., that D X and ...
Suppose that E is a nonempty subset of R and that fn f uniformly on E. Prove that if each fn is uniformly continuous on E, then f is uniformly continuous on E.
Write out the equation for the following chemical reaction and balance it. Solid potassium chlorate, KCIO3, decomposes to form solid potassium chloride and diatomic oxygen gas. What is the...
The Rolling Creek Textile Mill produces denim. The fixed monthly cost is $21,000, and the variable cost per yard of denim is $0.45. The mill sells a yard of denim for $1.30. a. For a monthly volume...
Magna Corporation has an issue of commercial paper with a face value of $1,060,000 and a maturity of six months. Magna received net proceeds of $1,032,186 when it sold the paper. What is the...
Show that if $\mu_{i j}=\mu+\alpha_{i}+\beta_{j}$, the mean of the $\mu_{i j}$ (summed on $j$ ) is equal to $\mu+\alpha_{i}$, and the mean of $\mu_{i j}$ (summed on $i$ and $j$ ) is...
The following transactions pertain to Smith Training Company for Year 1: Jan. 30 Established the business when it acquired $45,000 cash from the issue of common stock. Feb. 1 Paid rent for office...
You have just completed the appraisal of an office building and have concluded that the market value of the property is $3,500,000. You expect Potential Gross Income (PGI) in the first year of...
The radio music listener market is diverse. Listener formats might include adult contemporary, album rock, top 40, oldies, rap, country and western, classical, and jazz. In targeting audiences,...
Let f be continuous on the interval [0, 1] to R and such that f(0) = f(1). Prove that there exists a point c in [0, 1/2] such that f(c + 1/2). [Consider g(x) = f(x) - f(x + 1/2).] Conclude that there...
If g(x) := x for x (0, 1), show that there does not exist a constant K such that |g(x)| < K|x| for all x (0, 1). Conclude that the uniformly continuous g is not a Lipschitz function on [0, 1].
Consider Fig. 35.3, which could represent interference between water waves in a ripple tank. Pick at least three points on the anti nodal curve labeled "m = 3," and make measurements from the figure...
Analyze the process for monitoring claims data for detecting potential fraud and abuse and describe how it is a crucial financial management process?
Construct a financial model: DHPH has been presented with the opportunity to acquire a 4-acre site that is 176,041 SF zoned industrial with a 2 FAR. The site is currently encumbered with short term...
144. Which of the following is not a part of biotechnology:- (1) Gene therapy (2) Invitro fretilization leading to a test tube baby (3) Developing of DNA vaccine (4) Biomagnification of pesticide...
Two objects are attached together with a piece of string. The block (8.5 kg) slides along a rough horizontal surface. The watermelon (4.5 kg) hangs off the end of the table. If the objects accelerate...
Give an example of one piece of financial information that may be used differently for two stakeholders (users) and explain how it would be used and presented differently?
What international trade agreement(s) appear to allow Air Canada to easily expand into the U.S.?
9.Consider the reaction 3NO2(g)+H2O=2HNO3(aq)+NO(g) where Delta H=-137 kJ.How many kilojoules are released when 92.3g of NO2 reacts?
Determine the place value of the digit 4 in each whole number. 1. 7640 2. 46,200,120 Discuss.
Determine the place value of the digit 4 in each whole number. 1. 7640 2. 46,200,120 Discuss in detail.
Determine the place value of the digit 4 in each whole number. 1. 7640 2. 46,200,120 Discuss briefly.
In the Heckscher-Ohlin model, as trade occurs in a capital-abundant country, increased imports will force domestic import- competing firms to decrease prices and production. Labor and capital will...
Why has Gatorade been so successful in the sports drink market?
Mohali Foods has estimated that fixed costs per month are Rs . 1 1 4 , 8 4 0 and variable costs per unit of sales is 4 2 % . For the month the business anticipates sales of Rs . 3 0 0 , 0 0 0 . What...

Prove that if f is uniformly continuous on a bounded subset A of R, then f is

Question:

Step by Step Answer:

To summarize There exists 0 s...View the full answer

Introduction to Real Analysis

Students also viewed these Calculus questions