22 Pages

Questions Chapter 1

Course: BMGT 110, Fall 2010
School: Maryland
Rating:
 
 
 
 
 

Word Count: 1531

Document Preview

1 Managing Chapter Within The Dynamic Business Environment: Taking Risks and Making Profits CPS questions Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-1 1. the a. b. c. d. Often in business, the greater the risk, greater the potential reward. lower the expected revenues. lower the value provided to society. greater the number of stakeholders. Chapter 01:...

Register Now

Unformatted Document Excerpt

Coursehero >> Maryland >> Maryland >> BMGT 110

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
1 Managing Chapter Within The Dynamic Business Environment: Taking Risks and Making Profits CPS questions Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-1 1. the a. b. c. d. Often in business, the greater the risk, greater the potential reward. lower the expected revenues. lower the value provided to society. greater the number of stakeholders. Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-2 2. Kayla's income has remained stable over the past few years while the prices of the goods and services have gone up. Nevertheless, Kayla feels better off because the environment is cleaner, the crime rate has declined, she has more leisure time, and the quality of medical care has improved. If her experience is typical, we can conclude that the standard of living has: a. b. c. d. increased, but the quality of life has decreased. increased, and so has the quality of life. declined, but the quality of life has increased. declined, and so has the quality of life. Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-3 3. _______ are the resources that contribute to the creation of wealth. a. b. c. d. Production coefficients Factors of production Production technologies Production aggregates Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-4 4. The most accurate statement about factors of production is: a. the five factors of production are energy, capital, labor, leadership and money. b. wealth creation in poor nations is slowed by chronic shortages of labor. c. each of the factors of production is equally important in creating wealth. d. entrepreneurship and knowledge are the most important in creating wealth. Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-5 5. What environment of business are taxes and government regulations part of? a. b. c. d. Economic and legal Competitive Social Technological Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-6 6. Yashmi is an owner of a small coffee shop in Maryland. In order to open her shop she first had to: a. have many employees willing to work at all times of the day. b. go through a long, bureaucratic process to get permission to start a business. c. be sure her risk would be very low. d. get a lease for her business in the same building in which she lives. Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-7 7. Which of these refers to the amount of output generated with a given amount of input, e.g., number of burgers produced per worker per hour? a. b. c. d. Efficiency Technology Telecommuting Productivity Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-8 8. Which of the following best describes the main difference between B2B and B2C transactions? B2B transactions: a. involve transactions where the buyers and sellers are both businesses, while B2C involves transactions between businesses and consumers. b. focus on financial transactions while B2C ecommerce focuses on the sale of manufactured goods. c. are carried out by nonprofit organizations while B2C e-commerce is carried out by business firms seeking to earn a profit. d. involve sales in foreign markets while B2C ecommerce is restricted to domestic markets. Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-9 9. If a policy of empowerment was implemented, how might the organization be restructured? a. Managers would have more responsibility and employees learn to follow directions. b. Managers would have less authority while employees assume more responsibility. c. Workers would agree to work overtime without extra pay. d. An entire level of management would be removed from the organization. Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-10 10. Zim is in charge of production for a familyowned firm that makes and sells gloves. He has stated that speed of delivery is the most important factor for success in the competitive environment. Which of the following would be the best response to Zim? a. b. c. You are right on target, Zim. Time is money. You are the man, Zim. As long as our price is competitive, speedy delivery will win in today's changing marketplace. Well Zim, speed isn't everything. What would delight our customers? Some consumers may put more importance on high quality and/or lower prices. Dude, you couldn't be more wrong. Quality is the name of the game. He who has the best product will win in the competitive environment. 1-11 d. Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 11. _______ are likely to be opportunities in the future because the population aging. is a. Financial services to help clients plan for their education b. Home health care businesses c. Children's day-care centers d. Educational institutions Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-12 12. Finicky Felines, Inc. is considering a program that would allow some of its workers to use flextime. One group of workers who would probably benefit from flextime is: a. workers who do not have access to computers at home. b. workers who have little self-motivation. c. front-line workers who must frequently meet with customers who visit the office. d. workers with young children. Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-13 13. ______ would be due to more efficient distribution systems around the world. a. b. c. d. Increased world trade Decreased world trade Decreased international competition Reduced standards of living around the world Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-14 14. Bobby recently graduated with honors from his college. He has bragged to his friends that his fine academic performance has prepared him so well for a successful career that he can forget school or training in his future. In evaluating the workplace of the future, Bobby is: a. exactly right. His past performance should carry him to success. b. completely wrong. Studies show that a college education has little to do with success. c. over confident. Global competition means that continuous learning will be needed in the future to adapt to rapid changes. d. probably right. Specialized training today is a key to continued success in the future. Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-15 15. In what sector, in recent years, have almost all new jobs in the U.S. been created in? a. b. c. d. Service Manufacturing Agricultural Telecommunications Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-16 16. Which of these best describe the recent job growth in the service sector? a. The service sector has generated almost all new jobs in the American economy since the mid 1980s, but the rate of job growth in services has slowed in recent years. b. Jobs in the service sector have increased slowly over the past decade, but most new jobs are created in the manufacturing industries. c. Employment in the service sector has declined in recent years, and this decline is expected to continue. d. There has been little change in the number of jobs in the service sector in recent years, however employment is expected to increase rapidly. Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-17 17. Which of these refers to a country's general well-being and satisfaction derived from a variety of factors including political freedom, safety, education, and a clean environment? a. b. c. d. Standard of living Quality of life Gross national income Social satisfaction index 1-18 Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 18. What do high tax rates tend to do? a. b. c. d. Promote economic development Make a nation's currency tradable Discourage entrepreneurship Reduce the amount of money created by the government Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-19 19. Successful businesses are keenly focused on which of these? a. b. c. d. Customers Managers Creditors Bureaucrats Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-20 20. Certain sectors of the U.S. economy have experienced a significant decline in employment. Which of these best explains this job loss in specific industries? a. There has been a decline in the productivity of labor in these industries. b. Workers lost these jobs because worker productivity in the sector increased. c. The U.S. economy cannot compete in the global environment. d. Government regulations have eliminated profit opportunities in these industries. Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits 1-21 Answer Key 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Answer: A Answer: C Answer: B Answer: D Answer: A Answer: B Answer: D Answer: A Answer: B Answer: C Answer: B Answer: D Answer: A Answer: C Answer: A Answer: A Answer: B Answer: C Answer: A Answer: B LG: 1 LG: 1 LG: 2 LG: 2 LG: 3 LG: 3 LG: 4 LG: 4 LG: 5 LG: 5 LG: 6 LG: 6 LG: 7 LG: 7 LG: 8 LG: 8 LG: 1 LG: 3 LG: 5 LG: 8 Page: 4 Page: 5 Page: 9 Page: 10 Page: 11 Page: 12 Page: 13 Page: 14 Page: 16 Page: 15 Page: 17 Page: 18 Page: 18 Page: 20 Page: 21 Page: 21 Page: 5 Page: 11 Page: 16 Page: 20 21 1-22 Chapter 01: Managing Within The Dynamic Business Environment: Taking Risks and Making Profits
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Maryland - BMGT - 110
Chapter 2How Economics Affects Business: The Creation and Distribution of WealthCPS questionsChapter 02: How Economics Affects Business: The Creation and Distribution of Wealth 2-11. Which is the study of how to employ resources to produce goods and s
Maryland - BMGT - 110
Chapter 5Choosing a Form of Business OwnershipCPS questionsChapter 05: Choosing a Form of Business Ownership5-11. Which is usually the easiest form of business to start and end?a. b. c. d. Sole proprietorship Limited partnership Corporation Cooperat
Maryland - BMGT - 110
Chapter 8Adapting Organizations to Today's MarketsCPS questionsChapter 08: Adapting Organizations to Today's Markets8-111. Which of the following does organizing a business begins with?a. b. c. d. Acquiring the necessary resources Choosing the best
Maryland - BMGT - 110
Chapter 6Entrepreneurship and Starting a Small BusinessCPS questionsChapter 06: Entrepreneurship and Starting a Small Business6-11. Entrepreneurs' _ is an example of their importance to our economy.a. impact on the political process b. ability to cr
Maryland - BMGT - 110
STUDY QUIZ #3Student: _1. Which of the following describes the marketing era immediately after the development of mass production assembly lines? A. production era B. selling era C. marketing era D. customer relationship era2. A firm gathers _ data by
University of Maryland - COMM - 107
COMM107 Oral Communication: Principles and PracticeNonverbal CommunicationSteven D. CohenNonverbal CommunicationThree key characteristics: Sensitive to the relationship between sender and receiver Have meaning based on their context Part of, not sepa
University of Maryland - COMM - 107
COMM107 Oral Communication: Principles and PracticeIntrapersonal CommunicationSteven D. CohenIntrapersonal Communication The process of "internally communicating with yourself" Selftalk Learning sequence Prelinguistic/preconceptual Linguistic Concep
University of Maryland - COMM - 107
COMM107 Oral Communication: Principles and PracticeListeningSteven D. CohenListening Important for learning, work, life Listening is active Listening doesn't just involve the earsThe Listening Processon epti Rece sag s MeAtt en tio nSpeakerFe e
University of Maryland - BMGT - 367
BMGT 367 Personal Marketing PortfolioSpring 2012 | Section 0201Throughout the semester, BMGT 367 students will complete a Personal Marketing Portfolio (PMP). The assignments in the PMP will correspond with the material presented in class and steps each
University of Maryland - BMGT - 367
BGMT 367 Identifying Your Skill SetAgenda Review Last Week Clip of the Week Focusing on YOU Assessing your Strengths Where to go for Help Turning Strengths to Marketable Skills Mapping your Skills to the Job Description Looking Ahead Writing your Resu
South Carolina - MATH - 554
South Carolina - MATH - 554
South Carolina - MATH - 554
Math 554- 703 I - Analysis I Existence of Square RootsTheorem. If a is a nonnegative real number, then there exists a unique positive real number such that 2 = a. We use the notation a := . Lemma. Positive square roots are unique. Proof. Suppose not. If
South Carolina - MATH - 554
South Carolina - MATH - 703
COMPACT SETS IN METRIC SPACES NOTES FOR MATH 703ANTON R. SCHEPIn this note we shall present a proof that in a metric space (X, d) a subset A is compact if and only if it is sequentially compact, i.e., if every sequence in A has a convergent subsequence
South Carolina - MATH - 703
Complex Variables Notes for Math 703. Part I Updated Fall 2011 Anton R. SchepCHAPTER 1Holomorphic (or Analytic) Functions1. Definitions and elementary properties In complex analysis we study functions f : S C, where S C. When referring to open sets in
South Carolina - MATH - 703
Complex Variables Notes for Math 703. Updated Fall 2011 Anton R. SchepCHAPTER 1Holomorphic (or Analytic) Functions1. Definitions and elementary properties In complex analysis we study functions f : S C, where S C. When referring to open sets in C and c
South Carolina - MATH - 703
Homework 1, Additional Problem. 1 (1) Let 1 < p < a real number and let q be defined by 1 = p + 1 . q 1 a. Let f (t) = p tp + 1 - t. Show (by means of calculus), that f (t) 0 for all t 0. q p q a b. Show that ab ap + bq for all a, b > 0. (Hint: Take t = b
South Carolina - MATH - 703
Homework 2, Additional Problem. (1) Let (X, d) be a metric space and let A X be a non-empty subset. Define d(x, A) = infcfw_d(x, y) : y A. a. Prove d(x, A) = 0 if and only if x A. b. Show that |d(x, A) - d(y, A)| d(x, y), for all x, y X.1
South Carolina - MATH - 703
Homework 4, Additional Problem. (1) Let (X, d) be a compact metric space and f : X X a mapping such that d(f (x), f (y) < d(x, y) for all x = y. a. Show that there exists x0 X such that f (x0 ) = x0 . (Hint: Consider infcfw_d(x, f (x) : x X, show that it
South Carolina - MATH - 703
Homework 7 1. Express in the form a + bi. a. (1 + i)20 . b.1-2i . 2+i2. Solve z 2 - 4z + (4 + 2i) = 0. 3. Describe the sets whose points satisfy the following relations. Which of these sets are regions (i.e., open and connected sets)? a. |z + i| 1. b. d
South Carolina - MATH - 703
(1)(2)(3)(4)(5)Homework 8. Prove that if z = x + iy and f (z) = (|xy|), then the real part and imaginary part of f satisfy the Cauchy-Riemann equations at z = 0, but f is not differentiable at z = 0. Let G C be an open and connected set and let f : G
South Carolina - MATH - 703
Homework 9. (1) Let cn > 0 in R. Prove that cn+1 cn+1 lim n cn lim n cn lim . lim cn cn In particular, if limn cn+1 exists, then limn n cn = limn cn+1 . cn cn (2) Let an 0 and bn 0. Assume that both (an ) and (bn ) are bounded sequences. (a) Prove that li
South Carolina - MATH - 703
Homework 10 dz, using a branch of log z, where is the join of the line segments (1) Evaluate [1 - i, 1 + i], [1 + i, -1 + i],and [-1 + i, -1 - i], starting at 1 - i and traversing the curve once (see figure 1).1 zFigure 1. (2) Compute2ecos t [cos(sin
South Carolina - MATH - 703
Homework 11 (1) Evaluate (without parametrizing, but using Cauchy's Integral Theorem) for a. (t) = 1 + eit (0 t 2). b. (t) = -i + eit (0 t 2). c. (t) = 2eit (0 t 2). d. (t) = 3i + 3eit (0 t 2). (2) Let C with | = 1. Compute2 01 1+z 2dzdt 1 - 2 cos t +
South Carolina - MATH - 703
Homework 13. (1) Let G be open and connected and f, g analytic on G such that f (z)g(z) = 0 for all z G. Prove that either f (z) = 0 for all z G or g(z) = 0 for all z G. (2) (Quals '02) Let f, g : cfw_z : |z| < 1 C be analytic functions such that |f (z)|
South Carolina - MATH - 703
Homework 14. (1) (Schwarz's lemma) Let f be a holomorphic function on B(0, 1) with |f (z)| 1 for all |z| < 1 and f (0) = 0. a. Define f1 (z) = f (z) for z = 0 in B(0, 1). Prove that z = 0 is a removable z singularity of f1 . b. Prove that |f1 (z)| 1 on B(
South Carolina - MATH - 703
Math 703 Course Outline Fall 2011 TTH 2:00 -3:15A Second Course in Mathematical Analysis by: J. and H. Burkill Professor: Anton R. Schep Office: LeConte 300C Webpage: http:/www.math.sc.edu/~schep/math703-2011.html Phone: 7-6190 Email: schep@math.sc.edu O
South Carolina - MATH - 703
Solutions for HW 1 Problem 10;5. (1) y f (AC A) y = f (x) for some x AC A y f (A) for some A C y AC f (A). (2) Let y f (AC A). This implies y = f (x) for some x AC A. Hence y f (A) for all A C, i.e., y AC f (A) Assume now f is injective. Let y AC f (A). T
South Carolina - MATH - 703
Solutions for HW 2 Problem 25:8. Let xn x, yn y in the normed space V and n , n in the scalars. Then we have n xn - x = n xn - n x + n x - x |n | xn - x + |n - | x . Now (n ) is bounded, so |n | xn - x 0, and similarly |n - | x 0. Hence we have n xn - x 0
South Carolina - MATH - 703
Solutions for HW 3 Problem 47: 4. Sets consisting of one point are obviously connected. Let E R \ Q contain at least two points a < b. Then there exist a rational number r with a < r < b. Let G1 = (-, r) and G2 = (r, ). Then G1 , G2 are disjoint open sets
South Carolina - MATH - 703
Solutions for HW 4 Problem 55: 7. For each n pick xn Fn . We first show that (xn ) is a Cauchy sequence. Let > 0. Then there exists N such that (Fn ) < for all n N . Let n, m N and assume n < m. Then (xn , xm ) (Fn ) < . Hence (xn ) is a Cauchy sequence.
South Carolina - MATH - 703
Solutions for HW 5 Problem 66: 3. Define: 1 fn (x) = 2nx - 1 01 for n < x 1 2 1 for n < x n 2 for 0 x n .Then fn B(, 1), but (fn ) has no uniformly convergent subsequence, as (fn , fm ) = 1 for all n = m, where denotes the uniform metric. Problem 66: 5.
South Carolina - MATH - 703
Solutions for HW 5 Problem 107: 2. Let M = | + | and let > 0. Then there exists N such that supx |fn (x) - f (x)| < 2M for all n N and supx |gn (x) - g(x)| < 2M for all n N . Now sup |fn (x)+gn (x)-f (x)-g(x)| | sup |fn (x)-f (x)|+| sup |gn (x)-g(x)| < +
South Carolina - MATH - 703
Homework 7 1. Express in the form a + bi. a. (1 + i)20 . i Solution: 1 + i = 2e 4 . Hence (1 + i)20 = 210 e5i = -210 . b.1-2i . 2+iSolution:1-2i 2+i=1-2i 2-i 2+i 2-i=-5i 5= -i.2. Solve z 2 - 4z + (4 + 2i) = 0. Solution: z 2 - 4z + (4 + 2i) = (z -
South Carolina - MATH - 703
Solutions Homework 8. (1) Prove that if z = x + iy and f (z) = (|xy|), then the real part and imaginary part of f satisfy the Cauchy-Riemann equations at z = 0, but f is not differentiable at z = 0. v v Solution: u(x, y) = |xy| and v(x, y) = 0. Hence x (x
South Carolina - MATH - 703
Solutions Homework 9. (1) Let cn > 0 in R. Prove that cn+1 cn+1 lim n cn lim n cn lim . lim cn cn Solution: Let A = lim cn+1 and let > 0. If A = , then there is nothing to prove, cn so assume A < . Then there exists N such that cn+1 < A + for all n N . Th
South Carolina - MATH - 703
Homework 10 dz, using a branch of log z, where is the join of the line segments (1) Evaluate [1 - i, 1 + i], [1 + i, -1 + i],and [-1 + i, -1 - i], starting at 1 - i and traversing the curve once (see figure 1).1 zFigure 1. Solution: Let F (z) = log |z|
South Carolina - MATH - 703
Solutions homework 11 1 (1) Evaluate (without parametrizing, but using Cauchy's Integral Theorem) 1+z2 dz for a. (t) = 1 + eit (0 t 2). 1 1 1 1 Solution: f (z) = 1+z2 = 2i ( z-i - z+i ). Hence both z = i and z = -i are outside the curve and thus f (z) dz
South Carolina - MATH - 703
Solutions Homework 12 (1) (Quals 1995) Let f be an entire function on C and assume that |f (z)| A|z|k + B for some constants A, B, integer k and all z C. Prove that f is a polynomial. Solution: Let R > 0 and R = Reit , 0 t 2. From Cauchy's integral formul
South Carolina - MATH - 703
Solutions homework 13. (1) Let G be open and connected and f, g analytic on G such that f (z)g(z) = 0 for all z G. Prove that either f (z) = 0 for all z G or g(z) = 0 for all z G. Solution: Assume neither f (z) = 0 for all z G or g(z) = 0 for all z G. The
South Carolina - MATH - 703
Solutions Homework 14. (1) (Schwarz's lemma) Let f be a holomorphic function on B(0, 1) with |f (z)| 1 for all |z| < 1 and f (0) = 0. a. Define f1 (z) = f (z) for z = 0 in B(0, 1). Prove that z = 0 is a removable z singularity of f1 . Solution: Since f is
South Carolina - MATH - 703
Math 703 Course Outline Fall 2011 TTH 2:00 -3:15A Second Course in Mathematical Analysis by: J. and H. Burkill Professor: Anton R. Schep Office: LeConte 300C Webpage: http:/www.math.sc.edu/~schep/math703-2011.html Phone: 7-6190 Email: schep@math.sc.edu O
South Carolina - MATH - 703
Math 703 Course Outline Fall 2011 TTH 2:00 -3:15A Second Course in Mathematical Analysis by: J. and H. Burkill Professor: Anton R. Schep Office: LeConte 300C Webpage: http:/www.math.sc.edu/~schep/math703-2011.html Phone: 7-6190 Email: schep@math.sc.edu O
South Carolina - MATH - 555
Math 555/704I Course OutlineSpring 2011 Text : A First Course in Real Analysis Springer, Undergraduate Texts in Mathematics by: Sterling K. Berberian Supplemented with notes.Professor : Anton R. Schep Office : LeConte 300C Email : schep@math.sc.edu Web
South Carolina - MATH - 555
Homework 1. (1) Prove that [-1, 1) is not compact by using the definition of a compact set (to get credit for the problem, use the definition and not any theorems about compact sets). (2) What is an interior point? Prove that1 4is an interior point of (
South Carolina - MATH - 555
Homework 3, Additional Problems. (1) Let (X, d) be a metric space. a. Let Ei X (i cfw_1, , n) be a finite collection of subsets of X. Prove that n Ei = n Ei . i=1 i=1 b. Let Ei (i I) now be an arbitrary collection of subsets of X. Prove that iI Ei iI Ei a
South Carolina - MATH - 555
Extra problems Homework 4. (1) Let f, g : R R be uniformly continuous functions. Assume that both f and g are bounded. Prove that the product f g is uniformly continuous. (2) A function f : R R is periodic, if there exists a c R such that f (x + c) = f (x
South Carolina - MATH - 555
Extra problems Homework 7. (1) Let f : [0, 1 R be a continuous function. Prove that 1 lim n nn 1f (k/n) =k=1 0f (x) dx.(Hint: Use uniform continuity to show that for > 0 there exists a > 0 such that S() - s() < for all subdivisions with norm N () < .
South Carolina - MATH - 555
Homework 9. Prove that f (x) = limn fn (x) exists for all x R. Does (fn ) (1) Let fn (x) = converge uniformly to f ?x2n . 1+x2n(2) Define fn : [0, 1] [0, 1] by fn (x) = xn (1 - x). Prove that fn converges uniformly to 0. (3) Prove that nx + sin(nx2 ) n
South Carolina - MATH - 555
Solutions homework 1. (1) Prove that [-1; 1) is not compact by using the definition of a compact set (to get credit for the problem, use the definition and not any theorems about compact sets).1 Proof: Let On = (-1, 1 - n ). Then [-1; 1) n On , but [-1;
South Carolina - MATH - 555
Solutions homework 2. Page 32 Problem 6: Clearly d(x, y) 0 and d(x, y) = 0 if and only if x = y. Hence property (i) holds. It is also clear that d(x, y) = d(y, x), so it remains to show that the triangle inequality holds. Let x, y, z X. If x = y, then d(x
South Carolina - MATH - 555
Solutions homework 3. Page 69 Problem 10: a. Assume A and B are neigborhoods of x. Then there exist r1 > 0 such that Ur1 (x) A and r2 > 0 such that Ur2 (x) B. let r = mincfw_r1 , r2 . Then r > 0 and Ur A B. Hence A B is a neighborhood of x. b. Let Br (c)
South Carolina - MATH - 555
Solutions homework 4. Page 108 Problem 4: Let (xn ) be a Cauchy sequence and let > 0. Then there exists > 0 such that |x - y| < implies |f (x) - f (y)| < . For this there exist N such that |xn - xm | < for all n, m N . Hence |f (xn ) - f (xm )| < for all
South Carolina - MATH - 555
Solutions homework 5. Page 128 Problem 3: Using the substitution y = -x we get g(y) - g(-c) f (-y) - f (c) f (x) - f (c) = =- . y - (-c) y - (-c) x-c Now letting y -c- is the same as letting x c+ , from which the problem follows. Page 128 Problem 4. As g(
South Carolina - MATH - 555
Solutions homework 6. Page 141 Problem 2. If f g, then mk (f ) = infcfw_f (x) : xk-1 x xk mk (g) = infcfw_g(x) : xk-1 x xk and thus sf () sg () for any subdivision . By definition this implies thatb bfa ag.The corresponding inequalities for the upp
South Carolina - MATH - 555
Solutions homework 7. Page 182 Problem 1. The answer is 2 times the sum of the geometric series with c = 1 , 3 1 so the answer is 2 1- 1 = 3. 3 Page 182 Problem 4. For n 1 we have s2n+2 = s2n + a2n+1 + a2n+2 s2n (since a2n+1 +a2n+2 0), so (s2n ) is an inc
South Carolina - MATH - 555
Page 188 Problem 6. follows now fromn 1 1 xSolutions homework 8. dx = 2 n - 2 as n . The divergence of the seriesn+11 A simpler proof follows from the fact that diverges. n Page 188 Problem 7. From ln x x - 1 it follows that ln(1 + n) (1 + n) - 1 = n.
South Carolina - MATH - 555
Solutions homework 9. Prove that f (x) = limn fn (x) exists for all x R. Does (fn ) (1) Let fn (x) = converge uniformly to f ? Solution: There are 3 cases: |x| < 1, |x| = 1, and |x| > 1. In case |x| < 1, then x2n 0 as n , which implies that fn (x) 0 as n
South Carolina - MATH - 555
Math 555/704I Course OutlineSpring 2011 Text : A First Course in Real Analysis Springer, Undergraduate Texts in Mathematics by: Sterling K. Berberian Supplemented with notes.Professor : Anton R. Schep Office : LeConte 300C Email : schep@math.sc.edu Web
South Carolina - MATH - 554
Extra Credit problems, MATH 554/703I 1. Let (an ) be a sequence of real numbers such that for some = 0 we have an - = 0. n an + lim What can you say about (an ). 2. Let , > 0. Prove thatnlimnn + n = maxcfw_, .3. Assume an a in R. Put sn = a1 +an . Pr