Contemporary Mathematics for Business and Consumers
7th Edition
ISBN: 9781285189758
Author: Robert Brechner, George Bergeman
Publisher: Cengage Learning
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Chapter 17.I, Problem 16RE
To determine
To calculate: The sum-of-the-years’ digits and depreciation rate fraction for year 1, year 3 and year 5 when the useful life is 12 years.
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1. (i)
Identify which of the following subsets of R2 are open and which
are not.
(a)
A = (2,4) x (1, 2),
(b)
B = (2,4) x {1,2},
(c)
C = (2,4) x R.
Provide a sketch and a brief explanation to each of your answers.
[6 Marks]
(ii)
Give an example of a bounded set in R2 which is not open.
[2 Marks]
(iii)
Give an example of an open set in R2 which is not bounded.
[2 Marks
2.
(i)
Which of the following statements are true? Construct coun-
terexamples for those that are false.
(a)
sequence.
Every bounded sequence (x(n)) nEN C RN has a convergent sub-
(b)
(c)
(d)
Every sequence (x(n)) nEN C RN has a convergent subsequence.
Every convergent sequence (x(n)) nEN C RN is bounded.
Every bounded sequence (x(n)) EN CRN converges.
nЄN
(e)
If a sequence (xn)nEN C RN has a convergent subsequence, then
(xn)nEN is convergent.
[10 Marks]
(ii)
Give an example of a sequence (x(n))nEN CR2 which is located on
the parabola x2 = x², contains infinitely many different points and converges
to the limit x = (2,4).
[5 Marks]
2.
(i) What does it mean to say that a sequence (x(n)) nEN CR2
converges to the limit x E R²?
[1 Mark]
(ii) Prove that if a set ECR2 is closed then every convergent
sequence (x(n))nen in E has its limit in E, that is
(x(n)) CE and x() x
x = E.
[5 Marks]
(iii)
which is located on the parabola x2 = = x
x4, contains a subsequence that
Give an example of an unbounded sequence (r(n)) nEN CR2
(2, 16) and such that x(i)
converges to the limit x = (2, 16) and such that x(i)
#
x() for any i j.
[4 Marks
Chapter 17 Solutions
Contemporary Mathematics for Business and Consumers
Ch. 17.I - Wild Flour Bakery purchased a new bread oven for...Ch. 17.I - Prob. 2TIECh. 17.I - Prob. 3TIECh. 17.I - Prestige Limousine Sen ice purchased a limousine...Ch. 17.I - Prob. 1RECh. 17.I - Prob. 2RECh. 17.I - Prob. 3RECh. 17.I - Prob. 4RECh. 17.I - Prob. 5RECh. 17.I - Prob. 6RE
Ch. 17.I - Prob. 7RECh. 17.I - Prob. 8RECh. 17.I - The Huffy Laundromat purchased new washing...Ch. 17.I - Prob. 10RECh. 17.I - Prob. 11RECh. 17.I - Prob. 12RECh. 17.I - Prob. 13RECh. 17.I - Prob. 14RECh. 17.I - Prob. 15RECh. 17.I - Prob. 16RECh. 17.I - Prob. 17RECh. 17.I - Complete Exercises 18-23 as they relate to the...Ch. 17.I - Prob. 19RECh. 17.I - Prob. 20RECh. 17.I - Complete Exercises 18-23 as they relate to the...Ch. 17.I - Prob. 22RECh. 17.I - Complete Exercises 18-23 as they relate to the...Ch. 17.I - Prob. 24RECh. 17.I - Prob. 25RECh. 17.I - Prob. 26RECh. 17.I - Prob. 27RECh. 17.I - Prob. 28RECh. 17.I - Prob. 29RECh. 17.I - Prob. 30RECh. 17.I - Prob. 31RECh. 17.I - You are the accountant for Raleigh Industries, a...Ch. 17.I - BUSINESS DECISION: REPLACING AN ASSET Supreme Auto...Ch. 17.II - Prob. 5TIECh. 17.II - Prob. 6TIECh. 17.II - 1. Ink Masters Printing purchased a new printing...Ch. 17.II - Prob. 2RECh. 17.II - Prob. 3RECh. 17.II - Prob. 4RECh. 17.II - Prob. 5RECh. 17.II - All-That-Glitters Mining Company paid $49.250.000...Ch. 17.II - 7. Sequoia Timber Company purchased land...Ch. 17.II - Prob. 8RECh. 17 - Prob. 1CRCh. 17 - Prob. 2CRCh. 17 - 3. The useful _____ is the length of time an asset...Ch. 17 - Prob. 4CRCh. 17 - 5. Depreciation methods that assume an asset...Ch. 17 - Prob. 6CRCh. 17 - Prob. 7CRCh. 17 - 8. A method of accelerated depreciation that uses...Ch. 17 - Prob. 9CRCh. 17 - Prob. 10CRCh. 17 - Prob. 11CRCh. 17 - Prob. 12CRCh. 17 - Prob. 13CRCh. 17 - When natural resources are depleted, the average...Ch. 17 - Calculate the total cost, total depreciation, and...Ch. 17 - Calculate the total cost, total depreciation, and...Ch. 17 - Oxford Manufacturing. Inc., purchased new...Ch. 17 - Prob. 4ATCh. 17 - Prob. 5ATCh. 17 - Prob. 6ATCh. 17 - Prob. 7ATCh. 17 - Prob. 8ATCh. 17 - Prob. 9ATCh. 17 - Prob. 10ATCh. 17 - Prob. 11ATCh. 17 - Screen Gems Movie Theater purchased a new...Ch. 17 - Stone Age Concrete, Inc. MACRS Depreciation...Ch. 17 - Prob. 14ATCh. 17 - In January 2002. Marine Science Corporation was...
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- 1. (i) which are not. Identify which of the following subsets of R2 are open and (a) A = (1, 3) x (1,2) (b) B = (1,3) x {1,2} (c) C = AUB (ii) Provide a sketch and a brief explanation to each of your answers. [6 Marks] Give an example of a bounded set in R2 which is not open. (iii) [2 Marks] Give an example of an open set in R2 which is not bounded. [2 Marks]arrow_forwardsat Pie Joday) B rove: ABCB. Step 1 Statement D is the midpoint of AC ED FD ZEDAZFDC Reason Given 2 ADDC Select a Reason... A OBB hp B E F D Carrow_forward2. if limit. Recall that a sequence (x(n)) CR2 converges to the limit x = R² lim ||x(n)x|| = 0. 818 - (i) Prove that a convergent sequence (x(n)) has at most one [4 Marks] (ii) Give an example of a bounded sequence (x(n)) CR2 that has no limit and has accumulation points (1, 0) and (0, 1) [3 Marks] (iii) Give an example of a sequence (x(n))neN CR2 which is located on the hyperbola x2 1/x1, contains infinitely many different Total marks 10 points and converges to the limit x = (2, 1/2). [3 Marks]arrow_forward
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