EBK BASIC TECHNICAL MATHEMATICS
11th Edition
ISBN: 9780134508290
Author: Evans
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Chapter 22.4, Problem 30E
To determine
The percent of one, two, three standard deviations of the mean and to compare with the Empirical rule.
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The final answer is 8/π(sinx) + 8/3π(sin 3x)+ 8/5π(sin5x)....
Keity
x२
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]
Chapter 22 Solutions
EBK BASIC TECHNICAL MATHEMATICS
Ch. 22.1 - In Example 3, change the class limits to 1.0, 2.0,...Ch. 22.1 - Prob. 2ECh. 22.1 - In Exercises 3-6, indicate whether the variable is...Ch. 22.1 - In Exercises 3-6, indicate whether the variable is...Ch. 22.1 - In Exercises 3-6, indicate whether the variable is...Ch. 22.1 - In Exercises 3-6, indicate whether the variable is...Ch. 22.1 - In Exercises 7-10, use the following data. In a...Ch. 22.1 - In Exercises 7-10, use the following data. In a...Ch. 22.1 - In Exercises 7–10, use the following data. In a...Ch. 22.1 - In Exercises 7–10, use the following data. In a...
Ch. 22.1 - In Exercises 11–14, use the following data. In a...Ch. 22.1 - In Exercises 11–14, use the following data. In a...Ch. 22.1 - In Exercises 11–14, use the following data. In a...Ch. 22.1 - In Exercises 11–14, use the following data. In a...Ch. 22.1 - In Exercises 15–18, use the following data. In...Ch. 22.1 - In Exercises 15–18, use the following data. In...Ch. 22.1 - In Exercises 15-18, use the following data. In...Ch. 22.1 - In Exercises 15-18, use the following data. In...Ch. 22.1 - In Exercises 19-24, use the following data. In a...Ch. 22.1 - In Exercises 19-24, use the following data. In a...Ch. 22.1 - In Exercises 19-24, use the following data. In a...Ch. 22.1 - In Exercises 19-24, use the following data. In a...Ch. 22.1 - In Exercises 19-24, use the following data. In a...Ch. 22.1 - In Exercises 19-24, use the following data. In a...Ch. 22.1 - In Exercises 25 and 26, use the following data....Ch. 22.1 - In Exercises 25 and 26, use the following data....Ch. 22.1 - In Exercises 27 and 28, use the following data....Ch. 22.1 - In Exercises 27 and 28, use the following data....Ch. 22.1 - The data in the table show the global mean...Ch. 22.1 - The data in the following table show the...Ch. 22.2 - For the following numbers, find the indicated...Ch. 22.2 - For the following numbers, find the indicated...Ch. 22.2 - For the following numbers, find the indicated...Ch. 22.2 - Prob. 1ECh. 22.2 - Prob. 2ECh. 22.2 - Prob. 3ECh. 22.2 - In Exercises 1–4, delete the 5 from the data...Ch. 22.2 - In Exercises 5–16, use the following sets of...Ch. 22.2 - In Exercises 5–16, use the following sets of...Ch. 22.2 - In Exercises 5–16, use the following sets of...Ch. 22.2 - In Exercises 5–16, use the following sets of...Ch. 22.2 - In Exercises 5–16, use the following sets of...Ch. 22.2 - In Exercises 5–16, use the following sets of...Ch. 22.2 - Prob. 11ECh. 22.2 - Prob. 12ECh. 22.2 - Prob. 13ECh. 22.2 - Prob. 14ECh. 22.2 - Prob. 15ECh. 22.2 - Prob. 16ECh. 22.2 - In Exercises 17-34, the required data are those in...Ch. 22.2 - In Exercises 17-34, the required data are those in...Ch. 22.2 - In Exercises 17–34, the required data are those in...Ch. 22.2 - In Exercises 17–34, the required data are those in...Ch. 22.2 - Prob. 21ECh. 22.2 - Prob. 22ECh. 22.2 - Prob. 23ECh. 22.2 - Prob. 24ECh. 22.2 - Prob. 25ECh. 22.2 - Prob. 26ECh. 22.2 - In Exercises 17–34, the required data are those in...Ch. 22.2 - Prob. 28ECh. 22.2 - In Exercises 29–42, find the indicated measure of...Ch. 22.2 - In Exercises 29–42, find the indicated measure of...Ch. 22.2 - In Exercises 29–42, find the indicated measure of...Ch. 22.2 - In Exercises 29–42, find the indicated measure of...Ch. 22.2 - In Exercises 29–42, find the indicated measure of...Ch. 22.2 - In Exercises 29–42, find the indicated measure of...Ch. 22.2 - In Exercises 29–42, find the indicated measure of...Ch. 22.2 - In Exercises 29–42, find the indicated measure of...Ch. 22.2 - In Exercises 29–42, find the indicated measure of...Ch. 22.2 - In Exercises 29–42, find the indicated measure of...Ch. 22.2 - Add $100 to each of the salaries in Exercise 29....Ch. 22.2 - Multiply each of the salaries in Exercise 29 by 2....Ch. 22.2 - Change the final salary in Exercise 29 to $4000,...Ch. 22.2 - Find the median and mode of the salaries indicated...Ch. 22.3 - Find the standard deviation of the first eight...Ch. 22.3 - Prob. 1ECh. 22.3 - Prob. 2ECh. 22.3 - Prob. 3ECh. 22.3 - Prob. 4ECh. 22.3 - Prob. 5ECh. 22.3 - Prob. 6ECh. 22.3 - Prob. 7ECh. 22.3 - In Exercises 3–14, use the following sets of...Ch. 22.3 - Prob. 9ECh. 22.3 - Prob. 10ECh. 22.3 - Prob. 11ECh. 22.3 - Prob. 12ECh. 22.3 - Prob. 13ECh. 22.3 - Prob. 14ECh. 22.3 - Prob. 15ECh. 22.3 - Prob. 16ECh. 22.3 - Prob. 17ECh. 22.3 - Prob. 18ECh. 22.3 - Prob. 19ECh. 22.3 - Prob. 20ECh. 22.3 - Prob. 21ECh. 22.3 - Prob. 22ECh. 22.4 - Prob. 1PECh. 22.4 - Prob. 2PECh. 22.4 - Prob. 1ECh. 22.4 - In Exercises 1–4, make the given changes in the...Ch. 22.4 - Prob. 3ECh. 22.4 - Prob. 4ECh. 22.4 - Prob. 5ECh. 22.4 - Prob. 6ECh. 22.4 - Prob. 7ECh. 22.4 - In Exercises 5–8, use the following information....Ch. 22.4 -
In Exercises 9–12, use the following information....Ch. 22.4 -
In Exercises 9–12, use the following information....Ch. 22.4 -
In Exercises 9–12, use the following information....Ch. 22.4 -
In Exercises 9–12, use the following information....Ch. 22.4 -
In Exercises 13–16, use the following data. It...Ch. 22.4 -
In Exercises 13–16, use the following data. It...Ch. 22.4 -
In Exercises 13–16, use the following data. It...Ch. 22.4 -
In Exercises 13–16, use the following data. It...Ch. 22.4 -
In Exercises 17–24, use the following data. The...Ch. 22.4 - Prob. 18ECh. 22.4 - Prob. 19ECh. 22.4 - Prob. 20ECh. 22.4 -
In Exercises 17–24, use the following data. The...Ch. 22.4 - Prob. 22ECh. 22.4 - Prob. 23ECh. 22.4 - Prob. 24ECh. 22.4 -
In Exercises 25–30, solve the given problems,
25....Ch. 22.4 - Prob. 26ECh. 22.4 - Prob. 27ECh. 22.4 - Prob. 28ECh. 22.4 - Prob. 29ECh. 22.4 - Prob. 30ECh. 22.5 - Is either the mean or range affected if subgroup...Ch. 22.5 - Prob. 2PECh. 22.5 - Prob. 1ECh. 22.5 - Prob. 2ECh. 22.5 - Prob. 3ECh. 22.5 - Prob. 4ECh. 22.5 - Prob. 5ECh. 22.5 - Prob. 6ECh. 22.5 - Prob. 7ECh. 22.5 - Prob. 8ECh. 22.5 - In Exercise 9–12, use the following data.
Five AC...Ch. 22.5 - In Exercise 9–12, use the following data.
Five AC...Ch. 22.5 - Prob. 11ECh. 22.5 - Prob. 12ECh. 22.5 - Prob. 13ECh. 22.5 - Prob. 14ECh. 22.5 - Prob. 15ECh. 22.5 - In Exercises 13–16, use the following...Ch. 22.5 - In Exercises 17 and 18, use the following data.
A...Ch. 22.5 - Prob. 18ECh. 22.5 - Prob. 19ECh. 22.5 - Prob. 20ECh. 22.6 - In Exercises 1–14, find the equation of the...Ch. 22.6 - EXERCISE 22.6
In Exercises 1–14, find the equation...Ch. 22.6 - EXERCISE 22.6
In Exercises 1–14, find the equation...Ch. 22.6 - Prob. 4ECh. 22.6 - Prob. 5ECh. 22.6 - Prob. 6ECh. 22.6 - Prob. 7ECh. 22.6 - Prob. 8ECh. 22.6 - Prob. 9ECh. 22.6 - Prob. 10ECh. 22.6 - Prob. 11ECh. 22.6 - Prob. 12ECh. 22.6 - Prob. 13ECh. 22.6 - Prob. 14ECh. 22.6 - Prob. 15ECh. 22.6 - Prob. 16ECh. 22.6 - Prob. 17ECh. 22.6 - Prob. 18ECh. 22.7 - Prob. 1ECh. 22.7 - Prob. 2ECh. 22.7 - Prob. 3ECh. 22.7 - Prob. 4ECh. 22.7 - Prob. 5ECh. 22.7 - Prob. 6ECh. 22.7 - Prob. 7ECh. 22.7 - Prob. 8ECh. 22.7 - Prob. 9ECh. 22.7 - Prob. 10ECh. 22.7 - Prob. 11ECh. 22.7 - Prob. 12ECh. 22 - Prob. 1RECh. 22 - Determine each of the following as being either...Ch. 22 - Determine each of the following as being either...Ch. 22 - Prob. 4RECh. 22 - Prob. 5RECh. 22 - Prob. 6RECh. 22 - Prob. 7RECh. 22 - Prob. 8RECh. 22 - Prob. 9RECh. 22 - Prob. 10RECh. 22 - Prob. 11RECh. 22 - Prob. 12RECh. 22 - Prob. 13RECh. 22 - Prob. 14RECh. 22 - Prob. 15RECh. 22 - Prob. 16RECh. 22 - Prob. 17RECh. 22 - Prob. 18RECh. 22 - Prob. 19RECh. 22 - Prob. 20RECh. 22 - Prob. 21RECh. 22 - Prob. 22RECh. 22 - Prob. 23RECh. 22 - Prob. 24RECh. 22 - Prob. 25RECh. 22 - Prob. 26RECh. 22 - Prob. 27RECh. 22 - Prob. 28RECh. 22 - Prob. 29RECh. 22 - Prob. 30RECh. 22 - Prob. 31RECh. 22 - Prob. 32RECh. 22 - Prob. 33RECh. 22 - Prob. 34RECh. 22 - Prob. 35RECh. 22 - Prob. 36RECh. 22 - Prob. 37RECh. 22 - Prob. 38RECh. 22 - Prob. 39RECh. 22 - Prob. 40RECh. 22 - Prob. 41RECh. 22 - Prob. 42RECh. 22 - Prob. 43RECh. 22 - Prob. 44RECh. 22 - Prob. 45RECh. 22 - Prob. 46RECh. 22 - Prob. 47RECh. 22 - Prob. 48RECh. 22 - Prob. 49RECh. 22 - Prob. 50RECh. 22 - Prob. 51RECh. 22 - Prob. 52RECh. 22 - Prob. 53RECh. 22 - Prob. 54RECh. 22 - Prob. 55RECh. 22 - Prob. 56RECh. 22 - Prob. 57RECh. 22 - Prob. 58RECh. 22 - Prob. 59RECh. 22 - Prob. 60RECh. 22 - Prob. 61RECh. 22 - Prob. 1PTCh. 22 - Prob. 2PTCh. 22 - Prob. 3PTCh. 22 - Prob. 4PTCh. 22 - Prob. 5PTCh. 22 - Prob. 6PTCh. 22 - Prob. 7PTCh. 22 - Prob. 8PTCh. 22 - Prob. 9PTCh. 22 - In Problems 9–11, use the following information....Ch. 22 - Prob. 11PTCh. 22 - Prob. 12PTCh. 22 - Prob. 13PTCh. 22 - Prob. 14PT
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- 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 Marksarrow_forward1. (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_forward
- 2. 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_forward3. (i) Consider a mapping F: RN Rm. Explain in your own words the relationship between the existence of all partial derivatives of F and dif- ferentiability of F at a point x = RN. (ii) [3 Marks] Calculate the gradient of the following function f: R2 → R, f(x) = ||x||3, Total marks 10 where ||x|| = √√√x² + x/2. [7 Marks]arrow_forward1. (i) (ii) which are not. What does it mean to say that a set ECR2 is closed? [1 Mark] Identify which of the following subsets of R2 are closed and (a) A = [-1, 1] × (1, 3) (b) B = [-1, 1] x {1,3} (c) C = {(1/n², 1/n2) ER2 | n EN} Provide a sketch and a brief explanation to each of your answers. [6 Marks] (iii) Give an example of a closed set which does not have interior points. [3 Marks]arrow_forward
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