Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)
11th Edition
ISBN: 9780137554843
Author: Allyn Washington, Richard Evans
Publisher: PEARSON+
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Chapter 30.3, Problem 3E
To determine
The Maclaurin expansion of
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Suppose we have a linear program in standard equation form
maximize c'x
subject to Ax=b,
x≥ 0.
and suppose u, v, and w are all optimal solutions to this linear program.
(a) Prove that zu+v+w is an optimal solution.
(b) If you try to adapt your proof from part (a) to prove that that u+v+w
is an optimal solution, say exactly which part(s) of the proof go wrong.
(c) If you try to adapt your proof from part (a) to prove that u+v-w is an
optimal solution, say exactly which part(s) of the proof go wrong.
(a) For the following linear programme, sketch the feasible region and the direction
of the objective function. Use you sketch to find an optimal solution to the
program. State the optimal solution and give the objective value for this
solution.
maximize +22
subject to 1 + 2x2 ≤ 4,
1 +3x2 ≤ 12,
x1, x2 ≥0
(b) For the following linear programme, sketch the feasible region and the direction
of the objective function. Explain, making reference to your sketch, why this
linear programme is unbounded.
maximize
₁+%2
subject to
-2x1 + x2 ≤ 4,
x1 - 2x2 ≤4,
x1 + x2 ≥ 7,
x1,x20
Give any feasible solution to the linear programme for which the objective
value is 40 (you do not need to justify your answer).
find the domain of the function f(x)
Chapter 30 Solutions
Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)
Ch. 30.1 - Prob. 1PECh. 30.1 - Prob. 2PECh. 30.1 - Prob. 1ECh. 30.1 - Prob. 2ECh. 30.1 - Prob. 3ECh. 30.1 - Prob. 4ECh. 30.1 - Prob. 5ECh. 30.1 - Prob. 6ECh. 30.1 - Prob. 7ECh. 30.1 - Prob. 8E
Ch. 30.1 - Prob. 9ECh. 30.1 - Prob. 10ECh. 30.1 - Prob. 11ECh. 30.1 - Prob. 12ECh. 30.1 - Prob. 13ECh. 30.1 - Prob. 14ECh. 30.1 - Prob. 15ECh. 30.1 - Prob. 16ECh. 30.1 - Prob. 17ECh. 30.1 - Prob. 18ECh. 30.1 - Prob. 19ECh. 30.1 - Prob. 20ECh. 30.1 - Prob. 21ECh. 30.1 - Prob. 22ECh. 30.1 - Prob. 23ECh. 30.1 - Prob. 24ECh. 30.1 - Prob. 25ECh. 30.1 - Prob. 26ECh. 30.1 - Prob. 27ECh. 30.1 - Prob. 28ECh. 30.1 - Prob. 29ECh. 30.1 - Prob. 30ECh. 30.1 - Prob. 31ECh. 30.1 - Prob. 32ECh. 30.1 - Prob. 33ECh. 30.1 - Prob. 34ECh. 30.1 - Prob. 35ECh. 30.1 - Prob. 36ECh. 30.1 - Prob. 37ECh. 30.1 - Prob. 38ECh. 30.1 - Prob. 39ECh. 30.1 - Prob. 40ECh. 30.1 - Prob. 41ECh. 30.1 - In Exercises 39–48, solve the given problems as...Ch. 30.1 - Prob. 43ECh. 30.1 - Prob. 44ECh. 30.1 - In Exercises 39–48, solve the given problems as...Ch. 30.1 - Prob. 46ECh. 30.1 - Prob. 47ECh. 30.1 - Prob. 48ECh. 30.2 - Find the first four terms of the Maclaurin series...Ch. 30.2 - Prob. 1ECh. 30.2 - Prob. 2ECh. 30.2 - Prob. 3ECh. 30.2 - Prob. 4ECh. 30.2 - Prob. 5ECh. 30.2 - Prob. 6ECh. 30.2 - Prob. 7ECh. 30.2 - Prob. 8ECh. 30.2 - Prob. 9ECh. 30.2 - Prob. 10ECh. 30.2 - Prob. 11ECh. 30.2 - Prob. 12ECh. 30.2 - Prob. 13ECh. 30.2 - Prob. 14ECh. 30.2 - Prob. 15ECh. 30.2 - Prob. 16ECh. 30.2 - Prob. 17ECh. 30.2 - Prob. 18ECh. 30.2 - Prob. 19ECh. 30.2 - Prob. 20ECh. 30.2 - Prob. 21ECh. 30.2 - Prob. 22ECh. 30.2 - Prob. 23ECh. 30.2 - Prob. 24ECh. 30.2 - Prob. 25ECh. 30.2 - Prob. 26ECh. 30.2 - Prob. 27ECh. 30.2 - In Exercises 21–28, find the first two nonzero...Ch. 30.2 - Prob. 29ECh. 30.2 - Prob. 30ECh. 30.2 - In Exercises 29–44, solve the given problems.
Is...Ch. 30.2 - In Exercises 29–44, solve the given problems.
Is...Ch. 30.2 - Prob. 33ECh. 30.2 - Prob. 34ECh. 30.2 - Prob. 35ECh. 30.2 - Prob. 36ECh. 30.2 - In Exercises 29–44, solve the given problems.
The...Ch. 30.2 - Prob. 38ECh. 30.2 - Prob. 39ECh. 30.2 - Prob. 40ECh. 30.2 - Prob. 41ECh. 30.2 - Prob. 42ECh. 30.2 - Prob. 43ECh. 30.2 - Prob. 44ECh. 30.3 - Using the Maclaurin series for ln(1 + x), find the...Ch. 30.3 - Prob. 2PECh. 30.3 - Prob. 1ECh. 30.3 - Prob. 2ECh. 30.3 - Prob. 3ECh. 30.3 - Prob. 4ECh. 30.3 - Prob. 5ECh. 30.3 - In Exercises 3–10, find the first four nonzero...Ch. 30.3 - Prob. 7ECh. 30.3 - Prob. 8ECh. 30.3 - In Exercises 3–10, find the first four nonzero...Ch. 30.3 - Prob. 10ECh. 30.3 - Prob. 11ECh. 30.3 - Prob. 12ECh. 30.3 - In Exercises 11–16, evaluate the given integrals...Ch. 30.3 - Prob. 14ECh. 30.3 - Prob. 15ECh. 30.3 - Prob. 16ECh. 30.3 - Prob. 17ECh. 30.3 - Prob. 18ECh. 30.3 - In Exercises 17–30, find the indicated series by...Ch. 30.3 - Prob. 20ECh. 30.3 - Prob. 21ECh. 30.3 - In Exercises 17–30, find the indicated series by...Ch. 30.3 - Prob. 23ECh. 30.3 - Prob. 24ECh. 30.3 - Prob. 25ECh. 30.3 - Prob. 26ECh. 30.3 - Prob. 27ECh. 30.3 - Prob. 28ECh. 30.3 - Prob. 29ECh. 30.3 - Prob. 30ECh. 30.3 - Prob. 31ECh. 30.3 - Prob. 32ECh. 30.3 - Prob. 33ECh. 30.3 - Prob. 34ECh. 30.3 - Prob. 35ECh. 30.3 - Prob. 36ECh. 30.3 - Prob. 37ECh. 30.3 - Prob. 38ECh. 30.3 - Prob. 39ECh. 30.3 - Prob. 40ECh. 30.3 - Prob. 41ECh. 30.3 - Prob. 42ECh. 30.3 - Prob. 43ECh. 30.3 - Prob. 44ECh. 30.3 - Prob. 45ECh. 30.3 - Prob. 46ECh. 30.4 - Using three terms of the appropriate series,...Ch. 30.4 - Prob. 2PECh. 30.4 - Prob. 1ECh. 30.4 - Prob. 2ECh. 30.4 - Prob. 3ECh. 30.4 - Prob. 4ECh. 30.4 - Prob. 5ECh. 30.4 - Prob. 6ECh. 30.4 - Prob. 7ECh. 30.4 - Prob. 8ECh. 30.4 - Prob. 9ECh. 30.4 - Prob. 10ECh. 30.4 - Prob. 11ECh. 30.4 - Prob. 12ECh. 30.4 - In Exercises 3–20, calculate the value of each of...Ch. 30.4 - Prob. 14ECh. 30.4 - Prob. 15ECh. 30.4 - Prob. 16ECh. 30.4 - Prob. 17ECh. 30.4 - Prob. 18ECh. 30.4 - Prob. 19ECh. 30.4 - Prob. 20ECh. 30.4 - Prob. 21ECh. 30.4 - Prob. 22ECh. 30.4 - Prob. 23ECh. 30.4 - Prob. 24ECh. 30.4 - Prob. 25ECh. 30.4 - Prob. 26ECh. 30.4 - Prob. 27ECh. 30.4 - Prob. 28ECh. 30.4 - Prob. 29ECh. 30.4 - Prob. 30ECh. 30.4 - Prob. 31ECh. 30.4 - Prob. 32ECh. 30.4 - Prob. 33ECh. 30.4 - Prob. 34ECh. 30.4 - Prob. 35ECh. 30.4 - Prob. 36ECh. 30.4 - In Exercises 29–40, solve the given problems by...Ch. 30.4 - Prob. 38ECh. 30.4 - Prob. 39ECh. 30.4 - Prob. 40ECh. 30.5 - Expand f(x) = ex in a Taylor series with a = 3.
Ch. 30.5 - Prob. 1ECh. 30.5 - Prob. 2ECh. 30.5 - Prob. 3ECh. 30.5 - Prob. 4ECh. 30.5 - Prob. 5ECh. 30.5 - Prob. 6ECh. 30.5 - Prob. 7ECh. 30.5 - Prob. 8ECh. 30.5 - Prob. 9ECh. 30.5 - Prob. 10ECh. 30.5 - In Exercises 11–22, find the first three nonzero...Ch. 30.5 - Prob. 12ECh. 30.5 - Prob. 13ECh. 30.5 - Prob. 14ECh. 30.5 - Prob. 15ECh. 30.5 - Prob. 16ECh. 30.5 - In Exercises 11–22, find the first three nonzero...Ch. 30.5 - In Exercises 11–22, find the first three nonzero...Ch. 30.5 - Prob. 19ECh. 30.5 - Prob. 20ECh. 30.5 - Prob. 21ECh. 30.5 - Prob. 22ECh. 30.5 - Prob. 23ECh. 30.5 - Prob. 24ECh. 30.5 - Prob. 25ECh. 30.5 - Prob. 26ECh. 30.5 - Prob. 27ECh. 30.5 - Prob. 28ECh. 30.5 - Prob. 29ECh. 30.5 - Prob. 30ECh. 30.5 - Prob. 31ECh. 30.5 - Prob. 33ECh. 30.5 - Prob. 34ECh. 30.5 - In Exercises 31–38, solve the given...Ch. 30.5 - Prob. 36ECh. 30.5 - In Exercises 31–38, solve the given...Ch. 30.5 - Prob. 38ECh. 30.5 - In Exercises 39–42, use a calculator to display...Ch. 30.5 - In Exercises 39–42, use a calculator to display...Ch. 30.5 - In Exercises 39–42, use a calculator to display...Ch. 30.5 - In Exercises 39–42, use a calculator to display...Ch. 30.6 - In Example 2, in the definition of f(x), replace 1...Ch. 30.6 - Prob. 1ECh. 30.6 - Prob. 2ECh. 30.6 - In Exercises 3–14, find at least three nonzero...Ch. 30.6 - Prob. 4ECh. 30.6 - In Exercises 3–14, find at least three nonzero...Ch. 30.6 - Prob. 6ECh. 30.6 - In Exercises 3–14, find at least three nonzero...Ch. 30.6 - Prob. 8ECh. 30.6 - In Exercises 3–14, find at least three nonzero...Ch. 30.6 - Prob. 10ECh. 30.6 - Prob. 11ECh. 30.6 - Prob. 12ECh. 30.6 - Prob. 13ECh. 30.6 - Prob. 14ECh. 30.6 - Prob. 15ECh. 30.6 - Prob. 16ECh. 30.6 - Prob. 17ECh. 30.6 - Prob. 18ECh. 30.6 - Prob. 19ECh. 30.6 - Prob. 20ECh. 30.6 - In Exercises 21–24, solve the given problems.
21....Ch. 30.6 - In Exercises 21–24, solve the given problems.
22....Ch. 30.6 - In Exercises 21–24, solve the given problems.
23....Ch. 30.6 - Prob. 24ECh. 30.7 - Determine whether the following functions are even...Ch. 30.7 - Prob. 2PECh. 30.7 - Prob. 3PECh. 30.7 - In Exercises 1–4, write the Fourier series for...Ch. 30.7 - In Exercises 1–4, write the Fourier series for...Ch. 30.7 - In Exercises 1–4, write the Fourier series for...Ch. 30.7 - In Exercises 1–4, write the Fourier series for...Ch. 30.7 - In Exercises 5−12, determine whether the given...Ch. 30.7 - In Exercises 5–12, determine whether the given...Ch. 30.7 - In Exercises 5–12, determine whether the given...Ch. 30.7 - In Exercises 5–12, determine whether the given...Ch. 30.7 - In Exercises 5–12, determine whether the given...Ch. 30.7 - In Exercises 5–12, determine whether the given...Ch. 30.7 - In Exercises 5–12, determine whether the given...Ch. 30.7 - In Exercises 5–12, determine whether the given...Ch. 30.7 - In Exercises 13–16, determine whether the Fourier...Ch. 30.7 - In Exercises 13–16, determine whether the Fourier...Ch. 30.7 - In Exercises 13–16, determine whether the Fourier...Ch. 30.7 - In Exercises 13–16, determine whether the Fourier...Ch. 30.7 - Prob. 17ECh. 30.7 - Prob. 18ECh. 30.7 - Prob. 19ECh. 30.7 - Prob. 20ECh. 30.7 - Prob. 21ECh. 30.7 - Prob. 22ECh. 30.7 - Prob. 23ECh. 30.7 - Prob. 24ECh. 30.7 - Prob. 25ECh. 30.7 - Prob. 26ECh. 30.7 - Prob. 27ECh. 30.7 - In Exercises 23–28, solve the given problems.
28....Ch. 30 - Prob. 1RECh. 30 - Prob. 2RECh. 30 - Prob. 3RECh. 30 - Prob. 4RECh. 30 - Prob. 5RECh. 30 - Prob. 6RECh. 30 - Prob. 7RECh. 30 - Prob. 8RECh. 30 - Prob. 9RECh. 30 - Prob. 10RECh. 30 - Prob. 11RECh. 30 - Prob. 12RECh. 30 - Prob. 13RECh. 30 - Prob. 14RECh. 30 - Prob. 15RECh. 30 - Prob. 16RECh. 30 - Prob. 17RECh. 30 - Prob. 18RECh. 30 - Prob. 19RECh. 30 - Prob. 20RECh. 30 - Prob. 21RECh. 30 - Prob. 22RECh. 30 - Prob. 23RECh. 30 - Prob. 24RECh. 30 - Prob. 25RECh. 30 - Prob. 26RECh. 30 - Prob. 27RECh. 30 - Prob. 28RECh. 30 - Prob. 29RECh. 30 - Prob. 30RECh. 30 - Prob. 31RECh. 30 - Prob. 32RECh. 30 - Prob. 33RECh. 30 - Prob. 34RECh. 30 - Prob. 35RECh. 30 - Prob. 36RECh. 30 - Prob. 37RECh. 30 - Prob. 38RECh. 30 - Prob. 39RECh. 30 - Prob. 40RECh. 30 - Prob. 41RECh. 30 - Prob. 42RECh. 30 - Prob. 43RECh. 30 - Prob. 44RECh. 30 - Prob. 45RECh. 30 - Prob. 46RECh. 30 - Prob. 47RECh. 30 - Prob. 48RECh. 30 - Prob. 49RECh. 30 - Prob. 50RECh. 30 - Prob. 51RECh. 30 - Prob. 52RECh. 30 - Prob. 53RECh. 30 - Prob. 54RECh. 30 - Prob. 55RECh. 30 - In Exercises 43–80, solve the given...Ch. 30 - Prob. 57RECh. 30 - Prob. 58RECh. 30 - Prob. 59RECh. 30 - Prob. 60RECh. 30 - Prob. 61RECh. 30 - Prob. 62RECh. 30 - Prob. 63RECh. 30 - Prob. 64RECh. 30 - Prob. 65RECh. 30 - Prob. 66RECh. 30 - Prob. 67RECh. 30 - Prob. 68RECh. 30 - Prob. 69RECh. 30 - Prob. 70RECh. 30 - Prob. 71RECh. 30 - Prob. 72RECh. 30 - Prob. 73RECh. 30 - Prob. 74RECh. 30 - Prob. 75RECh. 30 - Prob. 76RECh. 30 - Prob. 77RECh. 30 - Prob. 78RECh. 30 - Prob. 79RECh. 30 - Prob. 80RECh. 30 - Prob. 81RECh. 30 - Prob. 1PTCh. 30 - Prob. 2PTCh. 30 - Prob. 3PTCh. 30 - Prob. 4PTCh. 30 - Prob. 5PTCh. 30 - Prob. 6PTCh. 30 - Prob. 7PT
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