Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition
11th Edition
ISBN: 9781305283831
Author: Tan
Publisher: Cengage Learning
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Chapter 4.2, Problem 8E
To determine
The solution to the primal problem
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Exercises
Evaluate the following limits.
1. lim cot x/ln x
+01x
2. lim x² In x
+014
3. lim x*
x0+
4. lim (cos√√x)1/x
+014
5. lim x2/(1-cos x)
x10
6. lim e*/*
818
7. lim (secx - tan x)
x-x/2-
8. lim [1+(3/x)]*
x→∞0
In Exercises 1 through 3, let xo =
O and calculate P7(x) and R7(x).
1. f(x)=sin x, x in R.
2. f(x) = cos x, x in R.
3. f(x) = In(1+x), x≥0.
4. In Exercises 1, 2, and 3, for |x| 1, calculate a value of n such that P(x)
approximates f(x) to within 10-6.
5. Let (an)neN be a sequence of positive real numbers such that L =
lim (an+1/an) exists in R. If L < 1, show that an → 0. [Hint: Let
1111
L
iation
7. Let f be continuous on [a, b] and differentiable on (a, b). If lim f'(x)
xia
exists in R, show that f is differentiable at a and f'(a) = lim f'(x). A
similar result holds for b.
x-a
8. In reference to Corollary 5.4, give an example of a uniformly continuous
function on [0, 1] that is differentiable on (0, 1] but whose derivative is not
bounded there.
9. Recall that a fixed point of a function f is a point c such that f(c) = c.
(a) Show that if f is differentiable on R and f'(x)| x if x 1 and hence In(1+x) 0.
12. For 0 л/2. (Thus,
as x л/2 from the left, cos x is never large enough for x+cosx to be
greater than л/2 and cot x is never small enough for x + cot x to be less
than x/2.)
Chapter 4 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition
Ch. 4.1 - Give the three characteristics of a standard...Ch. 4.1 - a. When the initial simplex tableau is set up, how...Ch. 4.1 - In the simplex method, how is a pivoted column...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - Prob. 6ECh. 4.1 - In Exercises 7-16, determine whether the given...
Ch. 4.1 - In Exercises 7-16, determine whether the given...Ch. 4.1 - Prob. 9ECh. 4.1 - Prob. 10ECh. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - In Exercises 7-16, determine whether the given...Ch. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - In Exercise 17-31, solve each linear programming...Ch. 4.1 - Prob. 20ECh. 4.1 - In Exercise 17-31, solve each linear programming...Ch. 4.1 - In Exercise 17-31, solve each linear programming...Ch. 4.1 - In Exercise 17-31, solve each linear programming...Ch. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - In Exercise 17-31, solve each linear programming...Ch. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - PRODUCTION SCHEDULING A company manufactures two...Ch. 4.1 - Prob. 35ECh. 4.1 - PRODUCTION SCHEDULING Kane Manufacturing has a...Ch. 4.1 - ASSETALLOCATION Justin has decided to invest at...Ch. 4.1 - ASSET ALLOCATION A financier plans to invest up to...Ch. 4.1 - PRODUCTION SCHEDULING A division of the Winston...Ch. 4.1 - CROP PLANNING A farmer has 150 acres of land...Ch. 4.1 - PRODUCTION SCHEDULING A company manufactures...Ch. 4.1 - ASSET ALLOCATION Ashley has earmarked at most...Ch. 4.1 - PRODUCTION SCHEDULING Ace Novelty manufactures...Ch. 4.1 - OPTIMIZING ADVERTISING EXPOSURE As part of a...Ch. 4.1 - PRODUCTION SCHEDULING Custom Office Furniture is...Ch. 4.1 - OPTIMIZING PROFIT FOR PREFABRICATED HOUSING Boise...Ch. 4.1 - ASSET ALLOCATION Sharon has a total of 200,000 to...Ch. 4.1 - OPTIMIZING PROFIT FOR BLENDED JUICE DRINKS...Ch. 4.1 - OPTIMIZING PROFIT FOR COLD FORMULAS Beyer...Ch. 4.1 - ASSET ALLOCATION A financier plans to invest up to...Ch. 4.1 - Consider the linear programming problem Maximize...Ch. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Solve the linear programming problems. Maximize...Ch. 4.1 - Prob. 2TECh. 4.1 - Prob. 3TECh. 4.1 - Prob. 4TECh. 4.2 - Suppose you are given the linear programming...Ch. 4.2 - Prob. 2CQCh. 4.2 - Prob. 3CQCh. 4.2 - Prob. 4CQCh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - In Exercise 16, use the technique developed in...Ch. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - In Exercise 1120, construct the dual problem...Ch. 4.2 - Prob. 13ECh. 4.2 - In Exercise 1120, construct the dual problem...Ch. 4.2 - In Exercises 1120, construct the dual problem...Ch. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - In Exercises 1120, construct the dual problem...Ch. 4.2 - Prob. 19ECh. 4.2 - In Exercises 1120, construct the dual problem...Ch. 4.2 - MINIMIZING CRUISE LINE COSTS Deluxe River Cruises...Ch. 4.2 - FERTILIZER COSTSA farmer uses two types of...Ch. 4.2 - DIET PLANNING The owner of the Health Juice Bar...Ch. 4.2 - OPTIMIZING ADVERTISING EXPOSURE Everest Deluxe...Ch. 4.2 - MINIMIZING SHIPPING Cons Acrosonic manufactures a...Ch. 4.2 - MINIMIZING SHIPPING COSTS Steinwelt Piano...Ch. 4.2 - MINIMIZING OIL REFINERY COSTS An oil company...Ch. 4.2 - Prob. 28ECh. 4.2 - In Exercises 28 and 29, determine whether the...Ch. 4.2 - Prob. 1TECh. 4.2 - Prob. 2TECh. 4.2 - Prob. 3TECh. 4.2 - Prob. 4TECh. 4.3 - Explain why the following linear programming...Ch. 4.3 - Prob. 2CQCh. 4.3 - Prob. 3CQCh. 4.3 - Prob. 1ECh. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - In Exercises 520, use the method of this section...Ch. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - In Exercises 520, use the method of this section...Ch. 4.3 - Prob. 20ECh. 4.3 - MAXIMIZING INVESTMENT RETURNS Natsano has at most...Ch. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - CROP PLANNING A farmer has 150 acres of land...Ch. 4.3 - PRODUCTION SCHEDULING A company manufactures...Ch. 4.3 - PRODUCTION SCHEDULING Wayland Company manufactures...Ch. 4.3 - DIET PLANNING A nutritionist at the Medical Center...Ch. 4.3 - MINIMIZING SHIPPING COSTS Steinwelt Piano...Ch. 4.CRQ - Prob. 1CRQCh. 4.CRQ - Prob. 2CRQCh. 4.CRQ - Prob. 3CRQCh. 4.CRQ - Prob. 4CRQCh. 4.CRE - Prob. 1CRECh. 4.CRE - Prob. 2CRECh. 4.CRE - In Exercises 1-8, use the simplex method to solve...Ch. 4.CRE - Prob. 4CRECh. 4.CRE - Prob. 5CRECh. 4.CRE - Prob. 6CRECh. 4.CRE - Prob. 7CRECh. 4.CRE - Prob. 8CRECh. 4.CRE - Prob. 9CRECh. 4.CRE - Construct the dual problem associated with the...Ch. 4.CRE - Prob. 11CRECh. 4.CRE - Prob. 12CRECh. 4.CRE - Prob. 13CRECh. 4.CRE - Prob. 14CRECh. 4.CRE - Prob. 15CRECh. 4.CRE - Prob. 16CRECh. 4.CRE - Prob. 17CRECh. 4.CRE - Prob. 18CRECh. 4.CRE - MINIMIZING MINING COSTS Perth Mining Company...Ch. 4.CRE - MINIMIZING RIVER CRUISE COSTS Nordic River Cruises...Ch. 4.CRE - MINIMIZING CITY WATER COSTS The water-supply...Ch. 4.CRE - INVESTMENT ANALYSIS Jorge has decided to invest at...Ch. 4.CRE - MAXIMIZING PROFIT A company manufactures three...Ch. 4.CRE - INVESTMENT ANALYSIS Sandra has at most 200,000 to...Ch. 4.BMO - Prob. 1BMOCh. 4.BMO - Prob. 2BMOCh. 4.BMO - Prob. 3BMOCh. 4.BMO - Prob. 4BMOCh. 4.BMO - Using the simplex method, solve the following...
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