EvenProblemSolutions

EvenProblemSolutions - Answers to even-numbered problems in...

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Answers to even-numbered problems in Mathematics for Economic Analysis Knut Sydsæter Peter Hammond
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Preface Mathematics for Economic Analysis , Prentice Hall, 1995 has been out for a long time, and over the years we have had many request for supplying solutions to the even-numbered problems. (Answers to the odd-numbered problems are given in the main text.) This manual provides answers to all the even-numbered problems in the text. These answers are taken from the old Instructors Manual which is no longer available. (In fact, some of the old answers have been extended.) For many of the more interesting and/or dif±cult problems, detailed solutions are provided. For some of the simpler problems, only the ±nal answer is presented. Appendix A in the main text reviews elementary algebra. This manual includes a Test I, designed for the students themselves to see if they need to review particular sections of Appendix A. Many students using our text will probably have some background in calculus. The accompanying Test II is designed to give information to the students about what they actually know about single variable calculus, and about what needs to be studied more closely, perhaps in Chapters 6 to 9 of the text. Oslo and Coventry, November 2010 Knut Sydsæter and Peter Hammond Contact addresses: knut.sydsater@econ.uio.no P.J.Hammond@warwick.ac.uk Version 1.0 07122010 1113 © Knut Sydsæter and Peter Hammond 2010
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CHAPTER 1 INTRODUCTION 1 Chapter 1 Introduction 1.3 2. (a) Put p/ 100 = x . Then the given expression becomes a + ax (a + ax)x = a( 1 x 2 ) , as required. (b) $2000 · 1 . 05 · 0 . 95 = $1995. (c) The result is precisely the formula in (a). (d) With the notation used in the answer to (a), a + (a = 1 x 2 ) , which is the same expression as in (a). 4. (a) F = 32 yields C = 0; C = 100 yields F = 212. (b) F = 9 5 C + 32 (c) F = 40 for C 4 . 4, F = 80 for C 26 . 7. The assertion is meaningless. 6. x = R( 1 p) S( 1 q) (p q)( 1 p , y = pS qR (p 1 p if (p 1 p 6= 0. (Use, for example, (A.39) in Section A.9.) 1.4 2. (a) Correct. (b) Incorrect. (c) Incorrect. (d) Correct. (e) Incorrect. (f) Incorrect. (“Usually” the sum of two irrationals is irrational, but not always. For example, π and π are both irrationals, but π + ( π) = 0, which is rational.) 4. (a) y 3 3 4 x (b) y> 3 2 z (c) y (m px)/q 6. | 2 · 0 3 |=|− 3 |= 3, | 2 · 1 2 3 2 2, | 2 · 7 2 3 |=| 4 4 8. (a) 3 2 x = 5o r3 2 x =− 5, so 2 x = 2o r 8. Hence x 1o r x = 4. (b) 2 x 2 (c) 1 x 3 (d) 1 / 4 x 1 (e) x> 2or x< 2 (f) 1 x 2 3, and so 1 x 3o r 3 x ≤− 1 1.5 2. (a) right, wrong (b) wrong, right (c) right, wrong (d) and both right (e) wrong (0 · 5 = 0 · 4, but 5 4), right (f) right, wrong 4. x = 2. ( x 1, 0 or 1 make the equation meaningless. Multiplying each term by the common de- nominator x(x 1 )(x + 1 ) yields (x + 1 ) 3 + (x 1 ) 3 2 x( 3 x + 1 ) = 0. Expanding and simplifying, 2 x 3 6 x 2 + 4 x = 0, or 2 2 3 x + 2 ) = 0, or 2 1 )(x 2 ) = 0. Hence, x = 2 is the only solution.) 6. (a) No solutions. (Squaring each side yields x 4 = x + 5 18 x + 5 +
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EvenProblemSolutions - Answers to even-numbered problems in...

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