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Mathematik für Wirtschaftswissenschaftler 2: Lineare Algebra, Funktionen mehrerer Variablen

Mathematik gehört zu den Grundfächern für jeden Studierenden der Wirtschafts- und Sozialwissenschaften. Er benötigt Kenntnisse der research, der Linearen Algebra sowie der Funktionen einer und mehrerer Variablen. Das zweibändige Taschenbuch, hervorgegangen aus Vorlesungen des Autors an der Universität Regensburg, stellt den Studienstoff sehr anschaulich dar, unterstützt durch eine Vielzahl von Beispielen und Abbildungen.

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If possible, find a real value of x such that: (A) (x2)1ր2 Ϫx (B) (x2)1ր2 ϭ Ϫx (C) (x3)1ր3 ϭ Ϫx 89. If n is even and b is negative, then b1րn is not real. If m is odd, n is even, and b is negative, is (bm)1րn real? 90. If we assume that m is odd and n is even, is it possible that one of (b1րn)m and (bm)1րn is real and the other is not? APPLICATIONS 91. 2 ϫ 10Ϫ3 pound, what is the mass of Earth in pounds? Express the answer to two significant digits in scientific notation. is produced by life alone.

63 ϫ 108 Ϫ9 Ϫ7 49. 2 ϫ 10 50. 6 ϫ 10 *The symbol denotes problems that are related to calculus. bar67388_chR_014-035 11/2/06 20:05 Page 26 26 CHAPTER R BASIC ALGEBRAIC OPERATIONS In Problems 71–78, evaluate to four significant digits using a calculator. ) 71. 155ր4 72. 223ր2 73. 103Ϫ3ր4 74. 827Ϫ3ր8 75. 8768ր5 76. 097ր3 77. 000 000 077 35)Ϫ2ր7 78. (491,300,000,000)7ր4 Problems 79–82, illustrate common errors involving rational exponents. In each case, find numerical examples that show that the left side is not always equal to the right side.

Radicals 1Ϫ v2 c2 where M0 ϭ mass at rest and c ϭ velocity of light. The mass of an object increases with velocity and tends to infinity as the velocity approaches the speed of light. Show that M can be written in the form Mϭ M0c 2c2 Ϫ v2 c2 Ϫ v2 88. PHYSICS—PENDULUM A simple pendulum is formed by hanging a bob of mass M on a string of length L from a fixed support (see the figure). The time it takes the bob to swing from right to left and back again is called the period T and is given by T ϭ 2␲ L Ag where g is the gravitational constant.

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