Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

14th Edition

ISBN: 9780134677972

Author: Barnett

Publisher: PEARSON

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Textbook Question

Chapter 10.1, Problem 2E

(A) Construct a frequency table and histogram for the data set of part (A) of Problem 1 using a

class interval width of 1, starting at 0.5.

(B) Construct a frequency table and histogram for the data set of part (B) of Problem 1 using a

class interval width of 1, starting at 0.5.

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Chapter 10.1, Problem 1E

Chapter 10.1, Problem 5E

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3. (a) Lety: [a, b] C be a contour. Let L(y) denote the length of y. Give a formula for L(y). (1 mark) (b) Let UCC be open. Let f: U→C be continuous. Let y: [a,b] → U be a contour. Suppose there exists a finite real number M such that |f(z)| < M for all z in the image of y. Prove that < ||, f(z)dz| ≤ ML(y). (3 marks) (c) State and prove Liouville's theorem. You may use Cauchy's integral formula without proof. (d) Let R0. Let w € C. Let (10 marks) U = { z Є C : | z − w| < R} . Let f UC be a holomorphic function such that 0 < |ƒ(w)| < |f(z)| for all z Є U. Show, using the local maximum modulus principle, that f is constant. (6 marks)

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(a) State, without proof, Cauchy's theorem, Cauchy's integral formula and Cauchy's integral formula for derivatives. Your answer should include all the conditions required for the results to hold. (8 marks) (b) Let U{z EC: |z| -1}. Let 12 be the triangular contour with vertices at 0, 2-2 and 2+2i, parametrized in the anticlockwise direction. Calculate dz. You must check the conditions of any results you use. (d) Let U C. Calculate Liz-1ym dz, (z - 1) 10 (5 marks) where 2 is the same as the previous part. You must check the conditions of any results you use. (4 marks)

Chapter 10 Solutions

Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

Ch. 10.1 - (A) Using Figure 3, estimate the median annual...Ch. 10.1 - (A) Using Figure 6 estimate the revenue and costs...Ch. 10.1 - Repeat Example 1 for the following intervals: (A)...Ch. 10.1 - The weights (in pounds) were recorded for 20...Ch. 10.1 - (A) Construct a frequency table and histogram for...Ch. 10.1 - (A) Construct a frequency table and histogram for...Ch. 10.1 - Gross domestic product. Graph the data in the...Ch. 10.1 - Corporation revenues. Graph the data in the...Ch. 10.1 - Gold production. Use the double bar graph on world...Ch. 10.1 - Gasoline prices .Graph the data in the following...

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