Excursions In Modern Mathematics, 9th Edition
Excursions In Modern Mathematics, 9th Edition
9th Edition
ISBN: 9780134494142
Author: Tannenbaum
Publisher: PEARSON
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Chapter 9, Problem 66E
To determine

To find:

The formula for the sum of first N even numbers.

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2. Consider the ODE u' = ƒ (u) = u² + r where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r: (a) Sketch ƒ(u) = u² + r and determine the equilibrium points. (b) Draw the phase line. (d) Determine the stability of the equilibrium points. (d) Plot the direction field and some sample solutions,i.e., u(t) (e) Describe how location of the equilibrium points and their stability change as you increase the parameter r. (f) Using the matlab program phaseline.m generate a solution for each value of r and the initial condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption. (g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to turn in a plot for (g), just describe what happens.
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Chapter 9 Solutions

Excursions In Modern Mathematics, 9th Edition

Ch. 9 - Consider the sequence 1,2,6,24,120,.... a. List...Ch. 9 - Consider the sequence 0,1,3,6,10,15,21.... a. List...Ch. 9 - Prob. 14ECh. 9 - Consider the sequence 1,85,2,167,208,.... a. List...Ch. 9 - Prob. 16ECh. 9 - Airlines would like to board passengers in the...Ch. 9 - When two fair coins are tossed the probability of...Ch. 9 - Consider a population that grows linearly...Ch. 9 - Consider a population that grows linearly...Ch. 9 - Consider a population that grows linearly...Ch. 9 - Consider a population that grows linearly...Ch. 9 - Consider a population that grows linearly, with...Ch. 9 - Consider a population that grows linearly, with...Ch. 9 - Official unemployment rates for the U.S....Ch. 9 - The world population reached 6 billion people in...Ch. 9 - The Social Security Administration uses a linear...Ch. 9 - While the number of smokers for the general adult...Ch. 9 - Use the arithmetic sum formula to find the sum...Ch. 9 - Prob. 30ECh. 9 - An arithmetic sequence has first term P0=12 and...Ch. 9 - An arithmetic sequence has first term P0=1 and...Ch. 9 - Find the sum a. 1+3+5+7++149.Hint: See Example...Ch. 9 - Find the sum a. 2+4+6++98. b. 2+4+6+75terms.Ch. 9 - The city of Lightsville currently has 137...Ch. 9 - Prob. 36ECh. 9 - A population grows according to an exponential...Ch. 9 - A population grows according to an exponential...Ch. 9 - A population grows according to the recursive rule...Ch. 9 - Prob. 40ECh. 9 - Crime in Happyville is on the rise. Each year the...Ch. 9 - Prob. 42ECh. 9 - Prob. 43ECh. 9 - Avian influenza A H5N1 is a particularly virulent...Ch. 9 - In 2010 the undergraduate enrollment at Bright...Ch. 9 - In 2009 there were 73 cases of avian influenza A...Ch. 9 - Consider the geometric sequence P0=2, P1=6, P2=18,...Ch. 9 - Consider the geometric sequence P0=4, P1=6, P2=9,...Ch. 9 - Consider the geometric sequence P0=4, P1=2, P2=1,....Ch. 9 - Consider the geometric sequence P0=10, P1=2,...Ch. 9 - Find the sum a. 1+2+22+23++215. b. 1+2+22+23++2N1...Ch. 9 - Find the sum a. 1+3+32+33++310. b. 1+3+32+33++3N1....Ch. 9 - A population grows according to the logistic...Ch. 9 - A population grows according to the logistic...Ch. 9 - For the population discussed in Exercise 53...Ch. 9 - Prob. 56ECh. 9 - Prob. 57ECh. 9 - Prob. 58ECh. 9 - Prob. 59ECh. 9 - Prob. 60ECh. 9 - A population grows according to the logistic...Ch. 9 - A population grows according to the logistic...Ch. 9 - Each of the following sequences follows a linear,...Ch. 9 - Each of the line graph shown in Figs. 9-19 through...Ch. 9 - Prob. 65ECh. 9 - Prob. 66ECh. 9 - Prob. 67ECh. 9 - Prob. 68ECh. 9 - Prob. 69ECh. 9 - Prob. 70ECh. 9 - Prob. 71ECh. 9 - Prob. 72ECh. 9 - Prob. 73ECh. 9 - Prob. 74ECh. 9 - Prob. 75ECh. 9 - Show that if P0,P1,P2,... is an arithmetic...
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