EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Textbook Question
Chapter 6, Problem 11P
Use the Newton-Raphson method to find the root of
Employ initial guesses of (a) 2, (b) 6, and (c) 8. Explain your results.
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Price (S)
The graph below depicts a firm with market power. In the graph, MC represents the firm's marginal costs, ATC represents the average total costs, D represents demand, and MR represents marginal revenue.
110
70
60
50
40
30
20
MC
ATC
D
0
40
50
70
80
95
Quantity/Units
MR
a. At 60 units of output, how much would this profit-maximizing monopolist charge?
b. How many units would it produce to maximize total revenue rather than total profit?
c. What is the maximum quantity this firm can produce without incurring economic losses?
d. Calculate the firm's profit at the profit-maximizing output and price.
e. Why is this firm's marginal revenue curve below its demand curve? Explain.
Shade the areas given
1. Sketch the following sets and determine which are domains:
(a) |z−2+i| ≤ 1;
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(c) Imz> 1;
(e) 0≤ arg z≤ л/4 (z ± 0);
Ans. (b), (c) are domains.
(b) |2z+3| > 4;
(d) Im z = 1;
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(f) | z − 4| ≥ |z.
Chapter 6 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 6 - 6.1 Use simple fixed-point iteration to locate the...Ch. 6 - 6.2 Determine the highest real root of...Ch. 6 - Use (a) fixed-point iteration and (b) the...Ch. 6 - Determine the real roots of f(x)=1+5.5x4x2+0.5x3:...Ch. 6 - 6.5 Employ the Newton-Raphson method to determine...Ch. 6 - Determine the lowest real root of...Ch. 6 - 6.7 Locate the first positive root of
Where x...Ch. 6 - 6.8 Determine the real root of, with the modified...Ch. 6 - 6.9 Determine the highest real root of:...Ch. 6 - 6.10 Determine the lowest positive root...
Ch. 6 - 6.11 Use the Newton-Raphson method to find the...Ch. 6 - 6.12 Given
Use a root location technique to...Ch. 6 - You must determine the root of the following...Ch. 6 - Use (a) the Newton-Raphson method and (b) the...Ch. 6 - 6.15 The “divide and average” method, an old-time...Ch. 6 - (a) Apply the Newton-Raphson method to the...Ch. 6 - 6.17 The polynomial has a real root between 15...Ch. 6 - Use the secant method on the circle function...Ch. 6 - You are designing a spherical tank (Fig. P6.19) to...Ch. 6 - 6.20 The Manning equation can be written for a...Ch. 6 - 6.21 The function has a double root at. Use (a)...Ch. 6 - 6.22 Determine the roots of the following...Ch. 6 - 6.23 Determine the roots of the simultaneous...Ch. 6 - Repeat Prob. 6.23 except determine the positive...Ch. 6 - A mass balance for a pollutant in a well-mixed...Ch. 6 - Fir Prob. 6.25, the root can be located with...Ch. 6 - 6.27 Develop a user-friendly program for the...Ch. 6 - Develop a user-friendly program for the secant...Ch. 6 - 6.29 Develop a user-friendly program for the...Ch. 6 - 6.30 Develop a user-friendly program for Brent’s...Ch. 6 - 6.31 Develop a user-friendly program for the...Ch. 6 - 6.32 Use the program you developed in Prob. 6.31...
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- 44 4. Write the function f(x)=2+ ANALYTIC FUNCTIONS 1 (z = 0) Z. in the form f(z) = u(r, 0) + iv(r, 0). Ans. f(z) = = (1 + ² ) cos+ir i ( r — 1 ) sin 0. r CHAP. 2arrow_forwardGiven the (3-2-1) Euler angle set (10,20,30) degrees, find the equivalent (3-1-3) Euler angles. All the following Euler angle sets are 3-2-1 Euler angles. The B frame relative to N is given through the 3-2-1 EAs (10,20,30) degrees, while R relative to N is given by the EAs (-5,5,5) degrees. What is the attitude of B relative to R in terms of the 3-2-1 EAsarrow_forward3. Suppose that f(z) = x² − y² −2y+i (2x-2xy), where z = x+iy. Use the expressions (see Sec. 6) x = z┼え 2 Z - Z and y = 2i to write f(z) in terms of z, and simplify the result. Ans. f(z)²+2iz.arrow_forward
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