EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 6, Problem 16P
(a) Apply the Newton-Raphson method to the function
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Consider a set of data ...
Design a Turing Machine recognizing each of the following languages and draw its state diagram.
Note that the transition functions of the Turing Machine must be in the format of “a → b,L/R", namely the machine
reads single symbol a from the tape, writes single symbol b to the cell to replace a, and then goes to either left L or
right R. You will receive 0 point if you do not follow this instruction.
(1) {w|w=a²b³, n ≥ 0}
(2) {w|w=a'b³,i0}
(3) {w|w a'bick,i
Design a PDA recognizing each of the following languages and draw its state diagram.
Note that the transition function must be in the format of “a, b →c", namely we can only push/pop one symbol
into/from the stack one time upon one input symbol. You will receive 0 point if you push/pop multiple symbols
into/from the stack one time upon one input symbol.
(1) {w|wa"b", n is odd}
=
(2) {w|w=w², length of w is odd and Σ = {a,b} }
(3) {w|w= = a²b²n, n ≥1 }
(4) {w|w=
=a^bn+mcm, n≥0, m ≥ 1 }
(5) {w|w=a²b³n, n≥0}
(6) {w|w= = a¹³, n ≥ 1, m≥ 1 and n‡m }
Hint: two cases: n > m and n
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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