4th Edition

ISBN: 9780495114765

Author: J. Douglas Faires, BURDEN

Publisher: Cengage Learning

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Textbook Question

Chapter 2.3, Problem 14E

The function f ( x ) = tan π x − 6 has a zero at ( 1 / π ) arctan 6 ≈ 0.447431543. Let p 0 = 0 and p 1 = 0.48 and use 10 iterations of each of the following methods to approximate this root. Which method is most successful and why?

Bisection method
method of False Position
Secant method

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Chapter 2.3, Problem 13E

Chapter 2.3, Problem 15E

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Chapter 2 Solutions

Numerical Methods

Ch. 2.2 - Use the Bisection method to find p3 for f(x)=xcosx...Ch. 2.2 - Let f(x)=3(x+1)x12(x1). Use the Bisection method...Ch. 2.2 - Use the Bisection method to find solutions...Ch. 2.2 - Use the Bisection method to find solutions...Ch. 2.2 - Sketch the graphs of y=x and y=2sinx. Use the...Ch. 2.2 - Sketch the graphs of y=x and y=tanx. Use the...Ch. 2.2 - Let f(x)=(x+2)(x+1)x(x1)3(x2). To which zero of f...Ch. 2.2 - Let f(x)=(x+2)(x+1)2x(x1)3(x2). To which zero of f...Ch. 2.2 - Use the Bisection method to find an approximation...Ch. 2.2 - Use the Bisection method to find an approximation...

Ch. 2.2 - Find a bound for the number of Bisection method...Ch. 2.2 - Prob. 12E Ch. 2.2 - The function defined by f(x)=sinx has zeros at...Ch. 2.3 - Let f(x)=x26,p0=3, and p1=2. Find p3 using each...Ch. 2.3 - Prob. 2E Ch. 2.3 - Use the Secant method to find solutions accurate...Ch. 2.3 - Use the Secant method to find solutions accurate...Ch. 2.3 - Prob. 5E Ch. 2.3 - Prob. 6E Ch. 2.3 - Use the Secant method to find all four solutions...Ch. 2.3 - Prob. 8E Ch. 2.3 - Prob. 9E Ch. 2.3 - Prob. 10E Ch. 2.3 - Prob. 11E Ch. 2.3 - Prob. 12E Ch. 2.3 - The fourth-degree polynomial...Ch. 2.3 - The function f(x)=tanx6 has a zero at (1/) arctan...Ch. 2.3 - The sum of two numbers is 20. If each number is...Ch. 2.3 - A trough of length L has a cross section in the...Ch. 2.3 - Prob. 17E Ch. 2.4 - Let f(x)=x26 and p0=1. Use Newtons method to find...Ch. 2.4 - Prob. 2E Ch. 2.4 - Prob. 3E Ch. 2.4 - Prob. 4E Ch. 2.4 - Prob. 5E Ch. 2.4 - Use Newtons method to find all solutions of...Ch. 2.4 - Prob. 7E Ch. 2.4 - Prob. 8E Ch. 2.4 - Prob. 9E Ch. 2.4 - Prob. 10E Ch. 2.4 - Prob. 11E Ch. 2.4 - Prob. 12E Ch. 2.4 - Prob. 13E Ch. 2.4 - Prob. 14E Ch. 2.4 - Prob. 15E Ch. 2.4 - Prob. 16E Ch. 2.4 - Prob. 17E Ch. 2.4 - Prob. 18E Ch. 2.4 - Prob. 19E Ch. 2.4 - Prob. 20E Ch. 2.5 - The following sequences are linearly convergent....Ch. 2.5 - Prob. 2E Ch. 2.5 - Prob. 3E Ch. 2.5 - Prob. 4E Ch. 2.5 - Prob. 5E Ch. 2.5 - Prob. 6E Ch. 2.5 - Prob. 7E Ch. 2.5 - Prob. 8E Ch. 2.6 - Find the approximations to within 104 to all the...Ch. 2.6 - Prob. 2E Ch. 2.6 - Prob. 3E Ch. 2.6 - Repeat Exercise 2 using Mullers method.Ch. 2.6 - Prob. 5E Ch. 2.6 - Prob. 6E Ch. 2.6 - Prob. 7E Ch. 2.6 - Prob. 8E Ch. 2.6 - Prob. 9E Ch. 2.6 - Two ladders crisscross an alley of width W. Each...Ch. 2.6 - Prob. 11E Ch. 2.6 - Prob. 12E

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The function f ( x ) = tan π x − 6 has a zero at ( 1 / π ) arctan 6 ≈ 0.447431543. Let p 0 = 0 and p 1 = 0.48 and use 10 iterations of each of the following methods to approximate this root. Which method is most successful and why? Bisection method method of False Position Secant method

Solution Summary: The author explains how to calculate the root of the given system using bisection method.

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Chapter 2 Solutions