Numerical Methods
Numerical Methods
4th Edition
ISBN: 9780495114765
Author: J. Douglas Faires, BURDEN
Publisher: Cengage Learning
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Concept explainers

Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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Chapter 2.3, Problem 13E

The fourth-degree polynomial f ( x ) = 230 x 4 + 18 x 3 + 9 x 2 − 221 x − 9 has two real zeros, one in [-1,0] and the other in [0,1]. Attempt to approximate these zeros to within 10 − 6 using each method.

a. method of False Position        b. Secant method

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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. 12ECh. 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. 2ECh. 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. 5ECh. 2.3 - Prob. 6ECh. 2.3 - Use the Secant method to find all four solutions...Ch. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 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. 17ECh. 2.4 - Let f(x)=x26 and p0=1. Use Newtons method to find...Ch. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Use Newtons method to find all solutions of...Ch. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.5 - The following sequences are linearly convergent....Ch. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.6 - Find the approximations to within 104 to all the...Ch. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Repeat Exercise 2 using Mullers method.Ch. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 9ECh. 2.6 - Two ladders crisscross an alley of width W. Each...Ch. 2.6 - Prob. 11ECh. 2.6 - Prob. 12E
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