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Apply six decimal place rounding where applicable.   The equation  f(x) = x^2 - 8 = 0 has a root near x = 3   a) Apply four iterations of the Secant Method, taking the initial approximations  and , to approximate the value of this root. Tabulate your iterations like in the lecture notes.       b) Determine the number of significant digits to which the last iteration’s -value approximates the true solution of the equation.

Apply six decimal place rounding where applicable.   The equation  f(x) = x^2 - 8 = 0 has a root near x = 3   a) Apply four iterations of the Secant Method, taking the initial approximations  and , to approximate the value of this root. Tabulate your iterations like in the lecture notes.       b) Determine the number of significant digits to which the last iteration’s -value approximates the true solution of the equation.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Apply six decimal place rounding where applicable.

 


The equation  f(x) = x^2 - 8 = 0 has a root near x = 3
 

a) Apply four iterations of the Secant Method, taking the initial approximations  and , to approximate the value of this root. Tabulate your iterations like in the lecture notes.  
 

 

b) Determine the number of significant digits to which the last iteration’s -value approximates the true solution of the equation.    
 

Expert Solution
Step 1

Secant's method uses the formula: xn+2=xn-f(xn)⋅xn+1-xnf(xn+1)-f(xn) to perform the iterations and to approximate the root of the equation: f(x)=0.

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