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  3. determine the positive real root of ln(x^2)=0.8 by

Determine the positive real root of ln(x^2)=0.8 by the following methods. (Note that you need to...

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Advance Math

Determine the positive real root of ln(x^2)=0.8 by the followingmethods. (Note that you need to show the details of yourderivations in MATLAB).

a) Graphically ( plot the function and copy your figure toword).

b) Using two iterations of the bisection method with initialguesses of xl=0.4 and xu=2 and populate the following table. Whatis the root after two iterations? Provide justification for thevalues you have obtained in your MATLAB code as comments.

i xl xu xr

1 0.4 2

2

c) Using two iterations of the false position method, with thesame initial guesses as in b) and populate the table below. What isthe root after two iterations? Provide justification for the valuesyou have obtained in your MATLAB code as comments.

i xl xu xr

1 0.4 2

2   

d) Compute the actual root of the function (use a built inMATLAB function) and identify which method (bisection or falseposition) achieves a better estimate of the root after twoiterations. Prove your answer by calculating the True PercentageError ( Assume that your answer in part d, obtained using theMATLAB Built in Function is the true value ). ALL Calculations mustbe performed in MATLAB.

Answer & Explanation Solved by verified expert
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We have developed a MATLAB code single code for all problemfor all the problemsMATLABcodefx logx208    See Answer
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