- Use Matlab Code Is Required Plz 1 (246.36 KiB) Viewed 60 times
use matlab, code is required, plz
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answerhappygod
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use matlab, code is required, plz
use matlab, code is required, plz
How many correct decimal places can the Bisection Method guarantee? = In this assignment, you will attempt to solve f(x) = 0 for three different versions of f(x). The three are: (A) f() (100.26 + (3x2 - 1)4 + 36x2 + 8)e – 24e3x2 (B) f(x) (104.2 + (3x2 – 194 + 36.x² + 8)e - 24e 312 (C) f(x) (108.06 + (3.x2 - 1)* + 36x² + 8)e – 24e3x2 Each of the functions has exactly one root between 0 and 1. For each of (A), (B), and (C), your goal is to find that root correct to at least 5 decimal places, using the Bisection Method. However, I believe you will find this impossible for one of the versions. This fact will eventually lead us to a limitation of finite precision computing that we will discuss more in the future. Note that Matlab always computes in double precision, which means every addition, multiplication, etc. is made with approximately 16 digits of accuracy. For now, let's try to use the Bisection Method to find the roots. To begin, you can use the starting interval (0, 1) since f(0)f(1) < 0. The Bisection Method will give you an approximate root. Now we want to investigate whether we trust the root to 5 decimal places (after the decimal point). To do this, run the Bisection Method with some other starting intervals (a, b) that contain the root and compare the first 5 decimal places. Be sure to randomize a and b a bit to make sure you're not repeating essentially the same computation. If the results agree, with several different starting intervals, one can be reasonably sure the digits are right A few details: For your starting interval (a, b), be sure to check f(a)f(b) < 0. You may want to use numbers a and b that are close to 0 and 1, respectively, to help meet this requirement. Use the Matlab library function exp(x) for e". In particular, use exp(1) for e. Use Matlab format long to see plenty of digits. Be sure to run enough steps to get the first five digits to stop changing. If using the textbook's code, choose a tolerance TOL that will guarantee at least 5 correct digits. More is fine if you think it will help. For each version (A) - (C), report your root r rounded to 5 digits after the decimal point. If you feel that you cannot get 5 correct digits, how many decimal places are you confident are correct? Begin your report by stating your conclusions about the three versions above, including your best guess for the root (you can stop at 5 digits) in each version. Explain your reasoning. Identify which version is the “difficult” one. Save the Matlab code used and your Matlab session, and include these with your report. Save your report as a .pdf file and upload it to Blackboard.
How many correct decimal places can the Bisection Method guarantee? = In this assignment, you will attempt to solve f(x) = 0 for three different versions of f(x). The three are: (A) f() (100.26 + (3x2 - 1)4 + 36x2 + 8)e – 24e3x2 (B) f(x) (104.2 + (3x2 – 194 + 36.x² + 8)e - 24e 312 (C) f(x) (108.06 + (3.x2 - 1)* + 36x² + 8)e – 24e3x2 Each of the functions has exactly one root between 0 and 1. For each of (A), (B), and (C), your goal is to find that root correct to at least 5 decimal places, using the Bisection Method. However, I believe you will find this impossible for one of the versions. This fact will eventually lead us to a limitation of finite precision computing that we will discuss more in the future. Note that Matlab always computes in double precision, which means every addition, multiplication, etc. is made with approximately 16 digits of accuracy. For now, let's try to use the Bisection Method to find the roots. To begin, you can use the starting interval (0, 1) since f(0)f(1) < 0. The Bisection Method will give you an approximate root. Now we want to investigate whether we trust the root to 5 decimal places (after the decimal point). To do this, run the Bisection Method with some other starting intervals (a, b) that contain the root and compare the first 5 decimal places. Be sure to randomize a and b a bit to make sure you're not repeating essentially the same computation. If the results agree, with several different starting intervals, one can be reasonably sure the digits are right A few details: For your starting interval (a, b), be sure to check f(a)f(b) < 0. You may want to use numbers a and b that are close to 0 and 1, respectively, to help meet this requirement. Use the Matlab library function exp(x) for e". In particular, use exp(1) for e. Use Matlab format long to see plenty of digits. Be sure to run enough steps to get the first five digits to stop changing. If using the textbook's code, choose a tolerance TOL that will guarantee at least 5 correct digits. More is fine if you think it will help. For each version (A) - (C), report your root r rounded to 5 digits after the decimal point. If you feel that you cannot get 5 correct digits, how many decimal places are you confident are correct? Begin your report by stating your conclusions about the three versions above, including your best guess for the root (you can stop at 5 digits) in each version. Explain your reasoning. Identify which version is the “difficult” one. Save the Matlab code used and your Matlab session, and include these with your report. Save your report as a .pdf file and upload it to Blackboard.