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**Lecture Notes Dr. Rakhmad Arief Siregar Universiti Malaysia Perlis**

Tutorial 2 Lecture Notes Dr. Rakhmad Arief Siregar Universiti Malaysia Perlis Applied Numerical Method for Engineers

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Quiz (60 Minutes) What do you know about mathematical model in solving engineering problem? (10 marks) Use zero through third order Taylor series expansions to predict f(2.5) for f(x) = ln x using a base point at x = 1. Compute the true percent relative error for each approximation. (15 marks) Determine the real root of f(x)= 5x3-5x2+6x-2 using bisection method. Employ initial guesses of xl = 0 and xu = 1. iterate until the estimated error a falls below a level of s = 15% (20 marks)

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Quiz (60 Minutes) What do you know about mathematical model in solving engineering problem? (10 marks) Use zero through third order Taylor series expansions to predict f(2.5) for f(x) = ln x using a base point at x = 1. Compute the true percent relative error for each approximation. (15 marks) Determine the real root of f(x)= 5x3-5x2+6x-2 using bisection method. Employ initial guesses of xl = 0 and xu = 1. iterate until the estimated error a falls below a level of s = 15% (20 marks)

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Solution 2 True value:f(2.5) = ln(2.5) =

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Solution 1 True value:f(2.5) = ln(2.5) =

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Solution 1 The process seems to be diverging suggesting that a smaller step would be required for convergence

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Quiz (60 Minutes) What do you know about mathematical model in solving engineering problem? (10 marks) Use zero through third order Taylor series expansions to predict f(2.5) for f(x) = ln x using a base point at x = 1. Compute the true percent relative error for each approximation. (15 marks) Determine the real root of f(x)= 5x3-5x2+6x-2 using bisection method. Employ initial guesses of xl = 0 and xu = 1. iterate until the estimated error a falls below a level of s = 15% (20 marks)

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Solution 3 Graphically

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Solution 3 First iteration

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**Solution 3 First iteration**

The process can be repeated until the approximate error falls below 10%. As summarized below, this occurs after 5 iterations yielding a root estimate of

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Problems 5.1 Solution A plot indicates that a single real root occurs at about x = 0.58

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Solution 5.1 Using quadratic formula First iteration:

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Solution 5.1 Second iteration:

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Solution 5.1 Third iteration:

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Solution 5.4 Solve for the reactions:

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Solution 5.4 A plot of these equations can be generated

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