QI. For the periodic function: ++1 -1<50 S(1) = {i Determine: 1. Isit Odd, Even, or neither? 2. The Fourier expansion. 3. The first 3 terms of the Fourier expansion with (x-0.5). 4. Does the function converge on each of its end points? Prove.
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- Say that the function f(x) is x for -π < x < 0 and zero for 0 < x < π. Find the a0 coefficient for the Fourier Series.Find the first three terms of the expansion (4 – 2x)°. О а. 4°(1 — O b. 2°(1 – *+ +...) О с. 25(1 + 5x +...) O d. 45 (1+ + +..) 28. Calaculate the Fourier series f(t) given in Question 2 as a half-range function showing the first three terms
- 1) Use Bisection to find a root of the function f(x) = ln x-2 on the interval [7, 8] to within 1 decimal place. Organize the results of all the calculations in the table below. You don't need to write down more than 5 decimal places. f(a.) C₁ ƒ (c₁) b₁ f(b) a₁ Half Interval Length5.4 (a) Determine the roots of f(x) = - 12 – 21x + 18x 2.75x using - bisection. initial guesses of x, = -1 and x„ = 0, Compute the estimated error ea and the true error et after each iteration= 0.70 using five iterations of the Bisection Method on ln(a*) : 1. Find one real root of (0.5, 2). the interval 2. Determine one real root of 2xcos2x – (x – 2)² = 0 on the - interval (2,3)using the Regula-Falsi Method. Do four iterations.
- Consider the following. -2 SxS -1, (x) -7x, -1• Prob.7. Find the Fourier series expansion of the function in fig. 4.15. A f(t) 4TO Fig. 4.15Consider the following. (A computer algebra system is recommended.) -23- . -3 Sxs 0, (x + 6) - (x) OQ3 A) Write the first five terms of the following: - 2. {1- (-1)") (3n+2 B) Determine which of the following is converge or diverge: 1 1. {√n +1 -√√n} 2. Σn=2n(Inn)²Find the Fourier series representation of the periodic function below if m = 3 and k = 13. Then, find the value of an if n = 2c + 1 and c = 3.Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,