3. Evaluate the following integrals using appropriate Laurent series. cos (a) Sci(0)dz (b) Sc₁(0) cos z sindz
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- 6. Find the sine series of Sx, - x, 7/26. Write the Fourier Sine series for f(x) =R - x (06. Find the sine series of х, f(x) = 01. Find a power series solution in powers of x when the series solution around x0=0 for the following differential equation: (1 – x³)y" – 2xy' + 2y = 0If f(t)= t2-2t where 0< t< find the following 1) The cosine series. 2) The sine series.Q1. Find (i) the Fourier cosine series and (ii) the Fourier sine series of the function f(x) = x, 0Q2 Let f(x) = sin( Q2.1 Express sin(x²) dx as an infinite series. si Q2.2 sin(x²)dx. Q2.3 Use the first two non- zero terms to estimate efsin sin(x²) dx Use the midpoint rule with four subdivisions to estime what you get in question 2.2. ['s sin(x²) dx. Compare this result with(b) Expand f(x) = x as a sine series in the half interval (0, L). Sketch the series you have found (right-hand side of Ans.) over (-2L, 2L). AL ANS. X = sin πT 2n+1 (2n+1)лx L n=01. Find the truncuated error of the Maclaurin series sinx cosx given that is truncated into 3 terms. These are the example that might help..see the picture belowQ5. Let the improper integrals sin(-)dx and Si sin?()dx (i) Write down the first 3 terms of Maclaurin series for f(x) in above two integrals. (ii) Use the series so obtained from part (i) for the 1st three terms of these functions to determine whether the integrals exists.Q5. Let the improper integrals ° sin(-)dx and sin?()dx (i) Write down the first 3 terms of Maclaurin series for f(x) in above two integrals. (ii) Use the series so obtained from part (i) for the 1st three terms of these functions to determine whether the integrals exists.1. Find the truncation error of the Maclaurin series sinx cosx given that is truncated into three (3) terms. See the picture below,,, hope it might help.SEE MORE QUESTIONSRecommended textbooks for youLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning