I only need Problem 2!! Need help!! Please provide a step-by-step solution throu

Question

I only need Problem 2!!

Need help!! Please provide a step-by-step solution through the use of MALAB code along with a detailed explanation!!!! It is alright if you handwrite the step-by-step solution but I would prefer the solution to be shown in MATLAB code. This is very URGENT!!! PLEASE reply as soon as possible!! Thank you!!

Proble (a) 1. (Best Approziamtion) Prove the following statements ,EN be an orthonormal system in an inner product space H, let , ,AN E C and Let e, let f E H. Then j=1 where e (f, e) and l Il is the norm induced by the inner product (b) Let fN-,f, ejej. Then Ilf-fNl s llf-gll for all g in the span of ei,.. . ,EN. Problem 2. This exercise is related to Problem1. Use Chebfun to generate the polynomial of degree 10 that is the best approximation of f(x) = exp(sin(52)) with respect to the L2-norm 11 1 19(x)2dz. Compute the 2 erron this approximation and in the Chebyshev intepolant of same degree. Hint: you can use the command legpoly to generate Legendre polynomials

Explanation / Answer

x = (0:0.02:5); y= exp(sin(5x)); subplot(1,2,1) plot(x,y),xlabel('x'),ylabel('y'), axis([0 5 -1 1]) hold on diff(y) %differentiation f = diff(y); plot(x,f,'r'),xlabel('x'),ylabel('f'), axis([0 5 -1 1])

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