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A: We have f(x) is even .
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- 5) a) Construct a Fourier Series for f(x) (x2 . 12x)for 12 < x < 3t b) Briefly explain the application of half - the range Fourier series in your SpecializationIf f is the Fourier series of g(x) = = f(x) = 32(-1)"+1 n²-² [16-r², What does f(-4) equal? f(-4) What does f(-2) equal? f(-2)= What does f(0) equal? f(0) n² What does f(1) equal? f(1) What does f(4) equal? ƒ(4) FIT 4 -4< <0 01. (a) Find the Fourier series of the function (x) = 1 - |x), - 2 < x< 2 (b) Hence prove that 1 + 32 52 +..... 72 8.BipinFor both of the given 2π-periodical functions,find1) expansion in Fourier series in real form;2) the sum of the Fourier series for each value of x that belongs tothe interval;3) graph of the sum of the Fourier series.(b) Using the answer to Part (a) and without using Theorem 2.2.4, find the real Fourier series of the function f(x) = -2x 2r-8 if 0 < x < 2 if 2 < x < 4 and f(x+4)=f(x).Example 3) Expand f(x) x - x-as a Fourier series in -15) a) Construct a Fourier Series for f(x) = (x² - 0x)for 0 < x < 3t b) Briefly explain the application of half – range Fourier series in your Specialization1. Express f(x) by the Fourier series where f(x)= {, 2, -7Recommended textbooks for youAlgebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSON
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