2. (a) Find the Fourier series for the function f(t) = t² on the interval [-7, 7].
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![2. (a) Find the Fourier series for the function f(t) = t2
on the interval [-7,7].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6e6d380-54a4-46c8-adc0-56f54d5d0909%2F884a7b5b-d37b-4847-a0f7-1e4268e98da3%2Fmltolid_processed.png&w=3840&q=75)
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- Q2. Find the Fourier series for the function f(x) = ›>-6 for for 02. Find the Fourier series for the function f(x)= (n – x)² in -n4. Express the f(x)=1+x function as a Fourier series in the interval of -TFind the Fourier series of the following functions (on [-π, π]). (1) sin²x. (2) r. Also sketch the curve of the Fourier series (on [-37, 3π]). Repeat the above problem on [-L, L].The Fourier series to represent the function f(x)=2x in the range - T to +n is 1 2x = 4 sin c,x - sin c,x + sin c,x - sin c̟x + sin c,x - sin cx + .. sin c̟x + Find: c,, C2, C2, C, C, Ce- C1= C2= C3= C4= C5= C6=(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).Consider the function f (t) =r² +2, 0The Fourier coefficient a, in the Fourier cosine series of f(x)%3D2X, 0Recommended 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,