Please solve the following by hand and without the use of AI, Please use detailed mathematical expression to solve and explain each step as you go. Ensure the answer is correct please. Thank you! 5. a. Sketch the Fourier series (on the interval -L≤c≤ L), and determine theFourier coefficients of the functionf(x)==1, x

Question

Please solve the following by hand and without the use of AI, Please use detailed mathematical expression to solve and explain each step as you go. Ensure the answer is correct please. Thank you! 5. a. Sketch the Fourier series (on the interval -L≤c≤ L), and determine theFourier coefficients of the functionf(x)==1, x <0{2, 350.b. Sketch the Fourier cosine series and determine the Fourier coefficients of thefunction0, x  L/2.

Accepted Answer

### Part (a): Fourier Series of the Piecewise FunctionConsider the function $ f(x) $ defined as:\[…

5. a. Sketch the Fourier series (on the interval -L≤c≤ L), and determine the Fourier coefficients of the function f(x)= = 1, x <0 {2, 350. b. Sketch the Fourier cosine series and determine the Fourier coefficients of the function 0, x L/2.