Differentiate the Fourier sine series term by term in Problem 18. Show that the result is not true. Why not?

Data from Problem 18

Consider the function \(f(x)=x, 0

a. Find the Fourier sine series representation of this function and plot the first 50 terms.

b. Find the Fourier cosine series representation of this function and plot the first 50 terms.

c. Extend and apply Parseval's identity in Problem 8 to the result in part \(b\).

d. Use the result of part

c, to find the sum \(\sum_{n=1}^{\infty} \frac{1}{n^{4}}\).