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Compute the Fourier cosine coefficients for f(x)

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Let \(f(x)= \begin{cases}0 & \text { for } 0 \leq x<2 \\ -(4-x) & \text { for } 2 \leq x \leq 4\end{cases}\)

- Compute the Fourier cosine coefficients for \(f(x)\).

- \(a_{0}=\)

- \(a_{n}=\)

- What are the values for the Fourier cosine series \(\frac{a_{0}}{2}+\sum_{n=1}^{\infty} a_{n} \cos \left(\frac{n \pi}{4} x\right)\) at the given points.

- \(x=2:\)

- \(x=-3\) :

- \(x=5:\)


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