4. (8%) Let f(x) be a periodic function with period $2\pi$ and defined by $$f(x) = \begin{cases} x + \pi, & |x| \le \frac{\pi}{2}, \\ 0, & \frac{\pi}{2} < |x| \le \pi. \end{cases}$$ for $-\pi \le x \le \pi$. Find the Fourier series of f(x).

4. (8%) Let f(x) be a periodic function with period 2π and defined by f(x) = cases x + π, & |x| π/2, \ 0,

阿摩線上測驗 · 2026-11-03T13:05:22+08:00

4. (8%) Let f(x) be a periodic function with period 2π and defined by f(x) = cases x + π, & |x| π/2, \ 0, & π/2 < |x| π. cases for -π x π. Find the Fourier series of f(x).

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4. (8%) Let f(x) be a periodic function with period $2\pi$ and defined by $$f(x) = \begin{cases} x + \pi, & |x| \le \frac{\pi}{2}, \\ 0, & \frac{\pi}{2} < |x| \le \pi. \end{cases}$$ for $-\pi \le x \le \pi$. Find the Fourier series of f(x).

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