[Steps Shown] Let f(x)=x^2 for -3≤ x≤ 3 . Write the Fourier series for f(x) on [-3,3]. Use the theorems to show that this series can be differentiated
Question: Let \(f\left( x \right)={{x}^{2}}\) for \(-3\le x\le 3\) .
- Write the Fourier series for f(x) on [-3,3].
- Use the theorems to show that this series can be differentiated term-by-term and use this fact to obtain the Fourier expansion of 2x on [-3,3].
- Now compute directly the Fourier series of 2x on [-3,3] and compare this result with that of part (b). Use your integrals.
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