Trigonometric Fourier series

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Problem: Expand function \( f(x)=\sin 2 x \) into Fourier series in cosines on the segment line \( [0 ; 1] \).

2.6.2.17 Trigonometric Fourier series

2.03 $

Problem: Expand function \( f(x)=\frac{\pi}{4}-\frac{x}{2} \) into Fourier series in cosines on the segment line \( [0 ; 1] \).

2.6.2.18 Trigonometric Fourier series

2.03 $

Problem: Expand function \( f(x) \) into Fourier series in cosines on the segment line \( [-\pi, \pi] \). Plot the graphs of function \( f(x) \) and sums of Fourier series. Write down the first three partial sums of the Fourier series and plot the graphs: \[ f(x)=\frac{x^{2}-1}{2}, x \in[-\pi, \pi] . \]

2.6.2.19 Trigonometric Fourier series

5.09 $

Problem: Expand periodic function \( f(x) \) with a period of \( T=2 \) into Fourier series. Plot the graphs of function \( f(x) \) and the sums of Fourier series. Write down the first three partial sums of the Fourier series and plot their graphs. \[ f(x)=\left\{\begin{array}{ll} x, & 0 \leq x \leq 1 \\ 1, & 1

2.6.2.20 Trigonometric Fourier series

6.36 $

Problem: Expand function \( f(x) \) into Fourier series in \( [-\pi ; 2) \) and plot the graph of function \( y=f(x) \) : \[ f(x)=\left\{\begin{array}{cc} 2 x, & -\pi \leq x \leq 0 \\ \frac{\pi}{2}, & 0

2.6.2.21 Trigonometric Fourier series

3.05 $

Problem: Expand function \( f(x) \) into the trigonometric Fourier series in \( [-2 ; 2] \), continuing function in \( [-2 ; 0] \) oddly. \[ f(x)=\left\{\begin{array}{ll} 2-(1-x), & 0 \leq x \leq 1 \\ x-1, & 1 \leq x \leq 2 \end{array} .\right. \]

2.6.2.14 Trigonometric Fourier series

2.54 $

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