For part 1 and 2 options are odd extension, even extension. Please answer the fo

Question

For part 1 and 2 options are odd extension, even extension.

Please answer the following questions which deal with the periodic extension of half-range expansions. Recall that Consider the function fit), shown in black. Indicate whether the lines A and B represent the even or odd half-range extensions of f (t) Line "A" is what extension of 'f(t)? Line "B" is what extension of f(t)? Find the periodic extension of the odd half-range expansion. Find the periodic extension of the even half-range expansion.

Explanation / Answer

1) Even

2) Odd

3) 2/pi * (pi*n - sin(pi*n))/n^2 = 2(pi*n - sin(pi*n))/(pi*n^2)

4) 2/pi * pi^2/2 = pi

5) 2/l * integral(pi - t) from 0 to pi with respect to t

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