Question

Please answer question 3&4 by using functions (a)-(e)

For most of the following problems, you need to refer to the following functions: (а) f(г) — т, х € (-п, т) 0 0 (b) f(x) x > 0 (c) sin(r (d) r, E (0, 1) (e) sin(r) 3. Graph at least 2 periods of functions (a), (b), (c), and (e). Assume the func- tions were originally defines on (-7,T) and are periodic with period 2t. State whether each function is odd, even, or neither 4. With the same assumptions as above, find the Fourier coefficients of (a), (c), and (e). (Hint: In the same way that you can use algebra to find the Taylor series of without taking any derivates, you can use trig identities to find the Fourier series of (c) without taking any integrals.)

Answer 1

I have shown that the functions are odd or even and have solved one Fourier coefficient problem.

As other are similar and you can compute the integration.

Have a good day!!!!

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