Exercise

EXERCISE 2.3

1. Express as a Fourier Sine Series

3. Find a Fourier sine series for f (x) = k in 0 < x < л

4. Find the Fourier cosine series, and Fourier sine series for

5. Find the Fourier sine series for f (x) =ax + b in 0 < x <

8. Expand x sinx as cosine series in 0 < x <л. Hence, show that

10. Find the half range sine series of f (x) = sin ax in (0, l)

11. Find the half range cosine series for

13. Obtain the half range cosine series for f (x)= cosh ax in  0<x<π

14. Obtain the half range cosine series for f (x) = (x-2)²

15. Obtain the Fourier sine series for sinx in 0 <x<л

17. Prove that in 0 < x < л

18. Obtain the sine series of the function

19. Find the Fourier sine series for the function

20. Find the half range sine series of

21. Find the half-range sine series of  of ƒ (x) = 4x − x² in the interval (0, 4). Hence, deduce the value of the series