Problems 1, 3 and 4

Carmen X 840b2c...: "Towar... 6.3 EXERCISES In Problems 1-6, determine whether the given function is In Problems 17-24, determine the function to which th even, odd, or neither. Fourier series for f(x), given in the indicated problem 1. f(x) = x' + sin2x 2. f(x) = sin x converges. 3. f(x) = (1-x2)-1/2 4. f(x) = sin(x + 1) 17. Problem 9 18. Problem 10 5. f(x) = e"* cos 3x 6. f(x) = x1/5 cosx2 19. Problem 11 20. Problem 12 21. Problem 13 22. Problem 14 7. Prove the following properties: 23. Problem 15 24. Problem 16 (a) If f and g are even functions, then so is the 25. Find the functions represented by the series obtained by product fg. the termwise integration of the given series from - to x. (b) If f and g are odd functions, then fg is an even function. (c) If fis an even function and g is an odd function, then 09 (-1 )"+ (a) 2 X - n - sinnx ~ x, -T