Problem 1: Determine whether f(x) 1]. (x+1 x0 = is piecewise continuous on [-1, x < 0 x Problem 2: Is the function f(x) = (x+1 1 (2x+1 x < 0 0 x 1 piecewise smooth on [-2,2]? x > 1 df(x) dx Note that a function f(x) is piecewise smooth on [a,b] if both f(x) and are piecewise continuous on [a,b]. Problem 3: Find a Fourier sine series for f(x) = 1 on (0,5). Do the same for the interval (0,1). Problem 4: Find a Fourier cosine series for f(x) = x on (0,3). Do the same for the interval (-3, 3). What do you observe for the result for the interval (-3, 3)? Problem 5: Find a Fourier sine series for f(x) = ex on (0, ). Then, find a Fourier cosine series for f(x) on the same interval.