1. Determine the Fourier series for the periodic function: -2, when - f(x)= +2, when 0<x< Which is periodic outside this range of period 2x. 2. For the Fourier series in Problem 1, deduce a series for at the point where 3. For the waveform shown in the following figure determine (a) the Fourier series for the function and (b) the sum of the Fourier series at the points of discontinuity. f(x) + 4. Find the term representing the third harmonic for the periodic function of period 2 r given by: f(x)= 0, when - 5. Show that the Fourier series for the periodic function of period 2. defined by when-co sin, when 0 is given by: --- 3x(7) com40 (3)(5) 1. Show that the Fourier series for the function f(x)=x over the range x=0 to -2л is given by 1 f(x)=-2(sin x + sin 2x + sin 3x+ ..) 2. Determine the Fourier series for the function defined by: when - <IAO 1+1. when 0 Draw a graph of the function within and outside of the given range. 3. Expand the function f(0)=02 in a Fourier series in the range -л<<л. Sketch the function within and outside of the given range. 1001 4. For the Fourier series obtained in Problem 3, let 0 = and deduce the series for Σn=1; 5. Determine the Fourier series for the function f(0)-02 in the range - <0 <. The function Draw a graph of the function within and outside of the given range. 3. Expand the function f(0) = 0² in a Fourier series in the range -<0. Sketch the function within and outside of the given range. 4. For the Fourier series obtained in Problem 3, let 0 =л and deduce the series for 700 5. Determine the Fourier series for the function f(0)-02 in the range -л<<. The function has a period of 2x. Sketch the graph over the given period and extend it to outside the range 6. For the Fourier series of Problem 5, let 0=x and show that Σ Half range Fourier Series: 7. Determine the half-range sine series for the function defined by: x. 0<x< T f(x)= л 0. AIMM 8. Obtain (a) the half-range cosine series and (b) the half-range sine series for the function 0, 0<<< f(t)= 1. T KIMM