(2) Consider the periodic function defined within one period by the formula: w ( x ) =x+ 5 x+- if - -Sxs- (a) . Simplify this function and plot it on the interval -2.5 .x $ 2.5. Determine whether the function is odd, even or neither. Determine the average value of the function on the period. Find coefficients of the Fourier series for this function. Present the Fourier series of the function in terms of the E-notation. Present the first four terms of the series plus the zero term in the explicit form. (b) Find the Fourier spectrum A, = va +b where a, and b, are the amplitudes of the cosine and sine Fourier harmonics respectively and plot it against n in the log-log scale. (c) Show that the Fourier spectrum is the decaying function of the harmonic number n and find the character of decay (exponential, power type, logarithmic-type, etc). (d) Plot again function w(x) together with its two approximations based on the Fourier series: (i) with only first harmonic and (ii) with three first harmonics. (e) Estimate the relative accuracy of approximations in percents at the function maximum