I. Introduce an even extension and find the fourier transform at the following half-range function 7 ( X ) = )1 - x OLX 1 2. find the fourier coefficients for the periodic extension ( with period , P = 4 ) of the following function . 3 . Give the definition of the orthogonal system of functions to ( x ) , t, ( x ) , tz ( x ) with weight r ( x) in the interval as xeb 4. Consider the function t( X ) = 1 1 ( x - 5 ) given only in the interval A. Can we represent this function in the form of the tourier series it a = 5 , b = 7 ? why ? B. Can we represent this function in the form of the tourier series it a = 0, b = y ? why ? 5 . Write equations for the fourier series and complex tourier amplitudes of some function f ( x ) that satisfies the Dirichlet conditions