6. Recall that, for each N = 1, 2, ..., the Dirichlet function (aka Dirichlet kernel) is defined as sin( (N+ = )=) DN(2) = 27 sin(x/2) ' x * 0, 12TT,... 2N+1 2 TT x = 0, 12TT, ... Showing your intermediate steps, calculate the following two limits: PTT / 2 lim DN(x) dx, No Jo lim DN(x) dx. N -YOO J T / 2 7. By using the first four non-zero terms in the Taylor expansion of sin(x) about x = 0, show that sin (x) dx = 1.18 ... TT o (We will see in class how this result is useful in studying the Gibb's phenomenon exhibited by Fourier series.)