Question: 6. Recall that, for each N = 1, 2, ..., the Dirichlet function (aka Dirichlet kernel) is defined as sin((N+ })x) DN(2) = 27 sin(x

6. Recall that, for each N = 1, 2, ..., the

6. Recall that, for each N = 1, 2, ..., the Dirichlet function (aka Dirichlet kernel) is defined as sin((N+ })x) DN(2) = 27 sin(x /2) , x7 0, 121, ... 2N+1 2 TT x = 0, 1271, ... Showing your intermediate steps, calculate the following two limits: PTT / 2 lim DN(x) dx, N - Jo lim DN(x) dx. NOO JT / 2

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