Evaluate the limit:

**Solution**

Let us begin with the Fourier series of which is of the form:

Hence

(1)

Integrating ( 1 ) we get that:

The Riemann – Lebesgue Lemma implies that

and thus .

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Evaluate the limit:

**Solution**

Let us begin with the Fourier series of which is of the form:

Hence

(1)

Integrating ( 1 ) we get that:

The Riemann – Lebesgue Lemma implies that

and thus .