Math Problem Statement

solve useing fourier series and match the options given

Solution

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Math Problem Analysis

Mathematical Concepts

Fourier Series
Piecewise Functions
Periodic Functions

Formulas

Fourier coefficient a_n = (2/T) ∫_0^T f(t) cos(2πnt/T) dt
f(t) = {2t for 0 ≤ t ≤ 2; 4 for 2 ≤ t ≤ 6}

Theorems

Fourier Series Theorem
Integration by Parts

Suitable Grade Level

Undergraduate Mathematics or Advanced High School (Calculus/Mathematics)