This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the questions: 1a) Define the following: i) Periodic function: A function f(x) is periodic if there exists a positive constant T such that f(x+T) = f(x) for all x in the domain of f. The smallest such positive T is called the period. ii) Even function: A function f(x) is an even function if f(-x) = f(x) for all x in its domain. Even functions are symmetric about the y-axis. iii) Fourier series: A Fourier series is an expansion of a periodic function into a sum of sines and cosines. It represents a