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Question 1 - Consider the function f(t) defined on the interval 0 ≤ t < 1 by f (t) = t(1 - t).
(a) Sketch the graph of the odd extension fodd of f for -3 ≤ t ≤ 3, and hence state the fundamental period of the odd extension.
(b) Sketch the graph of the even extension feven of f for -3 ≤ t ≤ 3, and hence state the fundamental period of the even extension.
Question 2 - Consider the periodic function f(t) with fundamental interval -π ≤ t ≤ π that is defined by
-t-π for -π ≤ t < 0
f(t) =
t - π for 0 ≤ t < π,
f(t + 2π) = f(t).
(a) Sketch the graph of the function f for -3π ≤ t ≤ 3π, and hence state whether the function is even, odd, or neither even nor odd.
(b) Calculate the Fourier series for f(t).
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