Question: On the interval [0, 3] the function f(t) is defined by f(t) = ( t 2 3 ) 2 + 4 9 1) Sketch the

On the interval [0, 3] the function f(t) is defined by f(t) =(t23)2+49

1) Sketch the odd extension of this function over the interval [6, 6]

2) Sketch the even extension of this function over the interval [6, 6]

3) From the graph above, provide an estimate of the value of the coefficient a0 of the cosine series of f(t).

4) Does the sine series or the cosine series converge faster? Provide brief justification for your answer

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