The phrase "miles per hour" is an example of a rate of change. What other commonly used rates of change can you think of in ever
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Assuming you want the cosine series expansion over an arbitrary symmetric interval ![[-L,L]](https://tex.z-dn.net/?f=%5B-L%2CL%5D)
, 
, the cosine series is given by
You have
Two successive rounds of integration by parts (I leave the details to you) gives an antiderivative of
and so
So the cosine series for
periodic over an interval is
You have
Two successive rounds of integration by parts (I leave the details to you) gives an antiderivative of
and so
So the cosine series for