Which part of the proof do you get hung up on?
I'm trying to understand the proof found here:
Calculus 9th edition, chapter 9, section 7, exercise 71
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The theorem is:
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If is an even function, then it's nth Maclaurin polynomial contains only terms with even powers of x.
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I don't understand why the coefficients of the terms are zero for the odd derivatives.
Take a MacLaurin series:
If you take the first derivative of this, you're going to make the constant term disappear, and you'll get
If the is not zero, then in general, you can't have be an odd function (which it must be, since it is the derivative of an even function). Get the idea?