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Best example is that an "odd" (or "even") function's Maclaurin series only has terms with odd (or even) powers. cos(x) and sin(x) are examples of odd and even functions with easy to calculate Maclaurin series.

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Q: Can properties of a function be discovered from its Maclaurin series Give examples.?
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What properties of a function can be discovered from its Maclaurin series?

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