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

Yes. If the Maclaurin expansion of a function locally converges to the function, then you know the function is smooth. In addition, if the residual of the Maclaurin expansion converges to 0, the function is analytic.


Can properties of a function be discovered from its Maclaurin series Give examples.?

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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Can every function be expanded in fouriers series?

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