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Cyclic Functions under Differentiation

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f(0)
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f'(0)
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f''(0)
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f'''(0)
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This Demonstration explores functions (such as sine and cosine) that are cyclic under differentiation with period four. Such a function is uniquely determined by its value and first three derivatives at a point. The thick curve is the cyclic function itself, and the dotted curves are the first four truncations of its Maclaurin series.
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