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of X for any X this tells you a lot
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of X for any X this tells you a lot
about the function sine of X but not
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about the function sine of X but not
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about the function sine of X but not
everything at all for example from this
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everything at all for example from this
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everything at all for example from this
formula it's very hard to see that the
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formula it's very hard to see that the
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formula it's very hard to see that the
sine of X is periodic not obvious at all
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sine of X is periodic not obvious at all
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sine of X is periodic not obvious at all
somewhere hidden away and this
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somewhere hidden away and this
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somewhere hidden away and this
expression is the number pi the half the
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expression is the number pi the half the
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expression is the number pi the half the
period but that's not clear from the
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period but that's not clear from the
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period but that's not clear from the
power series at all
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power series at all
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power series at all
so the power series are very good for
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so the power series are very good for
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so the power series are very good for
some things but they hide other
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some things but they hide other
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some things but they hide other
properties of functions
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properties of functions
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properties of functions
well so I want to spend a few minutes
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well so I want to spend a few minutes
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