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course you could derive that expression
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course you could derive that expression
by using Taylor's formula by the same
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by using Taylor's formula by the same
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by using Taylor's formula by the same
kind of calculation we did here to
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kind of calculation we did here to
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kind of calculation we did here to
taking higher and higher derivatives of
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taking higher and higher derivatives of
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taking higher and higher derivatives of
the cosine you get the same periodic
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the cosine you get the same periodic
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the cosine you get the same periodic
pattern of derivatives and values of
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pattern of derivatives and values of
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pattern of derivatives and values of
derivatives at x equals zero
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derivatives at x equals zero
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derivatives at x equals zero
but here's a cleaner way to do it
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but here's a cleaner way to do it
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but here's a cleaner way to do it
simpler way to do it because we already
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simpler way to do it because we already
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simpler way to do it because we already
knew the derivative of the sine
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knew the derivative of the sine
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knew the derivative of the sine
when you differentiate you keep the same
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when you differentiate you keep the same
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when you differentiate you keep the same
radius of convergence
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okay so we can multiply we can different
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okay so we can multiply we can different
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