How to evaluate A Taylor series at a specific value

08272018, 04:15 PM
Post: #36




RE: How to evaluate A Taylor series at a specific value
(08272018 02:33 PM)Wes Loewer Wrote: I see the difficulty in determining whether the x=0.5 should be evaluated before or after. It seems evaluation order is context based. This is my guess ... Differentiation had the dx, notifying the ∂(...) what to differentiate against. Variable x thus off limit for where substitution, until expression differentiated. In other words, where substitution is delayed. (same for integration) Regular expressions, there is no need to delay where replacement. We can think of where as running code with argument x, like parisse described earlier: f(x)x=a => (lambda x: f(x))(x=a) => f(a) taylor(sin(x))x=0.5, however, is inconsistent with above logic. It should be treated like ∂(...), since it had an off limit x, to "taylor" against. Perhaps implied x does not count ? What is the result of taylor(sin(x), x=0, 5)x=0.5 ? 

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