How to evaluate A Taylor series at a specific value

[Han]

(05-12-2018 02:56 PM)Joe Horn Wrote:  

(05-12-2018 02:44 PM)DrD Wrote:  (Variation on a theme):

taylor(sin(x))|x = 0.5

-Dale-

Hmmmm.... That seems to return sin(.5), not the desired result. Not sure why. Perhaps the x gets substituted right away, resulting in taylor(sin(.5))?

This is somewhat related to the original question. Computer software is not as adept at identifying the intended order of operations. While taylor(sin(x))|x = 0.5 seems "obvious" to most readers, one must ask (from the point of view of the software) when should substitution occur? Should it be after the evaluation of the taylor() command (or more generally, any command), or should it occur before the evaluation? Even extra parentheses would not help; think carefully as to why. To avoid such ambiguity, users should separate the operations into two separate steps.