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Taylor series


Taylor series

I have an exercise in a class where I have to perform a Taylor expansion.

I have read in the "help section" that the "series" keyword is able to perform this action. I have managed to do the expansion by hand an gotten the correct result, but as there is a keyword for being able to do this I would very much like some help figuring out how to do it, since it would be very help should it show up during the exam. I have tried to write it all kinds of different ways but with no result or the result being "0".
I inserted an image of the exercise below.Exercsie.png

One of the things that really boggles my mind is that fact that there is an x1 and x2, and not knowing how to handle those as all the examples I have found only have 1 variable. 


I really hope that someone is more experienced with this keyword than me, and is able to help.


I don't think that the series expansion can be done using a genuine vector x as function argument.

But you may do it using scalar arguments with literal indices:


f is showing in blue, the approximation g in red.


BTW, if you use real Mathcad (current: version 15) you find the information you need in the Quicksheet "Symbolic Calculus".

If you use Prime, the help is much more limited and cumbersome - I am not sure if you can find the information there. I attach a screenshot of the Mathcad help.


You can define the function using a vector argument and vector indices, but when it comes to the series expansion, you must (unfortunately) use literal subscripts.


In case you are voluntarily using Prime, here is the sheet in P5 format attached.


23-Emerald II

This is what I get in Mathcad 11: