Taylor's Theorem


To apply Taylor's theorem to get an approximation of nth order with n+1
th degree remainder, is it enough for the function to have n+1 th
degree derivative on an interval (containing the reference point), or
does it require that the n+1 th degree derivative be continuous on that
interval?

Also, for multivariable calculus, does anyone have a reference to the
most accurate and most general form of Taylor's theorem?

.

Relevant Pages

  • Re: Taylors Theorem
    ... To apply Taylor's theorem to get an approximation of nth order with n+1 ... th degree remainder, is it enough for the function to have n+1 th ... of course implies that the first n derivatives exist in some ... Also, for multivariable calculus, does anyone have a reference to the ...
    (sci.math)
  • Re: geography math?
    ... >>>I found this for calculating distance from 2 points given geographical ... >>I don't know what your reference is. ... >>But for higher precision you need an ellipsoidal approximation. ... When using an ellipsoidal model of the earth, ...
    (comp.lang.tcl)
  • Re: Circular motion in SR
    ... saying does not substantially change the value of what you are saying ... if the remainder is just as bad? ... preferred-frame reference to redefine all your lengths for you, ...     But after a few trial and error corrections, ...
    (sci.physics.relativity)
  • Re: Circular motion in SR
    ... saying does not substantially change the value of what you are saying ... if the remainder is just as bad? ... proof of a distance contraction that I could not disprove with the ... preferred-frame reference to redefine all your lengths for you, ...
    (sci.physics.relativity)
  • Re: Calculate the Circumference of an ellipse
    ... Hi J. Maybe we can expand your excellent reference to a Custom function. ... Here, we factor out a common expression, and add in the 2 Pi to get the Perimeter. ... I would say that's as good an approximation as it gets. ... gives me results shown on that same Wiki page for the various values of b with a value of 10000 for the major semi-axis value. ...
    (microsoft.public.excel.misc)