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series) or an expression of the form ‘variable = value’ indicating the point
of expansion of a Taylor series, and the order of the series to be produced.
Function SERIES returns two output items: a list with four items, and an
expression for h = x - a, if the second argument in the function call is ‘x=a’,
i.e., an expression for the increment h. The list returned as the first output
object includes the following items:
1. Bi-directional limit of the function at point of expansion, i.e.,
2. An equivalent value of the function near x = a
3. Expression for the Taylor polynomial
4. Order of the residual or remainder
Because of the relatively large amount of output, this function is easier to
handle in RPN mode. For example, the following screen shots show the
RPN stack before and after using the TAYLR function, as illustrated above:
The keystrokes that generate this particular example are:
~!s`!ì2/-
S~!s`6!Ö˜$OK$ ˜˜˜˜$OK$
Reference
Additional definitions and applications of calculus operations are
presented in Chapter 13 in the calculator’s user’s guide.
)(lim xf
ax→
SG49A.book Page 6 Friday, September 16, 2005 1:31 PM