Look for this session in /home/ceng303/maple/sessions as: ch1_10.mw

Session 1.10 Series Approximations

>taylor(tan(x),x,3); Taylor series of tan(x) around x. Maple assumes the center point to  be the origin.  The 3 in the arugument list gives the number of terms in the series.

series(x+O(x^3),x,3)

>taylor(tan(x),x,7);    Specifying the order of the first neglected term to be 7 gives two more terms in the series.

series(x+1/3*x^3+2/15*x^5+O(x^7),x,7)

>taylor(x/(x^2+3*x+2),x,5);    Another series centered at the origin.

series(1/2*x-3/4*x^2+7/8*x^3-15/16*x^4+O(x^5),x,5)

> taylor(x/(x^2+3*x+2),x=-1,5);

       Attempt to determine Taylor series around x=-1, but there is a pole there.

Error, does not have a taylor expansion, try series()

> series(x/(x^2+3*x+2),x=-1,5);

      The series is defined around x=-1.  The first term is the pole at -1.

series(-(x+1)^(-1)+2-2*(x+1)+2*(x+1)^2-2*(x+1)^3+O(x+1^4),x+1,4)

 

Defaults and problems with using the taylor and series functions

 

>taylor(sin(x),x); No order or point at the center specified.  Maple assumes a default value of 6 for the order and the origin as the center.

series(x-1/6*x^3+1/120*x^5+O(x^6),x,6)

>taylor(1/(1+x),x); Default order : 6

series(1-x+x^2-x^3+x^4-x^5+O(x^6),x,6)

>series(sin(x)); No variable specified as series variable

Error, wrong number (or type) of parameters in function series

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