[Maxima] Learning that limit is 0 from above

Barton Willis willisb at unk.edu
Thu Nov 1 05:46:18 CDT 2007

-----maxima-bounces at math.utexas.edu wrote: -----

>Thanks, Barton. I did not know Taylor series at infinity, although I
>do know Taylor series at finite points. Could you please tell me where
>I can learn about Taylor series at infinity?

Compare (%o3) to (%o4):

  (%i1) f(x) := sqrt(1+x^2) - x$

  (%i2) taylor(f(x),x,inf,5);
  (%o2) 1/(2*x)-1/(8*x^3)+1/(16*x^5)+...

  (%i3) taylor(f(1/x),x,0,5);
  (%o3) x/2-x^3/8+x^5/16+...

  (%i4) subst(1/x,x,%);
  (%o4) 1/(2*x)-1/(8*x^3)+1/(16*x^5)


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