Greetings,
Given the function:
(%i1) f(x,n) := x-x*(1-1/x)^n; 1 n (%o1) f(x, n) := x - x (1 - -) x x
And some assumptions:
(%i2) declare(n,integer); (%o2) done (%i3) assume(n>2); (%o3) [n > 2]
Maxima calculates the following limits correctly:
(%i4) limit(f(x,n-1),x,inf); (%o4) n - 1 (%i5) limit(f(x,n+1),x,inf); (%o5) n + 1
However, strangely, Maxima gives an incorrect result for:
(%i6) limit(f(x,n),x,inf); (%o6) inf
We can choose a large value of x as a sanity test:
(%i7) float(f(2^64,42)); (%o7) 42.0
This was tested on a relatively recent build:
(%i8) build_info(); (%o8) Maxima version: "5.30.0" Maxima build date: "2013-08-07 17:48:50" Host type: "i686-pc-linux-gnu" Lisp implementation type: "GNU Common Lisp (GCL)" Lisp implementation version: "GCL 2.6.7"
Thanks!
Travis Cross
2013-08-25
The first part above should say:
(%i1) f(x,n) := x-x*(1-1/x)^n; 1 n (%o1) f(x, n) := x - x (1 - -) x
(An extra x ended up in the output above somehow.)
Dan Gildea
2013-09-15
Dan Gildea
2013-09-15