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#2624 Erroneous limit result

None
closed
Dan Gildea
None
5
2013-09-15
2013-08-25
Travis Cross
No

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!

Discussion

  • Travis Cross
    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
    Dan Gildea
    2013-09-15

    • status: open --> closed
    • assigned_to: Dan Gildea