On Thu, Aug 21, 2008 at 11:11 PM, William Stein <[EMAIL PROTECTED]> wrote:
>
> On Thu, Aug 21, 2008 at 8:09 AM, William Stein <[EMAIL PROTECTED]> wrote:
> > On Thu, Aug 21, 2008 at 4:44 AM, Andelf <[EMAIL PROTECTED]> wrote:
> >> I am a starter, so I don't understand why this goes wrong
> >>
> >> I typed:
> >>
> >> x = var('x')
> >> f = log(2+sqrt(arctan(x)*sin(1/x)))
> >> lim(f, x=0)
> >>
> >> and got:
> >> Traceback (click to the left for traceback)
> >> ...
> >> Is sin(1/x)*atan(x) positive or zero?
> >> actually I should get a log(2).
> >>
> >> who can help me explain it?
> >
> > Use the assume command, as illustrated below. You'll eventually get
> log(2):
> >
> > sage: x = var('x')
> > sage: f = log(2+sqrt(arctan(x)*sin(1/x)))
> > sage: lim(f, x=0)
> > Traceback (most recent call last):
> > ...
> > TypeError: Computation failed since Maxima requested additional
> > constraints (use assume):
> > Is sin(1/x)*atan(x) positive or zero?
> > sage: assume(sin(1/x)*atan(x) > 0)
> > sage: x = var('x')
> > sage: f = log(2+sqrt(arctan(x)*sin(1/x)))
> > sage: lim(f, x=0)
> > Traceback (most recent call last):
> > ...
> > TypeError: Computation failed since Maxima requested additional
> > constraints (use assume):
> > Is sin(1/x) positive or zero?
> > sage: assume(sin(1/x)>0)
> > sage: x = var('x')
> > sage: f = log(2+sqrt(arctan(x)*sin(1/x)))
> > sage: lim(f, x=0)
> > Traceback (most recent call last):
> > ...
> > TypeError: Computation failed since Maxima requested additional
> > constraints (use assume):
> > Is atan(x) positive or zero?
> > sage: assume(atan(x) > 0)
> > sage: x = var('x')
> > sage: f = log(2+sqrt(arctan(x)*sin(1/x)))
> > sage: lim(f, x=0)
> > log(2)
>
> By the way, you could also try sympy, but it fails to do this limit:
>
> sage: import sympy
> sage: x = sympy.var('x')
> sage: f = sympy.log(int(2) + sympy.sqrt(sympy.atan(x)*sympy.sin(int(1)/x)))
> sage: f.limit(x,0)
> WARNING: Output truncated!
> <html><a target='_new' href='/home/admin/274/cells/11/full_output.txt'
> class='file_link'>full_output.txt</a></html>
>
> The limit algorithm needs to calculate the series of
> series: sin(1/_w)**(1/2)*_w
> expansion variable (expanding around 0+): _w
> But the series expansion failed. Check that this series is meaningful and
> make
> it work, then run this again. If the series cannot be mathematically
> calculated, the bug is in the limit algorithm.
> The limit algorithm needs to calculate the series of
>
thank you all, :)
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