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)
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