18.03.2011 12:42, Chris Smith пишет:
Hector wrote:
On Fri, Mar 18, 2011 at 4:57 AM, Aaron S. Meurer
<[email protected]> wrote:
For issue 2200, we didn't decide if limit(sin(x), x, oo) should
raise an error or should return nan (or something else).
Hello everyone,
Hi Aaron, I was wondering why limit(sin(x),x,oo) should have any
other value
than 0 ?
Is it not equal to k/oo where k is some finite number in [-1,1],
which
clearly tends to zero ?
It is sin(x), not sin(x)/x that has the problem. This continues to oscillate
between `+/-1` regardless of how large x becomes.
According strict mathematical definition of limits at infinity limit in
this case is not exists.
But, the nature aim of "limit" is the answer what is the behavior of
function in infinity.
So the question is only to determine the way how to tell to the user
that sin(x) has arbitary value in range [-1, 1].
I offer split into steps of realization:
1. If limit is not exist then return Non or something else
It is requirement.
2. If it is possible to known range ([-1, 1]) as in the sin(x) at oo
example, then return it.
But it is enchantment.
--
Alexey U.
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