On 3/18/2014 1:35 PM, Axel Vogt wrote: pt. > > PS: big grin for limit cos(x) or sin(x) = interval. I consider > such as a smart answer by Maple, giving an interval as estimate, > indicating "system gives up for details" >
I suppose one can have a discussion on whether this is helpful or meaningful, or consistent with the notion of interval.
I tend to think of an interval [-1,1] to mean that the true result is a particular number v such that -1<=v<=1. In the limit example, the result is apparently saying that there is no such v. Rather the value as x->oo is bounded.
And then there are these problems.
we know that if lim f(x) = A and lim g(x) = B then lim f(x)*g(x) = AB
from these programs we learn that lim sin(x) = lim cos(x) = [-1,1] also of course lim sin(2*x) = [-1,1]. putting these results together with
sin(2*x) = 2*sin(x)*cos(x)
and take the limit as x->oo we learn that [-1,1] = 2*[-1,1]*[-1,1] = [-2,2].
Backtrack here and try to figure out what we did that went wrong.