On Mon, 12 Mar 2007, Stavros Macrakis wrote:
> On 3/11/07, Andrey G. Grozin <A.G.Grozin at inp.nsk.su> wrote:
>> lim x^y
>>
>> does not exist when both x and y tend to 0 (and are positive). The limit
>> depends on the path along which (x,y) approaches (0,0). By choosing an
>> appropriate path, one can easily obtain any non-negative value for this
>> limit.
>
> I agree, Andrey, but isn't the value limited to [0,1]?
It can be >1, too, if y is allowed to be negative.
Suppose I want to get the limit equal to some c>0:
x^y = c => y = log(c)/log(x)
x -> +0, so log(x) -> -inf. If c<1, this path has y -> +0; if c>1, it has
y -> -0.
Andrey