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limit of sqrt(0)

Posted on 2008-09-01 03:34 By alla (Maple Rating 2 90)
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Maple says that the limit of sqrt(x), as x goes to 0, is 0, but Edwards of Larson et al. says that it isn't because "f(x) = sqrt(x) is not defined on an open interval containing 0 because the domain of f is x > = 0." 

 Comments?
 

Alla

Comments

Axel Vogt's picture

Maple is right

Comment on 2008-09-01 04:37 from Axel Vogt (Maple Rating 4 955)

do not know Edwards & Larson, but Maple is right - may be they have it only for positive Reals, while Maple knows sqrt(-1), since it works over the Complex numbers regarding brunch cuts

real bidirectional limit

Comment on 2008-09-01 11:46 from jakubi (Maple Rating 4 925)

?limits states:

limit(f, x=a, dir)
...
If dir is not specified, the limit is the real bidirectional limit,...

But this is the same issue of this past thread.

 

Robert Israel's picture

real bidirectional limit

Comment on 2008-09-02 21:26 from Robert Israel (Maple Rating 4 1467)

Just to clarify: what that "real" means is not that f is real, it is that x is real.  So for example

> limit(exp(-1/x^2), x=0);

0

(even though the limit as x -> 0 in the complex plane would not exist).

 

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