18.03.2011 12:49, Hector пишет:
Now mathematically, limit x tending to 0, abs(x)/x should not exist.
Why not? (tendind from the right.)
Consider definition of limit:
"the limit of f as x approaches 0 is L if and only if for every real ε >
0 there exists a real δ > 0 such that 0 < x < δ implies | f(x) − L | < ε"
Yes, abs(x)/x at point 0 is not well defined, but the limit with this
definition still exists.
The same with sin(x)/x (but in this case there is question whether this
function analytical or not, abs(x)/x is not).
--
Alexey U.
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