有關極限存在的問題

lim x->0+ f(x) = lim x->0+ 1/(x^2) = + infinity
故lim x趨向0 f(x) 不存在


001答者認為 "趨向無限"等同"有極限" 是絕對錯誤的
任何lim(x-->a) f(x) = infinity(無限) 即其極限不存在 (limit doesn't exist)

lim x->0+ f(x) = lim x->0+ 1/(x^2) = + infinity
lim x->0- f(x) = lim x->0- 1/(x^2) = + infinity
As lim x->0+ f(x) = lim x->0- f(x),so lim x->0 f(x) exists


2012-05-24 11:40:51 補充：
Acutally,both are correct.
From the graph,we know that lim x->0 tends to infinity as x tends to 0.
As the left hand limit = right hand limit,by definition,limit of f(x) exists as x approaches 0
On the other hand,infinity is not a real number.
So,it is also correct if we say that limit doesn't exist.

2012-05-24 11:41:00 補充：
Most of the properties of limits assume that limits to have a finite value.
So it is better to include finiteness as one of the conditions
However,it is meaningless to argue that whether a limit equals to infinity or does not exist.