Lim f(x) = +∞ value
x→x .
When x tends to positive infinity and the limit of f(x) is equal to negative infinity, how to describe the extended data in mathematical language?
For any ε > 0, there is a positive integer x, so for any x >；; x，| f(x)+∞| & lt； ε is a constant. It is called limf(x)=-∞(x→∞).
Extended data
For example:
It is proved that the limit of lim(x→+∞)f(x) is unique, which is proved by the reduction to absurdity as follows.
Suppose that the function f(x) is not unique when x tends to positive infinity.
Let lim(x→+∞)f(x)=A and lim(x→+∞)f(x)=B and a ≠ b.
From lim(x→+∞)f(x)=A
For any ε > 0, there exists n 1 > 0, which is satisfied when x > n 1
|f(x)-A| 0, N2 > 0 exists, which is satisfied when x > N2.
|f(x)-B| n, you can definitely find N=max{N 1, N2}
|f(x)-A|+|f(x)-B|