Current location - Training Enrollment Network - Mathematics courses - Math 0: 30
Math 0: 30
This is the written narration and oral expression of mathematical language.

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|