Limit can be divided into sequence limit and function limit, which are defined as follows.

Firstly, Liu Hui's Secant Circle is introduced. There is a circle with a radius of 1, and its area should be calculated when only the calculation method of straight side area is known. Therefore, he first inscribed a regular hexagon with an area of A 1, then inscribed a regular dodecagon with an area of A2 and an inscribed quadrilateral with an area of A3, thus doubling the number of sides. When n increases infinitely, An is infinitely close to the area of a circle, and he uses the inequality An+65438 to calculate the ninth power polygon of 3072=6*2. A & LTAN+2 [(an+1)-an] (n =1,2,3) ...) gets pi =3927/ 1250, which is about 3.14/kloc-.

Sequence limit: Let it be a sequence. If there is a constant a, when n increases infinitely, an approaches (approaches) A infinitely, which is called sequence convergence, and A is called sequence limit, or it is called sequence convergence to A, and it is recorded as Li Man = A. Or: an→a, when n→∞.

Properties of sequence limit

1. (Uniqueness) If the limit of the sequence exists, the limit value is unique;

2. Change the finite term of series without changing the limit of series.

Function limit: Let f be a function defined on [a, +∞) and A be a definite number. If given ε >; 0, with a positive number m (> =a), so when x>m has:

| f(x)-A | & lt； ε,

Then let's say that the function F takes A as the limit when X tends to +∞, and it is recorded as

Lim f(x) = A or f(x)→A(x→+∞)

Popular definition of function limit;

1, let the function y=f(x) be defined in (a,+∞). If the function f(x) infinitely approaches a definite constant a when x →+∞, then a is called the limit of the function f(x) when x tends to +∞. Write lim f (x) = a, x →+∞.

2. Let the function y=f(x) be defined near point A. When x approaches a infinitely (denoted as x→a), the value of the function approaches a constant infinitely, then A is called the limit of the function f(x) when x approaches a infinitely. Write lim f(x)=A, x → a.

In advanced mathematics, there are two important limits:

1、lim sin(x)/x = 1，x→0

2.lim (1+ 1/x) x = e, x→0 (e≈2.7 1828 18, irrational number).

Limit algorithm (or related formula):

lim(f(x)+g(x))=limf(x)+limg(x)

lim(f(x)-g(x))=limf(x)-limg(x)

lim(f(x)*g(x))=limf(x)*limg(x)

Lim (f (x)/g (x)) = LIMF (x)/LIMG (x) (LIMG (x) is not equal to 0).

lim(f(x))^n=(limf(x))^n

Only when the above limf(x) limg(x) exists can it be established.

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