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Share interests, spread happiness, grow insights, and leave a good life! Dear you, this is the new Academy of LearningYard. Today Xiaobian brings you the eagerness to learn high numbers (2): the operation of the limit
一、极限的运算法则
1、两个无穷小的和是无穷小，有限个无穷小的和是无穷小。
2、有界函数与无穷小的乘积是无穷小。
推论：常数*无穷小=无穷小
有限个无穷小的乘积是无穷小
3、当有限个极限进行加减乘除时，满足普通四则运算法则。
4、计算小技巧
（1）取主体部分
（2）代换
（3）利用无穷小与无穷大的关系
First, the algorithm of limits
1, the sum of two infinitesimals is infinitesimal, and the sum of finite infinitesimals is infinitesimal.
2. The product of a bounded function and an infinitesimal is infinitesimal. Corollary: Constant * infinitesimal = infinitesimal The product of finite infinitesimals is infinitesimal
3, and when the finite limit is added, subtracted, multiplied, and divided, the ordinary four algorithms are satisfied.
二、等价无穷小
1、分子与分母是若干因子的乘积，可对其中一个或几个因子做等价无穷小代换。（条件：求两个无穷小之比的极限）
1. The numerator and the denominator are the products of several factors, and one or more factors can be substituted for equivalent infinitesimals. (Condition: Find the limit of the ratio of two infinitesimals)
2、常用等价无穷小
三、初等函数的连续性
1、一切初等函数在其定义区间内都是连续的。
2、零点定理与介值定理
(1）零点定理：设函数f(x)在闭区间[a,b]上连续，且f(a)与f(b)异号（即f(a)*f(b)<0），则在开区间（a,b)内至少有一点c，使f(c)=0.
(2)介值定理：如果定义域为[a，b]的连续函数f，那么在区间内的某个点，它可以在f（a）和f（b）之间取任何值，也就是说，介值定理是在连续函数的一个区间内的函数值肯定介于最大值和最小值之间。
Third, the continuity of elementary functions
1.all elementary functions are continuous within their defined intervals.
2,.zero point theorem and medial theorem
(1) zero point theorem: let the function f(x) be continuous on the closed interval [a,b], and f(a) and f(b) different signs (that is, f(a) * f(b)<0), then at least one point c in the open interval (a, b), so that f(c) = 0.
(2) Medial theorem: If the defined field is [a,b], a continuous function f, then at a point in the interval, it can take any value between f(a) and f(b), that is, the mediation theorem is that the function value in an interval of a continuous function is definitely between the maximum and minimum values.
END
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