收敛和发散怎么判断收敛函数举例说明 _知识分享

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畅享聊;高数（上）重要知识点.mp31:52
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【收敛和发散怎么判断收敛函数举例说明】畅享聊：高数（上）重要知识点
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Enjoy chatting: Advanced Mathematics (Part I) Important Knowledge Points
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收敛函数的性质
1.如果一个数列收敛那么它的极限就唯一。
2.如果一个数列收敛那么它一定有界。
3.如果limxn（n趋向于无穷）=a，且a＞0（或a＜0），那么就有个正整数N使得当n＞N时有xn＞0（或xn小于0）。
Properties of Convergence Function
1. If a sequence converges, its limit is unique.
2. If a sequence converges, it must be bounded.
3. If limxn (n tends to infinity)=a, and a ＞ 0 (or a ＜ 0), then there is a positive integer N so that when n ＞ N, there is xn ＞ 0 (or xn is less than 0).
等价无穷小，顾名思义，两个无穷小是等价的，两个无穷小之比为1 。
Equivalent infinitesimals, as the name implies, two infinitesimals are equivalent, and the ratio of the two infinitesimals is 1.

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函数的连续性，判断一个函数在一个点处是否连续时我们可以通过判断该点的左右极限是否相等判断。若左右极限相等，那么连续，否则不连续。
The continuity of a function. When judging whether a function is continuous at a point, we can judge whether the left and right limits of the point are equal. If the left and right limits are equal, then it is continuous, otherwise it is discontinuous.
函数的间断点，大致分为两类，若左右极限都存在，就是第一类间断点，否则为第二类间断点。第一类间断点包括可去间断点和跳跃间断点。第二类间断点包括无穷间断点和震荡间断点。
Discontinuities of functions can be roughly divided into two types. If both the left and right limits exist, they are the first type of discontinuity, otherwise they are the second type of discontinuity. The first type of breakpoints includes removable breakpoints and jumping breakpoints. The second type of discontinuity includes infinite discontinuity and oscillatory discontinuity.
导数公式：
Derivative formula:

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两个重要极限，记住这两个公式，可以使我们更快速地算出一些极限。
Two important limits, remember these two formulas, we can calculate some limits more quickly.

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罗尔中值定理，函数满足在闭区间上连续，开区间上可导，且两端相等，则至少存在一个点和两端相等。
According to Rolle’s mean value theorem, if the function is continuous on the closed interval, derivable on the open interval, and both ends are equal, then there is at least one point and both ends are equal.
反常积分是指含无穷上限或下限，或者被积函数很有瑕点的积分。
Abnormal integral refers to an integral with an infinite upper or lower limit, or the integrand has very defective points.
分部积分法：
Partial integration method:

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收敛和发散怎么判断 收敛函数举例说明

收敛和发散怎么判断收敛函数举例说明