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暢享聊：高數（上）重要知識點
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Enjoy chatting: Advanced Mathematics (Part I) Important Knowledge Points
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收斂函數的性質
1.如果一個數列收斂那麼它的極限就唯一。
2.如果一個數列收斂那麼它一定有界。
3.如果limxn（n趨向於無窮）=a，且a＞0（或a＜0），那麼就有個正整數N使得當n＞N時有xn＞0（或xn小於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).
等價無窮小，顧名思義，兩個無窮小是等價的，兩個無窮小之比為1。
Equivalent infinitesimals, as the name implies, two infinitesimals are equivalent, and the ratio of the two infinitesimals is 1.
函數的連續性，判斷一個函數在一個點處是否連續時我們可以通過判斷該點的左右極限是否相等判斷。若左右極限相等，那麼連續，否則不連續。
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.
函數的間斷點，大致分為兩類，若左右極限都存在，就是第一類間斷點，否則為第二類間斷點。第一類間斷點包括可去間斷點和跳躍間斷點。第二類間斷點包括無窮間斷點和震盪間斷點。
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.
導數公式：
Derivative formula:
兩個重要極限，記住這兩個公式，可以使我們更快速地算出一些極限。
Two important limits, remember these two formulas, we can calculate some limits more quickly.
羅爾中值定理，函數滿足在閉區間上連續，開區間上可導，且兩端相等，則至少存在一個點和兩端相等。
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.
反常積分是指含無窮上限或下限，或者被積函數很有瑕點的積分。
Abnormal integral refers to an integral with an infinite upper or lower limit, or the integrand has very defective points.
分部積分法：
Partial integration method:
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參考資料：高等教育出版社 高等數學第七版上同濟大學數學系
翻譯來源：百度翻譯
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