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Dear you, this is the new LearningYard Academy.
Today, the editor brings you
the studious high number (seven): Review of Functions and Limits.
一、四则运算求极限
1、易错点
①无穷减去无穷不等于0
②1的无穷次方不等于1，要利用等价无穷小或者利用取对数求解
③使用等价无穷小时要注意x是需要趋近于0的
④等价无穷小代换要在乘积时才能替换
2、常见有界函数：三角函数
有界函数乘无穷小量等于0
3、运用夹逼定理求极限
One, four, calculate the limit
1. The error prone point
① Infinity minus infinity is not equal to 0
② The infinite power of 1 is not equal to 1. Use equivalent infinitesimal or take logarithm to solve it ③ When using equivalent infinity, note that x needs to approach 0
④ Equivalent infinitesimal substitution can only be replaced when multiplying
2. Common bounded functions: bounded trigonometric function multiplied by infinitesimal is equal to 0
3. Use the pinch theorem to find the limit
二、判断函数连续性
1、一般题目会给出分段函数，使函数连续就需要使间断点两侧极限相等。
2、易漏知识点：同阶无穷小、高阶无穷小等概念
Judge the continuity of function
1. The general problem will give a piecewise function. To make the function continuous, you need to make the limits on both sides of the breakpoint equal.
2. Leaky knowledge points: concepts such as infinitesimal of the same order and infinitesimal of higher order
三、判断间断点
1、做题步骤
①分析哪些是间断点（根据定义域判断）
②对相应点求极限
③根据极限情况判断间断点类型
2、易错点：在遇到a^x、e^x,arctanx,arccotx...这些函数时，需要讨论左右极限。对于分段函数也要讨论左右极限。
Judgment of breakpoints
1. Steps for doing the question:
① Analyze which breakpoints are (according to the definition domain)
② Calculate the limit of the corresponding points
③ Judge the type of breakpoints according to the limit situation
2. Mistakes: When encountering functions such as a ^ x, e ^ x, arctanx, arccotx, etc., you need to discuss the left and right limits. The left and right limits should also be discussed for piecewise functions.
四、零点、介值定理
1、函数f(x)在闭区间[a,b]上连续，并且f(a),f(b)一正一负，那么开区间(a,b)内至少有一个点使f(x)=0
2、例题
Zero point, intermediate value theorem
1. The function f (x) is continuous on the closed interval [a, b], and f (a), f (b) is positive and negative, then there is at least one point in the open interval (a, b) so that f (x)=0
五、判断渐近线
1、水平渐近线：y=a
铅直渐近线：x=b
斜渐近线：
Judge asymptote
1. Horizontal asymptote: y=a
Vertical asymptote: x=b
Oblique asymptote:
（还是希望大家多多练题，见识不一样的题型，练出手感！！！）
(I still hope you can practice more, see different types of questions, and practice your hand!!!)
END
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翻译：百度翻译参考：哔哩哔哩高数叔视频内容声明：本文由LearningYard新学苑原创，若有侵权请联系删除！
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