Each chapter is essentially a limit, expressed in the form of a function, so it also has the nature of a function. The nature of function is manifested in various aspects. First of all, it is summarized as follows: the sign preservation of limit is very important, that is to say, in a certain interval, the positive and negative functions are consistent with the limit. 1 limit is divided into general limit and sequence limit, which is one of the general limits. The way to find the limit is as follows: (I have listed everything I can! ! ! ! ! Do you have anything to add? ) 1 is equivalent to infinitesimal transformation, (it can only be used in multiplication and division, but it doesn't mean that it can't be used in addition and subtraction, but it just proves that the limit still exists after splitting). The x power of e-1 or the a power of (1+x)-1 is equivalent to Ax and so on. Memorize it all (when x approaches infinity, it will become infinitesimal) 2. Write other rules (big topics sometimes imply that you want to use this method). First of all, there are strict preconditions for its use! ! ! ! ! ! It must be x close, not n close! ! ! ! ! ! ! Therefore, when facing the limit of a series, we must first convert it into the limit in the case of seeking X approximation. Of course, N approximation is only a case of X approximation, and it is a necessary condition. (one more thing, of course, the limit n of the sequence is approaching positive infinity, and it can't be negative infinity! ) must be the derivative of the function to exist! ! ! ! ! ! ! ! (If I tell you g(x), but I don't tell you whether it is differentiable, it will undoubtedly be directly used to die! ! ) must be 0 to 0, infinity to infinity! ! ! ! ! ! ! ! ! Of course, it should also be noted that the denominator cannot be zero. His law is divided into three cases: 1 0 to 0. When the ratio of infinity to infinity is infinite, we can directly multiply infinity by 2 0 and subtract infinity (which should be the reciprocal relationship between infinity and infinitesimal), so infinity is written as the reciprocal form of infinitesimal. After the general term, it can be changed into the form of 1, which is the 0 th power of 3 0 and the infinite power of 1. The method of (exponential power) equation is mainly to take exponent and logarithm, so that the power function moves down and is written in the form of 0 and infinity. (This is why there are only three forms. When the two ends of LNx approach infinity, its power moves down and approaches 0. When his power moves down and approaches infinity, LNX approaches 0. 3 Taylor formula (especially when it contains the x power of e, especially when it contains the addition and subtraction of positive co-operation, pay special attention! ! ! ! ) E's X expansion Sina expansion cos expansion ln 1+x expansion is very helpful to simplify the topic. The solution of infinite form is greater than infinity. Take the big head principle and divide the numerator and denominator by the largest term! ! ! ! ! ! ! ! ! ! ! It looks complicated and easy to handle! ! ! ! ! ! ! ! ! ! 5 treatment method of infinitely less than bounded function When facing complex variable function, especially when the complex variable function which is positive coincidence is multiplied with other functions, we must pay attention to this method. Faced with a very complex function, you may only need to know its scope, and the result will come out! ! ! 6 pinch theorem (mainly dealing with the limit of sequence! ) This is mainly because the function in the limit is in the form of equation division, scaling and expansion. 7 The application of arithmetic progression formula of equal proportion (dealing with the limit of series) (the sign that the absolute value of q is less than 1) 8 items are divided and added (eliminating the majority in the middle) (dealing with the limit of series). The simplified function 9 can be divided by the undetermined coefficient method to find the left and right limit (dealing with the limit of series). For example, given the relationship between Xn and Xn+ 1, there exists the limit of Xn, then the limit of xn is the same as that of Xn+ 1, and it should be an application in which the limit is removed and the limit value remains unchanged. These two are very important! ! ! ! ! For the first one, it is the ratio of sinx to x when x approaches 0. If x approaches infinity, the infinitesimal has a corresponding form (the second place is actually an infinite form for the function 1) (when the cardinality is 1, two important limits may be paid special attention to) 1 1. There is another way, which is very convenient. Different functions approach infinity at different speeds! ! ! ! ! ! ! ! ! ! ! ! ! ! ! The x power of x is faster than x! Faster than exponential function, faster than exponential function, faster than logarithmic function (you can also see the drawing speed)! ! ! ! ! ! When x approaches infinity, the limit of their ratio becomes clear at a glance. 12 method of substitution is a skill. A topic not only needs to change elements, but also will be mixed with 13. If you want to calculate, four algorithms are also a method. Of course, there is also a method to deal with the limit of series, which can be considered when you are really cornered by the topic. Generally from 0 to 1. The monotonic bounded property of 15 is used to prove monotonicity when dealing with recursive sequences! ! ! ! ! ! 16 directly use the definition of derivative to find the limit. (Generally, when X approaches 0, f(x plus or minus a value) is added or subtracted on the molecule, so pay special attention when you see it. When the topic tells you that F(0)=0 and F(0) derivative =0 implies that you must use the derivative definition! ! ! ! ) If you do more exercises in this math class, you will definitely get results. You can buy a reference answer book if you can't do the problem. If you are skilled, you can do it.

Hope to adopt