1, applicable conditions:

When a straight line passes through the focus, there must be ecosA=(x- 1)/(x+ 1), where a is the included angle between the straight line and the focus axis, which is an acute angle. X is the separation ratio and must be greater than 1. Note: The above formula is applicable to all conic curves. If the focus is internally divided (meaning that the focus is on the cutting line segment), use this formula; If it is divided (focusing on the extension line of the section), the right side is (x+ 1)/(x- 1), and the rest remains unchanged.

2, the periodicity of the function (memory 3):

If f(x)=-f(x+k), then t = 2k If f(x)=m/(x+k)(m is not 0), then t = 2k3. If f(x)=f(x+k)+f(x-k), then T=6k. Note: A. Periodic function, the period must be infinite B. Periodic function can have no minimum period, such as constant function. C. periodic function plus periodic function is not necessarily a periodic function, for example, y=sinxy=sin pie x is not a periodic function.

3. The symmetry problem (a problem that countless people can't understand) can be summarized as follows: 1, if it is satisfied on r (the same below):

F(a+x)=f(b-x) holds, and the symmetry axis is x = (a+b)/2; 2. Images with functions y=f(atx) and y=f(b-x) are symmetrical about x=(b-a)/2. If f(a+x)+f(a-x)=2b, the image of f(x) is symmetrical about (a, b).

4. Functional parity:

For odd function belonging to R, there is f (0) = 0; 2. For parametric functions, odd function has no even power term, and even functions have no odd power term. Parity has little effect and is generally used to fill in the blanks.

5, the explosion intensity sequence law:

Arithmetic progression middle: s odd = middle, such as s13 =13a7 (13 and 7 are the lower corners); 2 In arithmetic progression, S(n), s(2n)-s(n) and s(3n)-S(2n) are equal. In geometric series, when the common ratio is not negative, the above two terms are equal. When q= 1, Equation 4, explosion intensity of geometric series may not hold:: s (n+m