What's the relationship between the opening of quadratic function and zero? Let's talk about it in detail

Opening has nothing to do with zero
Whether the opening is up or down, there can be zero points (1 or 2) or no zero points
The opening direction is only related to the sign of the quadratic coefficient A. if a > 0, the opening direction is upward and a > 0

How to judge the poles of complex function

In the complex variable function and integral transformation, how can the pole be calculated quickly and easily? Is there a simple way to calculate the residue? The experience in solving problems

Question 2: according to the type of singularity, the method of residue calculation is different
1. Removable singularity: according to the definition, the residue is 0
2. Pole:
(1) In general, according to the following theorem: let m be a series of poles, then
(2) If some functions are not easy to be solved directly according to 2 (1) theorem, they can be expanded into Laurent expansion according to the definition, and the coefficient of - 1 power term can be obtained
(3) If the sum of the residuals of a finite singular point or the residuals of some singular points are difficult to be solved directly, it can be transformed into solving the residuals of a function at infinity
3. Essential singularity: the above theorem 2 (1) can not be used, but the above 2 (2) method is generally used
4. Residue at nonsingular point: in the process of 2 (3), we often encounter the residue at nonsingular point, but the residue at nonsingular point is 0

Ask a limit question
When X - > 0, y = 0
So why is Lim Y / y '= 0 when X - > 0

First, there must be a precondition that y 'exists. Second, y' is not equal to 0 and must be a constant. If y '= 0, lobita's rule is OK

What's the relationship between the opening of quadratic function and zero? Let's talk about it in detail