1. Limits of multivariate functions
1. Prove the limit of a multivariate function
|. In order to distinguish the limit of the unary function, we call the limit of the two-variable function the double limit. Three yuan and above, and so on.
2. Necessary conditions for extreme values
The function z has a partial derivative at x0, y0, and the extreme value is obtained at the change point, then there is fx (x0, y0) = 0, fy (x0, y0) = 0.
3. Sufficient condition for extreme value
Let the function z be continuous in a certain neighborhood of the point (x0, y0), and have a first-order and second-order reciprocal, and fx(x0,y0)=0, fy(x0,y0)=0;
令fxx(x0,y0)=A,fxy(x0,y0)=B,fyy(x0,y0)=C,
Then when AC-B*B>0, there is an extreme value, when A<0, there is a maximum value, and vice versa
When AC-B*B<0, there is no extreme value,
When AC-B*B=0, it needs to be discussed.
4. Conditional extrema
1. Clearly there are several conditions
2. Multiply the condition by the parameter
3. Link with L (unknown quantity);
4. Simultaneous equation solving