How to draw the image of (L x L-1) & #178; + (l y L-1) & #178; = 4?

1.x>0,y>0
( l x l －1）²＋（ l y l －1）²＝4
Change to (x-1) ^ 2 + (Y-1) ^ 2 = 4, that is, the circle with (1,1) as the center and 2 as the radius is in the first quadrant
two
x>0,y

What is the linear equation obtained by rotating the line y = x 15 degrees counterclockwise around the origin

If the slope of the straight line y = x is k = 1, then the inclination angle α = arctan1 = 45 ° and α = 45 °
Rotate 15 ° counterclockwise around the origin, α '= 45 ° + 15 ° = 60 °
If the slope k '= tan60 ° = root sign 3, then the new linear equation is y = (root sign 3) X

Rotate the line y = 3x 90 degrees counter clockwise around the origin, and then translate it 1 unit to the right. The obtained line is?

Y = - X / 3 after rotation and y = - (x-1) / 3 after right translation

Double integral, triple integral, four kinds of surface curve integral: which of these six can bring the given field conditions into the integral formula
If you can, you'd better analyze it

This can't be summarized in such a general way. The equation of Z is used to calculate the area of curve and surface. From the bottom to the top, they are the upper and lower limits respectively. The main purpose of triple integral is to determine the upper and lower limits. Some questions of triple integral need to be taken to the given equation

The relationship between surface integral and double integral
What I understand is that surface integral is for volume, and double integral is for volume. What's the relationship between them?
What are the properties of surfaces?

When the surface is a part of the coordinate plane, the surface integral is a double integral
Surface integral is usually calculated by transforming it into double integral
When calculating the area of a surface with double integral, it is equivalent to the surface integral whose integrand is 1

Double integral and curved area of surface
The area of a surface can be obtained by double integral and surface integral of area. What's the difference between the two? In which case should we adopt which method?

If we give the function f (x, y) and the solution area, we will find the double integral; if we just let you find the area of a certain surface, we will find the first kind of surface area

What's the difference between surface integral and double integral

Let ∑ be a smooth surface and f (x, y, z) be bounded on ∑. Let ∑ be arbitrarily divided into n small surfaces Δ S. take any point (Xi, Yi, Zi) on each small surface Δ Si as the product f (Xi, Yi, Zi) ds, and sum ∑ f (Xi, Yi, Zi) ds. Note that λ = max (the diameter of Δ s). If the limit of F (Xi, Yi, Zi) ds exists when λ→ 0

What are the physical meanings of the first type of curve integral, the second type of curve integral, the first type of surface integral and the second type of surface integral,

The first kind of curve is the length of the curve, the second kind is the X, y coordinates. How to understand it? Tell you the linear density of a line, ask you the quality of the line, use the first kind. Tell you the path curve equation, tell you the force in X, y directions, work, use the second kind. The second kind of curve can also separate x, y, so it is not difficult to understand the product of the first and second kind of curve

What is the practical significance of curve integral and surface integral?
I have learned these two things, but I still can't fully understand their practical significance,

Question: what is the practical significance of curve integral and surface integral? Question: I have learned these two things, but I still can't fully understand their practical significance after learning them well. Which expert is the best to dial it? A: through curve integral, people can get the area surrounded by the curve through calculation

What's the meaning of the second kind of surface?

In the second type of curvilinear integral, the direction of the curve should be specified. In the second type of curvilinear integral to be discussed below, the normal direction of the surface should also be specified. Consider a smooth surface s, fix a point M0 on S, and introduce a normal at this point. There are two possible directions for the normal. We determine one of them, Draw a closed loop (closed curve) on the surface, which starts from point M0 and returns to M0. Assume that the closed loop does not cross the edge of the surface, make point m circle around the closed loop, and give a direction to the normal at each position it passes through. These directions are continuously transformed from the normal direction selected at the starting point M0, There must be one of the following two cases: let point m circle for one circle and then return to M0, the direction of the normal is either the same as or opposite to that determined at the time of departure. If the latter case occurs for a point M0 and a closed circuit passing through M0, the surface is said to be unilateral; the other case is said to be bilateral, that is, assuming that no matter what point M0 is, No matter how closed the curve passing through M0 without crossing the edge of the surface is, when it returns to the starting point M0, the direction of the normal is always the same as that initially determined. This kind of surface is called bilateral

How to draw the image of (L x L-1) & #178; + (l y L-1) & #178; = 4?