What is the invariance of differential forms?

What is the invariance of differential forms?

Let y = f (U), u = g (x). If u = g (x) is differentiable to x, and y = f (U) is differentiable to corresponding u, then y = f [g (x)] is differentiable to x, Dy = f [g (x)] 'DX = f' (U) g '(x) DX = f' (U) Du. We can know that dy = f '(U) Du remains unchanged no matter u is the differentiable function of independent variable or other independent variables. This is the form invariance of first order total differential

The sum of length and width of a rectangular vegetable field is 8 meters. How many meters is the perimeter of this rectangular vegetable field?

8 × 2 = 16 meters. A: the perimeter of this vegetable field is 16 meters

A cylinder has a side area of 12.56 square decimeters and a height of 4cm. What is its volume in cubic decimeters?

A cylinder has a side area of 12.56 square decimeters and a height of 4cm. What is its volume in cubic decimeters?
The bottom circumference is: 12.56 / 0.4 = 31.4 decimeters
The radius is: 31.4 / (2 * 3.14) = 5 decimeters
The volume is: 3.14 * 5 * 5 * 0.4 = 31.4 cubic decimeter

If the image of function y = a to the power of X-B + 1 (a > 0 and a is not equal to 1) passes through the second, third and fourth quadrants, there must be
Is the x power of a, minus B plus 1
A. 01 and b > 2
C.0

The answer is a!
Exclusion method, take special points, if a > 1, the image must pass the first quadrant! So exclude B, D
Then select a = 1 / 2, B = 1, you can find y > 0, that is, through the first quadrant, excluding C
The final choice is a!
Don't forget to verify a, that's right~

We need to learn how to use our brains and how to use our hands

We should not only learn to think, but also learn to do

There is a cylinder and a cone with the same base radius and height. The volume of the cylinder is 6 cubic decimeters, and that of the cone is 2 cubic decimeters______ ．

The volume of a cylinder with equal base and height is three times that of a cone, 6 △ 2 = 3

Use 4 7S to make 4 numbers. Add the operation symbol to make the result equal to 6

(7*7-7)/7=6

If x = 1, y = 1 is the equation of XY | ax + by-12 | + | ay BX + 1 | = 0, find the value of a and B,

Because x = 1, y = 1 is about the XY equation of x = 1, y = 1, because x = 1, y = 1 is about the XY equation | + ax + by-12 | + | ay-bx + 1 = 0, so a + A + B-12 | + B-12 | + B-12 | + and A-B + 1 | are all non negative numbers, so a + A + B-12 a + B-12 |a + B-12 = 0, and a-a-b + B + 1 A-B + A-B + 1 A-B + 1 = 0, then a + B-12 = 0, a + B-12 = 0, a + B-12 = 0, and a-b-b-b-12 = 0, and a-b-b + B + B-12 + B-12 = 5

Let f (x) = ax square + BX + 1 (a, B are real numbers) f (x) = {f (x), x > 0 - f (x), x0, N0, a > 0, f (x) be even functions, and prove f (m) + F (n) > 0

(1) When x > 0, f (x) = f (x) = ax & sup2; + BX + 1, ｜ f (1) = a + B + 1 = 4, that is, a + B = 3;
When x0, N0
F (x) is even function, B = 0
When x > 0, f (x) = x & sup2; + 1, when x0

Given that a four digit ABCD is 9 times DCBA, find the four digit

If the product of 4-digit ABCD and 9 is 4-digit DCBA, then 0 < a < 2, a = 1, then d = 9, B × 9 has no carry, so B = 0 or 1. ① if B = 0, then 10c9, verified C = 8, ② if B = 1, then c ≥ 9, does not hold, so this 4-digit is 1089