How to write a function in the form of an odd function and an even function Take F (x) = x + 1 / (2 + x) as an example,

How to write a function in the form of an odd function and an even function Take F (x) = x + 1 / (2 + x) as an example,

Let f (x) = f (x) + G (x) f (x) be an odd function, G (x) be an even function, f (x) = x + 1 / (2 + x) = f (x) + G (x) f (- x) = - x + 1 / (2-x) = f (- x) + G (- x) = - f (x) + G (x) f (x) = [f (x) - f (- x)] / 2 = x + X / (x ^ 2-4) g (x) = [f (x) + F (- x)] / 2 = - 2 / (x ^ 2-4)

Any function defined on a symmetric interval can be uniquely expressed as the sum of an even function and an odd function

Let f (x) = H (x) + G (x), where H (x) is an even function and G (x) is an odd function, then f (- x) = H (- x) + G (- x) = H (x) - G (x). From these two expressions, we can get H (x) = [f (x) + F (- x)] / 2, G (x) = [f (x) - f (- x)] / 2. Obviously, this solution satisfies the condition and is unique, that is, any function on a symmetric interval can be uniquely expressed as a

For rational numbers a and B, definition: a * b = 3a-2b, if x and y are rational numbers, try to calculate [(x + y) * (X-Y)] * 2x
For rational numbers a and B, definition: a * b = 3a-2b, if x and y are rational numbers, try to calculate [(x + y) * (X-Y)] * 2
x.

Analysis:
By definition:
（x+y）*（x-y）=3（x+y）-2（x-y）=3x+3y-2x+2y=x+5y
Then: [(x + y) * (X-Y)] * 2x
=(x+5y)*2x
=3(x+5y)-2(2x)
=3x+15y-4x
=-x+15y

The geometric meaning of double integral is as follows
Why?

The ruler with only three scale lines has a 9cm long ruler. Please determine the position of the three scale lines on the ruler so that the ruler with only three scale lines can measure all the whole centimeter line segments from 1 to 9cm. Please design at least three schemes on the ruler shown below

As shown in the figure, any one of the four methods can meet the requirements

The first person in the world to calculate pi to the seventh decimal place

The math book is about Zu Chongzhi. I think it should be him

The solution of the plane equation of the tetrahedron Volume 1 which is parallel to the known plane 2x-y + 2Z + 5 = 0 and formed by the coordinate plane

Plane 2x-y + 2Z + 5 = 0 sectional axis-2.5,5, - 2.5
In the sixth hexagram, the length ratio is 1:2:1
Let x, 2x, X
1/3*1/2*x*2x*x=1
x=3^(1/3)
Get intercept - 3 ^ (1 / 3), 2 * 3 ^ (1 / 3), - 3 ^ (1 / 3) or 3 ^ (1 / 3), - 2 * 3 ^ (1 / 3), 3 ^ (1 / 3)
The intercept equation of plane X / A + Y / B + Z / C = 1

Given that f (x) = 4 to the x power + 1 / 4 to the x power, find f (0.1) + F (0.2) +... + F (1)

The description of G (x) and K (x) is about the y-axis symmetry, so the ∑ (x = 0.1,1) f (x = 0.1,1) f (x = 0.1,1) f (x = 0.1,1) f (x = 0.1,1) f (x = 1.1,1) f (x = 0.1,1) f (x = 1.1,1) f (x) = 2 ∑ (x = 0.1,1,1,1,1) g (x) (4 ^ 1 / 10) and 4 ^ (3 / 10 / 10) 4 ^ (3 / 10 / 10) 4 (10 / 10 / 10) 4 (10 / 10 / 10) 4 (10 / 10) is the number of the series A1 = 4 (1 ^ (1 / 10) (A1 = 4 (1 / 10) (1 / 10) (1 / 10) (1 / 10) (1 / 10) (1 / 10), q = 4 (1 / 10) Sn = 4 (1 / 10) sn= - 6 * 4 ^ (1 / 10) / (1-4 ^ (1 / 10)) ≈ 46.35

Can a divide B?

B/A=C
A. If B and C are integers, then a can divide B
It can also be said that B is divisible by A

Given that the distances from one focus of an ellipse to the two ends of the long axis are 10 and 4 respectively, calculate the eccentricity

Let the ellipse be x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0)
According to the title, there are
a+c=10
a-c=4
The solution is a = 7, C = 3
So eccentricity e = C / a = 3 / 7