What's the meaning of the beautiful word "Sheng"

The word "Sheng" means "complete"
Beautiful: describe a lot of beautiful things, can't see over, too late to appreciate
Group words: countless
Innumerable: there are a lot of people visiting the lantern on the 15th of the first month

Let a primitive function of F (x) be e ^ - SiNx, then ∫ XF '(x) DX =?
I know ∫ f (x) DX = e ^ - SiNx
But I don't understand what happened in the back

A primitive function of F (x) is e ^ - SiNx
f（x）=e^-cosx+C
Integral by parts, let a = x, B = f (x)
∫xf'（x）dx
=xf(x)-∫ f(x)dx
=x(e^-cosx)-e^-sinx+C
=(x-1)e^-sinx-xcosx+C

What is the plural of duck?

ducks
Basic translation
n. A thin canvas overalls or trousers; a duck
v. To dodge; submerge
Network interpretation
Ducks: Canvas pants | thin canvas overalls | canvas clothes
Sitting ducks: fighting ducks, sitting ducks, beating ducks
Roasted ducks

The radish from the market is 1.52 tons more than the cabbage. After selling 0.2 tons of radish and 0.4 tons of cabbage, the weight ratio of cabbage and radish is 7:9. How many tons of radish were transported?

There are x tons of Chinese cabbage and 1.52 + X tons (x-0.4): (1.52 + x-0.2) (1.52 + x-0.2) = 7:9 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp& nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 2x=9.24+3.6， 2x=12.84， X = 6.42; radish: 1.52 + 6.42 = 7.94 (tons), a: 6.42 tons of cabbage and 7.94 tons of radish

How many double digits can be formed by taking any three digits from 1, 3, 5, 7 and 9 and any two digits from 2, 4, 6 and 8
There is a 0 in front of 2

I don't know how the computer presses that key, that is, C, a, etc

It is known that f (x) is an odd function on R. for X ∈ R, f (x + 4) = f (x) + F (2) holds. If f (1) = 2, then f (2011) is equal to ()
A. 2011B. 2C. -1D. -2

∵ for any x ∈ R, f (x + 4) = f (x) + F (2) holds ∵ f (- 2 + 4) = f (- 2) + F (2), that is, f (- 2) = 0, ∵ f (x) is an odd function on R, ∵ f (2) = - f (- 2) = 0, ∵ f (x + 4) = f (x), that is, f (x) is a function with period of 4, and f (1) = 2, ∵ f (2011) = f (4 × 503-1) = f (- 1) = - f (1) = - 2

There is a plate 8 cm away from the fulcrum, a packet of candy on the plate, and a 600 gram weight 10 cm away from the fulcrum. In this way, the balance is achieved. If the sugar packet is increased by half, the weight should be moved 3 cm to the left to balance. Find the weight of a plate and a packet of candy

Plate + candy = 600 * 10 / 8 = 750g
Plate + heavy candy = 600 × 13 / 8 = 975g
975-750 = 225 is the weight of half a packet of sugar, so a packet of sugar weighs 450g, and the plate weighs 750-450 = 300g

The properties of triangle center of gravity

1. The ratio of the distance from the center of gravity to the vertex and the distance from the center of gravity to the midpoint of the opposite side is 2:1
2. The area of the three triangles composed of the center of gravity and the three vertices of the triangle is equal
3. The minimum sum of the distances from the center of gravity to the three vertices of a triangle (equilateral triangle)
4. The point where the product of distances from the inside to the three sides of a triangle is the largest

Given that a, B, C > 0, prove that a ^ a times b ^ B times C ^ C is greater than or equal to (ABC) ^ [(a + B + C) / 3]

Because when x > 0,
(xlnx)"=1/x>0,
Then:
(alna+blnb+clnc)/(a+b+c)
≥ln[(a^2+b^2+c^2)/(a+b+c)],
Then:
a^a*b^b*c^c
≥[(a^2+b^2+c^2)/(a+b+c)]^(a+b+c)
≥[(a+b+c)/3]^(a+b+c)
≥(abc)^[(a+b+c)/3]
Take the equal sign if and only if a = b = C
That is to prove the original proposition

Calculus, definite integral and so on?

To sum up: derivative: refers to the independent variable at a certain point, the increment of the independent variable is the rate of change of an infinite short-time function, and its geometric meaning is the tangent slope of the function at that point

What's the meaning of the beautiful word "Sheng"