Higher numbers for postgraduate entrance examination - using monotone bounded criterion to prove the existence of sequence limit Let a > 0, X1 = root sign (2 + a), xn + 1 = root sign (2 + XM) prove the existence of LIM n - > infinite xn and find its value

Higher numbers for postgraduate entrance examination - using monotone bounded criterion to prove the existence of sequence limit Let a > 0, X1 = root sign (2 + a), xn + 1 = root sign (2 + XM) prove the existence of LIM n - > infinite xn and find its value

1. A "2x1 = √ (2 + a)" 2x (n + 1) = √ (2 + xn); √ (2 + 2) = 2xn has upper bound, 2x2 = √ (2 + x1) = √ (2 + √ (2 + a)); √ (2 + a) = X1X (n + 1) = √ (2 + xn); (2 + XN-1) = xn xn single increase 2. A > 2x1 = √ (2 + a) > 2x (n + 1) = √ (2 + xn) > √ (2 + 2) = 2xn has lower bound, 2x2 = √ (2 + x1) = √ (2 + √

X + y = 2, xy = 7, find x square, y + XY square

X²Y+XY²
=XY（X+Y）
=7×2
=14

Given that | x | = 4, | y | = 1 / 2, and XY is less than 0, then the value of X / y is

When x = 4, due to XY

Solve inequality: (3x + 1) square - (2x-1) square ＞ (x-1) (x-1) (5x + 2) - 24,
Solving inequality: (3x + 1) square - (2x-1) square ＞ (x-1) (x-1) (5x + 2) - 24. Mathematics (multiplication and division of integral and factorization)

（3x+1-2x+1)(3x+1+2x-1）＞（x2-2x+1）（5x+2)-24
5x (x+2)＞5x3+2x2-10x2-4x+5x+2-24
5x2+10x＞5x3-8x2+x-22
-5x3+8x2+5x2+10x-x+22＞0
5x3+13x2-9x-22＞0

A rectangular vegetable field, 110 meters long and 44 meters wide. Draw it on a 1; 2000 scale plan. How many centimeters should it be long and wide

Length = 110 / 2000 = 0.055m = 5.5cm
Width = 44 / 2000 = 0.022m = 2.2cm

Fantasy composition 400 words

When the night is quiet, I sit alone at the window and look up at the golden little stars. The sun is so bright and the moon is so perfect, but its spirit is lovely. I think: I can become a little star, flying freely in the Milky way, with the clear moon shining on the pedestrians at night, to guide the way forward; when I'm not happy, You can also hide in the screen like clouds, take the white clouds as my bedding, the curved moon as my easy chair, the twinkling stars, and my good companions. Let's sing, dance and play together!
I really become a little star, I want to get rid of human troubles, and my companions in space forever twinkle, with my brilliance shine on the world, do not let the dark in the universe, I want to let the fire of peace and happiness never go out

The sum of squares of three consecutive odd numbers is 251?
The teacher's solution is that if the odd number in the middle is n, then the other two odd numbers are n + 2 and n-2
Then the equation is: n ^ 2 + (n + 2) ^ 2 + (n-2) ^ 2 = 251
But isn't the way to represent continuous odd numbers like this: let the odd number in the middle be 2n + 1, and the other two be 2N-1, 2n + 3
Let the odd number in the middle be n, then the other two odd numbers are n + 2 and n-2 respectively. What's the reason?
Let the odd number in the middle be 2n + 1, and the other two be 2N-1, 2n + 3

The same thing
You set the middle as 2n + 1 and the other two as 2N-1 and 2n + 3
Look at the wordy, then set up
Let k = 2n + 1
The other two become K-2 and K + 2, the same thing

Cut the largest circle with a rectangular iron plate 3 meters long and 2 meters wide
(1) What's the area of the circle in square meters?
(2) What's the area of the rest in square meters
Who wants a formula?

The short side of the rectangle, that is, the diameter of the circle is 2, the radius is 1, the area of the circle is 3.14 m2, and the area of the remaining part is 6-3.14 = 2.86 m2

Explain 15 scientific phenomena in daily life

(1) Wearing glasses, from cold outdoor to warm indoor, glasses will be covered with white fog, which is the phenomenon of gas liquefaction
(2) When the water boils, the lid will be lifted. It is the gas that does the work on the lid
(3) Sitting in a fast car, when you turn, you will feel outward swing, which is centrifugal phenomenon
(4) The corner of long-term piling coal will turn black, which is the diffusion phenomenon of solid molecules
(5) Drilling wood can make fire, which is to do work to change internal energy
(6) You will feel warm when you lean on the heater. It's heat transfer
(7) Nail scissors, scissors, tweezers work principle, is the lever
(8) There is weightlessness in a pirate ship
(9) Incandescent lamp permanent, bulb wall will have a layer of black, is the sublimation of tungsten
(10) In daily life, people often encounter this phenomenon: when they take off their clothes and go to bed at night, they often hear crackling sound in the dark, accompanied by blue light. When they meet and shake hands, when their fingers just touch each other, they will suddenly feel a pricking pain of their fingertips; when they get up in the morning to comb their hair, their hair will often "float" up, the more disorderly they are, and they will "get an electric shock" when they pull the door handle or turn on the tap, Often issued "Pa, Pa" sound, this is the static electricity in the human body
(11) Salt water will not be frozen until 20-50 degrees below zero. The more salt, the lower the temperature
Vinegar freezes around minus 20 degrees
(12) The density of soup is higher than that of water, not oil,
(13) Add a small amount of dilute hydrochloric acid or sodium hydroxide solution to the water, which can make the conductivity of the water better
(14) add a few drops of cooking oil to a small amount of white vinegar, shake it up for a moment, then appear floc; if you add a small amount of detergent, shake it will appear a bubble.
(15) Take a glass bottle, put a dollar coin on the mouth of the glass bottle, cover the glass bottle with your hand and keep rubbing to get hot, you will see the coin will dance

The square of X - the square of Y - 2XY = 0
How to calculate the relationship between X and y?

x^2-y^2-2xy=0
x^2-2xy+y^2-2y^2=0
(x-y)^2-2y^2=0
(x-y+√2y)(x-y-√2y)=0
We get x = (- √ 2 + 1) y
Or x = (√ 2 + 1) y