Given the function f (x) = 2x / x2 + 1, we prove that it is a decreasing function in [1, positive infinity]

Given the function f (x) = 2x / x2 + 1, we prove that it is a decreasing function in [1, positive infinity]

Given the function f (x) = 2x / x2 + 1, we prove that it is a decreasing function in [1, positive infinity]. We prove that: take any x2 & gt; X1 & gt; 1. X2-x1 & gt; 0, 1-x2x1 & lt; 0. F (x2) - F (x1) = [2x2 / (x2 ^ 2 + 1)] - [2x1 / (x1 ^ 2 + 1)] = {[2x2 (x1 ^ 2 + 1)] - 2x1 (x1 ^ 2 + 1)]} / [

A rectangular wooden box, 2 meters long, 52 meters wide, 82 cm high, the thickness of the box is 1 cm, do you know the volume of this wooden box?

1.98 x 51.98 x 0.8 = 82.33632m³

An unknown divided by five is four, divided by eight is three, divided by eleven is two

299

Given the first n terms of the sequence {an} and Sn = n (20-n), then when Anan + 1 < 0, n=______ ．

A1 = S1 = 20-1 = 19, an = sn-sn-1 = - 2n + 21, when n ≥ 2A1, it is also consistent with 〈 an = - 2n + 21anan + 1 = (- 2n + 21) (- 2n + 19) ＜ 0 〉 192 ＜ n ＜ 212 ∵ n ∈ n 〉 n = 10, so the answer is: 10

One by three plus three by five plus five by seven plus seven by nine Plus 97 times 1 / 99 equals (?)

One by three plus three by five plus five by seven plus seven by nine Add 97 by 1 / 99 equals (49 / 99) 1 by 1 / 3 plus 3 by 1 / 5 plus 5 by 1 / 7 plus 7 by 1 / 9 plus Add 97 times 1 / 99 = (1-1 / 3 + 1 / 3-1 / 5 + 1 / 5-1 / 7 + 1 / 7-1 / 9 +...) +1/97-1/99）/2=（1-1/99）...

Calculate | 5a-2b | * | 2b-5a|

75 = fraction 12 = fraction 36 = fraction 9 = fraction 4 + fraction 3 * fraction 20

75 = 12 / 16 = 27 / 36 = 9 / 12 = 4 + 3 / 20 * 6

It is known that 3x plus y equals 1, x minus 2Y equals M. if x is greater than y, the range of M is

Known
3x+y=1
x-2y=m
x>y
be
y=1-3x
x-2(1-3x)=7x-2=m
X = (M + 2) / 7 > y = 1-3 (M + 2) / 7
m+2>1-3m
m>-1/3

19+199+1999+.+199.99
300 9 processes to write out
Second question
198198+98198+8198+198+98+8
Write out the process
Both problems need simple operation

20-1+200-1+…… +200…… 00-1 300 1
=22…… 2220-300=22…… In front of 221920 is 301-4 = 297 2
200000-1000-2+100000-1000-2+10000-1000-2+200-2+100-2+10-2=310310-3000-12=

Proof: can the 53rd power of 33 - the 33rd power of 33 be divisible by 20?

The 53rd power of 33 - the 33rd power of 33
The 53rd power of 3 is the 53rd power of 3, the 53rd power of 33 - the 33rd power of 33, and the difference must be 0, divisible by 10;
33 to the 53rd power = (32 + 1) ^ 53, each term is k32 ^ I * 1 ^ J, that is, each term is a multiple of 32, divisible by 4
33 = (32 + 1) ^ 33, each term is k32 ^ I * 1 ^ J, that is, each term is a multiple of 32, divisible by 4
33 to the 53rd power - 33 to the 33rd power, divisible by 40, also divisible by 20