If SiNx is greater than or equal to - 1 / 2, what is the value range of X

If SiNx is greater than or equal to - 1 / 2, what is the value range of X

sinx>=-1/2 ,
Then 2K π - π / 6

When SiNx is greater than or equal to 0, what is the value range of X?

(2k π, π + 2K π) k is an integer

One third derivative of (1-x)?
The second floor is right

That is (- 3) power of (1-x)
So derivative = (- 3) [(1-x) (- 3-1) power] * (1-x) '
=The (- 4) power of 3 (1-x)
=The fourth power of 3 / (1-x)

If M-1 / 2 ＜ x ≤ m + 1 / 2 (where m is an integer), then M is called the integer nearest to the real number x, denoted as {x}, that is {x} = M
On this basis, the following propositions about the function f (x) = x - {x} are given, where the true proposition is
(1) The definition field of function y = f (x) is r, and the maximum value is 1 / 2
(2) Y = f (x) is an increasing function on [0,1]
(3) The function y = f (x) is periodic and the minimum positive period is 1
(4) The symmetry center of the image of the function y = f (x) is (0,0)

Let me have a try
1. True proposition;
The domain of definition is obviously R, then according to the problem, let x ≤ m + 1 / 2, {x} = m, then f (x) = x - {x} ≤ 1 / 2
2. False proposition;
Function f (x) = x, [0,1 / 2]
X-1, (1 / 2,1], so the function is not continuous in [0,1], it can not be directly said that it is an increasing function
3. True proposition
When Z-1 / 2

When x = - 2, the value of formula x (2-m) + 4 is 18, then when x = 3, the value of this formula is ()
A. -10B. -12C. -17D. 20

∵ when x = - 2, the value of the formula x (2-m) + 4 is 18, ∵ - 2 (2-m) + 4 = 18, the solution is m = 9, ∵ the algebraic formula is x (2-9) + 4, when x = 3, X (2-9) + 4 = - 7x + 4 = - 7 × 3 + 4 = - 17

When x = - 2, the value of formula (2-m) x + 4 is equal to 8. Try to find the value of this formula when x = 3

When x = - 2 is taken into (2-m) x + 4 = 8, M = 4 can be obtained
Then, when x = 3, (2-m) x + 4 = - 2

When x = - 2, the value of formula x (2-m) + 4 is equal to 18, then M=

When x = - 2, the value of formula x (2-m) + 4 is equal to 18
∴-2(2-m)+4=18
-4+2m+4=18
2m=18
m=9

What is the formula for the value of m with the value of Y three times that of X?
Solving the satisfaction equations
2X-Y-4M=0
In 14x-3y-20 = 0, the value of Y is the value of M which is three times the value of X

2x-y=4m
14x-3y=20
So x = (5-3m) / 2, y = 5-7m
5-7m=3*(5-3m)/2
So m = - 1
So x = 4, y = 12

Given 5ab-1b = 1A + 3, find the value of integers a and B

∵ the original formula can be changed into: (1 + 3a) (1 + 3b) = 16, ∵ B = 5 − a1 + 3a, ∵ there are three cases: when a = 1, B = 1; when a = - 3, B = - 1; when a = - 1, B = - 3

Given that a and B are nonnegative integers and satisfy | A-B | + AB = 1, all possible values of a and B are obtained

0≤|a-b|≤1
1.|a-b|=0
a=b
ab=1
a²=1
A = 1 or - 1
Namely
a=1,b=1
a=-1,b=-1
2.|a-b|=1
ab=0
a=0
|b|=1
b=±1
That is, a = 0, B = 1; a = 0, B = - 1
In the same way
b=0,a=1;b=0,a=-1
There are 6 cases