![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
The graph of the function y = - 3x + 12 is drawn, and the solution set of inequality - 3x + 12 > 0 is obtained by using the image. (2) the solution set of inequality - 3x + 12 ≤ 0 is obtained
The image of the function y = - 3x + 12 is a straight line passing through points (0,12) and (4,0). As shown in Figure 1, the X axis divides the line into three parts: y is greater than 0, equal to 0 and less than 0. The corresponding value range of X corresponds to the three parts of x < 4, x = 4 and x > 4
Solving inequality 2 / 2 X-5 + 1 > x-3
Favor in the sun:
(x-5)/2+1>x-3
(x-5)/2>x-4
x-5>2(x-4)
x-5>2x-8
x-2x>-8+5
-x>-3
X
What is the solution set of the root sign 2 of the inequality cosx > 2?
cosx ＞ √2/2
2K π - π / 4 < x < 2K π + π / 4, where k ∈ Z
What is the solution set of the inequality cosx > root 2?
Then, Cos2 π
The solution set of inequality radical 2 / 2 ≤ cosx ≤ 1 / 2 is
-Radical 2 / 2 ≤ cos x ≤ 1 / 2
2K π + π / 3 ≤ x ≤ 2K π + 3 π / 4,2k π - 3 π / 4 ≤ x ≤ 2K π - π / 3, where k ∈ Z
Namely:
x∈【2kπ-3π/4,2kπ-π/3】,【2kπ+π/3 ,2kπ+3π/4】k∈Z
Is the solution set of inequality 1 / 2 ≤ cosx ≤ radical 3 / 2?
[2kπ-(π/3),2kπ-(π/6)]∪[2kπ+(π/6),2kπ+(π/3)]
If x ∈ [0,2 π), what is the solution set of inequality SiNx ≤ cosx?
sinx-cosx≤0
√2sin(x-π/4)≤0
-π/4≤x-π/4<7π/4
So - π / 4 ≤ X - π / 4 ≤ 0, π ≤ X - π / 4 < 7 π / 4
So 0 ≤ x ≤ π / 4,5 π / 4 ≤ x < 2 π
Given the functions SiNx and cosx, X ∈ (0360), find the solution set of inequality SiNx ≤ cosx
Understand the characteristics of SiNx and cosx
In the upper left part of the line y = x, SiNx > cosx
The lower right part of the line y = x is SiNx
Solving inequality SiNx > cosx How many solutions do you have?
Using the combination of number and shape
1. Draw a circle in the coordinate system, the radius of the circle is unit 1, and find the set of SiNx > cosx in the circle
2. Draw the images with function image method and find the set of SiNx > cosx
Solve the inequality group cosx ≤√ 3 / 2, cosx > SiNx
Consider 0 ≤ x first
RELATED INFORMATIONS
- 1. Solving inequality: 1 + SiNx + cosx ≠ 0
- 2. How to solve the inequality with absolute value? For example: | 1-3x | 4 problem solving process, as long as detailed steps, don't say a lot, I think we all understand a kind of problem do not understand, as long as you look at the problem-solving process can roughly understand it? So don't copy some theories to send up! At present, just read senior one, senior one solution priority, other night can!
- 3. What is the solution formula of quadratic inequality of one variable Isn't the result of two values? It doesn't become to understand the quadratic equation of one variable
- 4. What is the concept of inequality?
- 5. In the inequalities with unknowns, () is called inequality solution of inequality
- 6. Find the solution set of the inequality system 1.2x-75 3x-2≥4 3.1-2（1+y)-3/4 x≥5
- 7. After y = SiNx (2x + π / 4) image translation vector (π / 4,0), the function corresponding to the new image is y=
- 8. How to find tangent equation of curve at a certain point according to the geometric meaning of derivative
- 9. Exercises on extremum and derivative of function 1. Find the extremum of the following functions （2）y=48x-x^3 （3）y=6+12x-x^3 （4）y=5x+x^3 （5）y=x^2-7x+6 （6）y=x-x^3 5. It is known that f (x) = ax ^ 3 + BX ^ 2 + CX (a ≠ 0) has an extreme value when x = ± 1, and f (1) = - 1, (1) Try to find the values of constants a, B and C (2) Try to judge whether the function gets minimum or maximum when x = ± 1, and explain the reason 6. Let f (x) = x ^ 3-3ax + B (a ≠ 0) (1) If the curve y = f (x) is tangent to the straight line y = 8 at the point (2, f (x)), find the values of a and B; (2) Find the monotone interval and extreme point of function f (x) 7. Let y = f (x) be a cubic function and the image is symmetric about the origin. When x = 1 / 2, the minimum value of F (x) is - 1, and the analytic formula of function f (x) is obtained 8. F (x) = x ^ 3 + 3ax ^ 2 + BX + A ^ 2 has an extreme value of 0 when x = - 1 (1) Find the values of constants A and B; (2) Find: monotone interval of F (x) Don't talk if you don't answer!
- 10. The equation of conic curve. Find the hyperbolic equation with two vertices of ellipse x squared / 16 + y squared / 9 = 1 as focus and ellipse focus as vertex
- 11. Using function image to solve inequality 5x-1 > 2x + 5
- 12. What is the area of the plane area represented by the absolute value of inequality x + absolute value y less than or equal to 3
- 13. Try to determine the value range of a, so that the inequality group x+x+1 4＞1 1.5a−1 2(x+1)＞1 2 (a − x) + 0.5 (2x − 1) has only one integer solution
- 14. Using monotonicity of function to prove inequality Prove x-x ^ 2 > 0, X ∈ (0,1) by monotonicity of function
- 15. On Sunday, the class leader Wang Xiaoming organized 50 students to go to Nanhu Park. There are two kinds of boats available for hire in the park. Each big boat can seat 5 people at most, and the rent is 30 yuan for each boat, and the rent is 20 yuan for each boat. Please use what you have learned to design a scheme so that the boat does not leave vacant seats and pays the least rent. Remember: use the solution of one variable linear inequality equation~
- 16. A practical problem of inequality in grade two To welcome the Universiade and beautify Shenzhen, the garden department decided to use the existing 3490 pots of A-type flowers and 2950 pots of B-type flowers with 50 gardening styles of a and B on both sides of Yingbin Avenue. It is known that 80 pots of A-type flowers and 40 pots of B-type flowers are needed to match a type-A flower, and 50 pots of A-type flowers are required to match a B-type flower, The extracurricular activity group of class 1 of the third grade of a school undertook the design of the horticultural modeling collocation scheme?
- 17. Let x > 0, Y > 0, and (x-1) (Y-1) ≥ 2, then the value range of XY is?
- 18. The algebraic and geometric meanings of absolute values should be explained separately
- 19. How to prove that the derivative of a pair of inverse functions is reciprocal
- 20. Let y = 3x + 1, then the derivative X '(y) of its inverse function x = x (y)=