Given the function f (x) = x-ax ^ 3 (a > 0), G (x) = SiNx, when x belongs to 0 to half of π, G (x) greater than or equal to f (x) is constant, the range of a is obtained

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• 1. Given the function f (x) = / SiNx /, (1) if G (x) = ax-f (x) > = 0 is constant for any x ∈ [0, + infinity), find the value range of real number a 2) If the image of the function f (x) = | SiNx | and the line y = KX (k > 0) have and only have three common points, and the maximum abscissa of the common point is α, it is proved that cos α / (sin α + SIN3 α) = (1 + α 2) / 4 α
• 2. Let f (x) = SiNx (x ≥ 0), G (x) = ax (x ≥ 0), where a is a real number 1. If f (x) ≤ g (x) is constant, find the value range of real number a 2. When a = 1, we prove that G (x) - f (x) ≤ (1 / 6) x & # 179; (x ≥ 0)
• 3. If there are two tangents perpendicular to each other on the function f (x) = ax + SiNx, the range of real number a is obtained But the answer is a = 0. how?
• 4. It is known that f (x) is a piecewise function: when x ≥ 0, f (x) = 1, X
• 5. Let the minimum value of function f (x) = x2-4x-4 in the interval [T, t + 1] (t belongs to R) be g (T), and try to find the function analytic expression of G (T) Thank you And write the minimum value of G (T).
• 6. The analytic expression of F (x) by function f (2x) = 4x + 1
• 7. The known function f (x) = x-4x + A + 3, G (x) = MX + 5-2m 1: If y = f (x) has zero point on [- 1,1}, find the value range of real number a 2: When a = 2, if any x 1 belongs to [1,3], there is always x 2 belonging to [1,4], if f (x 1) = g (x 2) holds, then the value range of real number m is obtained
• 8. The square of function f (x) = 4x - MX + 5 is an increasing function on [- 2, positive infinity] and a decreasing function on (negative infinity, - 2]. Find the value of M
• 9. Let the function defined on R satisfy f (f (x) - x2 + x) = f (x) - x2 + X, and have and only have one x0, such that f (x0) = x0, and find the analytic expression of F (x)
• 10. It is known that the function f (x) whose domain is r satisfies that f (f (x) - x2 + x) = f (x) - x2 + X has only one real number x0, such that f (x0) = x0 Why should the two values obtained from the analytic expression of function f (x) be rounded off x = 0?
• 11. Let f (x) = ax + cosx, X ∈ [0, π]. (I) discuss the monotonicity of F (x); (II) Let f (x) ≤ 1 + SiNx, find the value range of A
• 12. If f (x) = (1 - λ) SiNx - (1 / 2 + 1 / 2 λ) cosx + 1 is an increasing function in [- π / 2, π / 2], find the range of λ!
• 13. Let the function FX = ax + cosx, x [O, π], let the function FX be less than or equal to 1 + SiNx, and find the value range of A
• 14. It is known that y = f (x) is a function with a period of 2 π. When x ∈ [0, 2 π], f (x) = sinx2, then the solution set of F (x) = 12 is () A. {x|x=2kπ+π3，k∈Z}B. {x|x=2kπ+5π3，k∈Z}C. {x|x=2kπ±π3，k∈Z}D. {x|x=2kπ+（-1）kπ3，k∈Z}
• 15. In a series circuit, there are two resistors R1, R2, where R1 = 4 ohm In a series circuit, there are two resistors R1 and R2, in which R1 = 4 Ω. When the resistor is installed in the circuit with voltage of 6V after series connection, the actual power consumed by R2 is 2W. Calculate the resistance value of R2! Clear thinking, the right person is much better than the right person within 1 hour
• 16. What is the fourth digit to the left of the decimal point in the decimal? What is its counting unit?
• 17. A resistor with a resistance value of 6 ohm, in a period of time, the amount of electricity passing through it is 2 banks, and the heat generated by the resistor is 12 joules______ V, it's been a long time______ Seconds
• 18. Solution: to make the image of function y = (2m-3) x + (3m + 1) pass through the positive half axis of X and Y axis, what is the value range of M?
• 19. The power loss of the conductor is 20% of the transmission power when the voltage of 220 V is used in a substation. If the power loss of the conductor is to be reduced to 5% of the transmission power, what is the transmission voltage?
• 20. On several mathematical problems of fractions (1) The distance between station a and station B is 1280km. After adopting the "harmony" EMU to increase the speed, the running speed of the train is 3.2 times of the original, and the time from station a to station B is shortened by 11 hours, so the speed of the train after increasing the speed can be calculated (2) The distance between a and B is 36km. A and B start from a and B at the same time and walk towards each other. When they meet, a is 16km away from B. after meeting, they continue to move forward. A arrives at B 1.8h earlier than B arrives at a. find out the walking speed of a and B