The odd function f (x) = f (x-2k) whose domain is r, and when x belongs to (0,1), f (x) = 2 ^ X / (4 ^ x + 1) 1, find the analytic expression of F (x) on [- 1,1] 2. Prove that f (x) is a decreasing function on (0,1) 3. When m takes what value, the equation f (x) = m has a solution on (0,1)

The odd function f (x) = f (x-2k) whose domain is r, and when x belongs to (0,1), f (x) = 2 ^ X / (4 ^ x + 1) 1, find the analytic expression of F (x) on [- 1,1] 2. Prove that f (x) is a decreasing function on (0,1) 3. When m takes what value, the equation f (x) = m has a solution on (0,1)

1. By odd function, f (x) = - f (- x), so f (0) = 0
When x belongs to (- 1,0), - x belongs to (0,1), so f (- x) = 2 ^ (- x) / [4 ^ (- x) + 1]
Furthermore, because of the odd function, f (x) = - f (- x) = - 2 ^ (- x) / [4 ^ (- x) + 1]
Reduced to f (x) = - 2 ^ X / (4 ^ x + 1)
From the periodicity, we can see that f (- 1) = f (1), from the odd function, f (- 1) = - f (1), so f (1) = f (- 1) = 0
So when x is [- 1,1], f (x) is a piecewise function, and the interval is divided into - 1, (- 1,0), 0, (0,1), and 1. Five piecewise functions are 0, - 2 ^ X / (4 ^ x + 1), 0,2 ^ X / (4 ^ x + 1), and 0, respectively
2. The stupid way is to find the derivative, and then see if the derivative is less than zero
There's another way. Maybe it's easier
Let g (x) = 2 ^ x, then f (x) on (0,1) is f (x) = f [g (x)] = g (x) / [g (x) * g (x) + 1]
Obviously, G (x) is an increasing function on (0,1), and 1

The odd function f (x) with the domain r satisfies f (x) = f (x-2k) (K ∈ z) and f (x) = 2 ^ X / (4 ^ x + 1) when x ∈ (0,1)
Q: when m takes what value, the equation f (x) = m has a solution on [- 1,1]

1) When x ∈ [0,1], f (x) = 2 ^ X / (4 ^ x + 1)
f'(x)=(2^x*ln2(4^x+1)-2^x*4^xln4)/(4^x+1)^2=2^x*ln2(1-4^x)/(4^x+1)^2

I have an electric car. It used to be a 500W motor. I want to replace it with an 800W motor. Is the 500W controller 48v20a battery controller durable? How many kilometers can it run? Can the power be increased?

Better not change 4820 battery with 500W motor has been very hard, but also increase the power, the controller is easy to burn, the battery is easy to damage
If it is changed to 800W, the power of the motor can increase the mileage. If it is new, the battery can only be about 40km, but the controller will not be durable

(- 0.5) + 3 and 1 / 4 + 2.75 + (- 5 and 1 / 2)

(- 0.5) + 3 and 1 / 4 + 2.75 + (- 5 and 1 / 2)
=-0.5+3.25+2.75-5.5
=-0.5-5.5+3.25+2.75
=-6+6
=0

The letter of the instrument used to measure the alternating current is the symbol?

There are many kinds of instruments used to measure AC flow, such as AC current, AC voltage, etc. there is no unified letter. As for the symbol AC flow, it usually has the symbol of sine wave

38.75-15.8 + 61.25-4.62 disjunction operation

38.75-15.8+61.25-4.62
=22.95+61.25-4.62
=84.2-4.62
=79.58

Power supply voltage 9V, R1 = 3 ohm, sliding rheostat 0-20 ohm, ammeter 0-0.6a, voltmeter 0-3v, calculate sliding rheostat resistance
There are pictures

In terms of the upper limit, the maximum current is 0.6A, and the total resistance is 9V / 0.6A = 15 ohm, so the slip resistance is at least 12 ohm. In terms of the voltmeter, because the slip resistance is at least 12 ohm, the voltmeter must be at both ends of R1 (the voltage at both ends of the slip resistance is at least 4 times that at both ends of R1, that is to say, there is at least 7.2V). The larger the slip resistance is, the smaller the voltage at both ends of R1, the smaller the current, So the resistance of the sliding rheostat is 12-20 ohm

50 real number problems in Volume 1 of Grade 8
Do not fill in the blanks, do not choose, is the calculation problem, binary linear equations can also be, the more the better, 50 can

1、(3ab-2a)÷a 2、（x^3-2x^y)÷(-x^2) 3、-21a^2b^3÷7a^2b 4、(6a^3b-9a^c)÷3a^2 5、(5ax^2+15x)÷5x 6、(a+2b)(a-2b) 7、(3a+b)^2 8、(1/2 a-1/3 b)^2 9、(x+5y)(x-7y) 10、(2a+3b)(2a+3b) 11、(x+5)(x-7) 12、5x^3×8x^2 13、-3x×(2x^2-x+4) 14、11x^12×(-12x^11) 15、(x+5)(x+6) 16、(2x+1)(2x+3) 17、3x^3y×(2x^2y-3xy) 18、2x×(3x^2-xy+y^2) 19、(a^3)^3÷(a^4)^2 20、(x^2y)^5÷(x^2y)^3 21、(y^3)^3÷y^3÷(-y^2)^2 22、(-2mn^3)^3 23、(2x-1)(3x+2) 24、(2/3 x+3/4y)^2 25、2001^2-2002×2002 26、(2x+5)^2-(2x-5)^2 27、-12m^3n^3÷4m^2n^3 28、2x^2y^2-4y^3z 29、1-4x^2 30、x^3-25x 31、x^3+4x^2+4x 32、(x+2)(x+6) 33、2a×3a^2 34、(-2mn^2)^3 35、（-m+n)(m-n） 36、27x^8÷3x^4 37、(-2x^2)×(-y)+3xy×(1-1/3 x) 38、am-an+ap 39、25x^2+20xy+4y^2 40、(-4m^4+20m^3n-m^2n^2)÷(-4m^2) 41、(12p^3q^4+20p^3q^2r-6p^4q^3)÷(-2pq)^2 42、[4y(2x-y)-2x(2x-y)]÷(2x-y) 43、(x^2y^3-1/2 x^3y^2+2x^2y^2)÷1/2 xy^2 44、(4a^3b^3-6a^2b^3c-2ab^5)÷(-2ab^2) 45、（ax+bx)÷x 46、(ma+mb+mc)÷m 47、(9x^4-15x^2+6x)÷3x 48、(28a^3b^2c+a^2b^3-14a^2b^2)÷(-7a^2b) 49、(6xy^2)^2÷3xy 50、24a^3b^2÷3ab^2

The formula of people's education press in the second semester of Physics

Four basic formulas (the most critical)
Ohm's law I = u / R
Electric power definition formula P = w / T
Electric power calculation formula P = u i
Joule's law q = I2 r t
In particular, the first three, together, can be used to derive other formulas
For example: P = U2 / r = I2 R
W= (U2 / R) t =I2 R t
We should also combine the characteristics of series parallel circuit, especially the characteristics of voltage and current
If you master the relationship among voltage, current and resistance very skillfully, it's almost the same
As long as the three physical quantities of voltage, current and resistance can be worked out, the rest can be basically worked out

Beauty in composition life

There are many beauties in life. Of course, everyone has different understanding of beauty. But I think beauty lies in the mutual help among classmates, in the harmonious coexistence of neighbors, and in the love donation of society In school, the mutual help between students is beautiful