It is proved that f (x) = 1 / 2 + 1 / 2 is a product function It is proved that f (x) = 1 / 2 + 1 / 2 is a product function

It is proved that f (x) = 1 / 2 + 1 / 2 is a product function It is proved that f (x) = 1 / 2 + 1 / 2 is a product function

f(x) = 1/2 - 1/(2^x+1) = (2^x-1) / (2*(2^x+1)
f(-x) = 1/2 -2^x/(1+2^x) = (-2^x+1) / (2*(2^x+1) = -f(x)
So f (x) is an odd function

It is proved that f (x) is differentiable on [a, b], the derivative function f '(x) is integrable, and f (b) - f (a) = 1. It is proved that ∫ a to B [f' (x)] ^ 2DX > = 1 / (B-A)

∫ a to B [f '(x)] ^ 2DX * ∫ a to B DX ≥ [∫ a to BF' (x) DX] ^ 2, this step is derived from Schwarz inequality, the left is equal to (B-A) * ∫ a to B [f '(x)] ^ 2DX, the right is equal to 1, the conclusion comes out
Can not read online questions or messages

F (x) is a monotone nonnegative function and continuous in [0, b]

Discuss the situation according to the situation, there is a situation that hasn't been thought out for a long time
(1) When f (x) is a monotonically decreasing positive continuous function on [0, b]
There are: left > b ∫ [0, a] f (a) DX = ABF (a)
right

Limx → 0 + (lnx-2 / π) / Cotx

LIM (x → 0 +) (lnx-2 / π) / Cotx = LIM (x → 0 +) (1 / x) / (- CSC & # 178; x) [lobida's Law] = LIM (x → 0 +) (1 / x) / (- 1 / Sin & # 178; x) = LIM (x → 0 +) - (Sin & # 178; x) / x = LIM (x → 0 +) - SiNx [last step equivalent infinite substitution, when x → 0, SiNx] = 0 answer: 0

Given that a is not equal to 3, then the solution of the equation ax-3 = 3x about X is

ax-3=3x
ax-3x-3=0
x(a-3)-3=0
x(a-3)=3
x=3\a-3
Because a is not equal to 3
So the answer is true

Calculation of 11 * 11 * 11-11 * 11-11 * 10 with simple method

11*11*11-11*11-11*10
=11*(11*11-11-10)
=11*(121-11-10)
=11*100
=1100

The inequality X & sup2; - ax + 2x-2a ＞ 0 holds on the interval (0,2), and the range of real number a is obtained

The method of separating variables can be used to move the one with a to one side, that is, a ＜ x, and 0 ＜ x ＜ 2, so a ≤ 0

If the polynomial (x-1) (x + 3) (x-4) (X-8) + m is a complete square, then M is equal to____ I can't understand what you wrote earlier

(x-1)(x-4)=x^2-5x+4
(x-8)(x+3)=x^2-5x-24
(x-1)(x+3)(x-4)(x-8)+m=(x^2-5x)^2-20(x^2-5x)-96+m;
The right side of the equal sign should be (x ^ 2-5x) ^ 2-20 (x ^ 2-5x) + 100
m-96=100
m=196.

53.5×35.5＋53.5×43.2＋78.5×46.5

53.5×35.5＋53.5×43.2＋78.7×46.5
=53.5x(35.5+43.2)+78.7x46.5
=53.5x78.7+78.7x46.5
=(53.5+46.5)x78.7
=100x78.7
=7870
There is something wrong with the title. I changed 78.5 to 78.7. Please check the title to see if you have a wrong number

How to find the general solution of differential equation 1 / (x ^ 2Y '') = LNX?
y‘’/x^2=lnx
dial the wrong number

1/(x^2y'')=lnx
y''=1/(x^2lnx)
Two sides integral
y'=-1/(xlnx)-1/x^2+C1
Integral on both sides
y=-lnlnx+1/x+C1x+C2