It is known that the coefficient with X term in the expansion of F (x) = (1 + 2x) m + (1 + 4x) n (m, n ∈ n *) is 36. The minimum coefficient with x 2 term in the expansion and the value of M, n are obtained

∵ f (x) = (1 + 2x) m + (1 + 4x) n the coefficients of x-term in the expansion of (1 + 2x) m + (1 + 4x) n (m, n ∈ n *) are 36, ∵ m + 2n = 18, ∵ f (x) = (1 + 2x) m + (1 + 4x) n the coefficients of x2 term in the expansion of (1 + 2x) m + (1 + 4x) n are t = c2m · 22 + C2n · 42 = 2m2-2m + 8n2-8n, ∵ m + 2n = 18, ∵ M = 18-2n, ∵ t = 2 (18-2n) 2-2 (18-2n) + 8n2-8n = 16n2-148n + 612 = 16 (n2-374n + 1534), when n = 378, t is the minimum, but when n ∈ n *, ｜ n = 5, t is the minimum, that is, the coefficient of x2 term is the minimum, and the minimum is 272, then n = 5, M = 8

It is known that the coefficient of quadratic term of quadratic function f (x) is positive, and for any real number x, f (2-x) = f (x + 2). The monotonicity of function f (x) is discussed

From the fact that the coefficient of quadratic term of the quadratic function f (x) is positive, we can see that the opening of its image is upward, so the images on both sides of the symmetry axis are left down and right up. For any real number x, there is f (2-x) = f (x + 2), so the equation of the symmetry axis of the function is x = 2. Therefore, the function f (x) is a decreasing function on (- ∞, 2] and an increasing function on (2, + ∞)

Given the function f (x) = (- 3x + 1) ^ 9, find the sum of the coefficients and the detailed explanation,
Is there any basis for bringing in the value of X to be 1 or - 1, or is there any substitution for 1?
I don't understand this kind of problem

The expanded form of F (x), if you think about it, is it the 9th power of x plus the 8th power of x plus the 7th power of X What do you want to calculate? That is, how much to add and how much to add? As long as x = 1 is substituted, and such substitution should not be expanded to the power of 9. Answer: (- 2) ^ 9 = - 512

What is the coefficient of the second term in the binomial (1 / 2x-1) * 8 expansion

The second term = C8, take the 7th power of 1 times (1 / 2x) and the 1st power of (- 1)
So the coefficient = (1 / 2) 7 times (- 8)

Derivative function of F (x) = LNX + ln (2-x) + X

f(x)=lnx+ln(2-x)+x
f'(x)=1/x+1/(2-x)*(-1)+1
=1/x+1/(x-2)+1

If the line y = a intersects the image of the function y = SiNx, the maximum distance between two adjacent intersections in a period is 0

π
When y = 0, there are three intersections in a period, and the adjacent intersections are sin0 to sinπ
I don't know how to write the process

If the line y = a intersects the image of the function y = SiNx, the maximum distance between the two adjacent intersections is?
Another problem is to shift the image of the function y = sin4x to the left by π / 12 unit length to get the image of y = sin (4x + a), then a is equal to?

1. The maximum value is 2 * PI. Draw both graphs by itself, and translate the image of y = a upward and downward. When y = + 1 or y = - 1, it is the maximum value
2. The left plus right subtraction of translation is only for X, so we only add and subtract on X, so y = SiN4 (x + π / 12) = sin (4x + π / 3), so a = π / 3

Let the line x = m intersect the image of the function y = SiNx and y = sin (x + π 2) at two points m and N respectively, then the maximum distance between M and N is______ ．

In the intersection of two functions y = SiNx and y = a, the maximum distance between two adjacent points is

∵ y = SiNx and y = a have intersection points
∴a∈[-1,1]
The maximum distance is two adjacent peaks of sine function
∴Dmax=2π

Find the continuous space of function, break point
f(x)=(1-cosx)/sinx
Finding continuous intervals and discontinuities

When x = k π (K ∈ z) is SiNx = 0, so x = k π (K ∈ z) is the discontinuity of F (x) = (1-cosx) / SiNx. There are two types of discontinuities: the first type and the second type. You can discuss them separately. When x = 2K π, it is the first type, when x =

It is known that the coefficient with X term in the expansion of F (x) = (1 + 2x) m + (1 + 4x) n (m, n ∈ n *) is 36. The minimum coefficient with x 2 term in the expansion and the value of M, n are obtained