If f (x) = SiNx + X3 + 2 and f (1) = 1, then f (- 1)= X3 is the third power of X

If f (x) = SiNx + X3 + 2 and f (1) = 1, then f (- 1)= X3 is the third power of X

Take it in directly. From F (1) = 1, we get sin1 = - 2, and f (- 1) = sin (- 1) + 1 = sin1 + 1 = - 1

It is known that the line L passes through the point P (- 1,1), which is divided by two parallel lines L1: x + 2y-1 = 0, L2: x + 2y-3 = 0,
The midpoint m of the segment M 1 m 2 is on the line L 3: x-y-1 = 0. Try to find the equation of the line L

Two parallel lines L1: x + 2y-1 = 0 and L2: x + 2y-3 = 0
The trajectory of the midpoint m is: x + 2y-2 = 0
Solving equations
X-Y-1=0
x+2y-2=0
The results are as follows
x=4/3,y=1/3
Therefore, the equation of line L is: (Y-1) / (1 / 3-1) = (x + 1) / (4 / 3 + 1)
Namely:
2x+7y-5=0

A, B and C are all positive real numbers, a + B + C = 1. Find the min of √ (1 / a) + √ (1 / b) + √ (1 / C)

The specific solution is not easy to say, but this kind of problem is let a = b = C, so the answer is root 3
I hope it's a question to fill in the blanks, so it's not easy to solve the question

Taylor formula in the process of proving Taylor formula, how to get RN (X.) = f (X.) - P (X.) = 0, why the higher derivative of RN (x) should be equal to 0

Because P (x) is assumed to be an approximate value of F (x), the higher the derivative order of F (x), the closer the value of P (x) is to f (x), but there is always an error. The error is RN (x)
The higher derivatives of RN (x) are not all equal to 0. When f (x) is expanded by Taylor at x0, there are 0,1,2 of RN (x) at x0 The derivative of order n is equal to 0 (if f (x) has derivative of order n + 1). You should notice that in the RN (X.) function, there is a factor of (x-x0) ^ to the power of N + 1, so at the point of x0, 0,1,2 The n-order derivative is equal to 0, but the N + 1-order derivative is not equal to 0

F (x) is a monotone non decreasing function, f (0) = 0, f (x / 3) = 1 / 2F (x) f (1-x) = 1-f (x), find f (1 / 3) + F1 / 8)

f(1-x)=1-f(x),
Let x = 0
Then f (1) = 1-f (0) = 1
f(x/3)=1/2f(x)
Let x = 1
f(1/3)=1/2*f(1)=1/2
f(1-x)=1-f(x)
Let x = 1 / 2, then 1-x = 1 / 2
So f (1 / 2) = 1-f (1 / 2)
So f (1 / 2) = 1 / 2
f(x/3)=1/2f(x)
Let x = 1 / 3
f(1/9)=1/2f(1/3)=1/4
f(x/3)=1/2f(x)
Let x = 1 / 2
f(1/6)=1/2f(1/2)=1/4
So f (1 / 6) = f (1 / 9)
F (x) is a monotone nondecreasing function
1/6>1/8>1/9
So f (1 / 6) > = f (1 / 8) > = f (1 / 9)
So f (1 / 8) = 1 / 4
So f (1 / 3) + F (1 / 8) = 1 / 2 + 1 / 4 = 3 / 4

Let a be a matrix of order n and have N orthogonal eigenvectors. It is proved that a is a real symmetric matrix

Are the verbs after three years singular or plural?

Singular, whether it is a year or a hundred years, use the singular
For example:
Three years is a long time.
Three years is a long time

ax-b=cx+d
We need to discuss it by category

ax-b=cx+d
ax-cx=b+d
(a-c)x=b+d
x=(b+d)/(a-c)

The usage of one of and only one of in attributive clauses

In the attributive clause, the noun after one of is the antecedent of the attributive clause. If the only one of is followed by the attributive clause, the antecedent is the only one

if AB.BC + AB.AB=0 Then the shape of triangle ABC is
The front is vector

If it means multiplication, then this triangle is a right triangle,
AB*(AB+BC)=0
AB*AC=0
So ABC is a triangle