The relationship between sequence limit and function limit? There is a question about limx - > + ∞ f (x) / X. I have proved that the value of LIM n - > + ∞ f (n π) / N π is (2 π / 4). Where n is a natural number, can we prove that limx - > + ∞ f (x) / X is (2 π / 4)? Please ask the mathematicians to solve the problem,

The relationship between sequence limit and function limit? There is a question about limx - > + ∞ f (x) / X. I have proved that the value of LIM n - > + ∞ f (n π) / N π is (2 π / 4). Where n is a natural number, can we prove that limx - > + ∞ f (x) / X is (2 π / 4)? Please ask the mathematicians to solve the problem,

No, Lim n → + ∞ can be understood as a subsequence of LIM x → + ∞. The existence of LIM n → + ∞ does not mean that LIM x → + ∞ also exists
Counterexample: Let f (x) = xsinx
Then LIM (n → + ∞) f (n π) / N π
=lim(n→+∞) nπsin(nπ)/nπ
=lim(n→+∞) sin(nπ)
=0
lim(x→+∞) f(x)/x
=lim(x→+∞) xsinx/x
=lim(x→+∞) sinx
Limits obviously don't exist

If a is a 4 * 3 matrix and B is a 3 * 4 matrix, then ABX = 0 must have a nonzero solution
The conclusions are as follows
r(AB)

Since the rank of the product of two matrices is less than or equal to the rank of any of them, R (AB)

2 * 2 Matrix x x 3 power = 0 prove that (I-X) inverse function is I + X + x 2 power. I don't know if the inverse function is I + X + x 2 power!

Is (I-X) inverse = I + X + X & sup2;
Here, because (I-X) (I + X + X & sup2;) = I-X & sup3; = I
So the conclusion is true

The problem of mathematical matrix
A=[1 0 0
2 1 0
2 4 6],
Finding A-1
And | a + A-1|

A-1=A-E=[0 0 0
2 0 0
2 4 5]
A+A-1=[1 0 0
4 1 0
4 8 11]
|A+A-1|=11

Several comprehensive exercises of mathematical calculation,
1、 Formula calculation
1. The sum of 4 times of a number and 1 / 2 of it is 1
2、 Calculation
1.36-8 / 9 △ 1 / 27
9 / 17 × 16
3.(28.85-17.5)÷1.2＋8.5

1、 1.4x + 0.5x = 1 --- > x = 1 / 4.5 = 2 / 9, 1.8 / (36-9) / (1 / 27) = (8 / 27) / (1 / 27) = 82.9x16 / 17 = 144 / 17 = 8 and 83 of 17. (28.85-17.5) / (1.2 + 8.5) = 11.35 ／ 1.2 + 8.5 = (12-0.65) / (1.2 + 8.5 = 18.5-65 / 120 = 18-5 / 120 = 17 + 23 / 24

In the matrix calculation in mathematics, a and B are two matrices. What operation does a: B represent?
What calculation symbol does this colon represent?
Like the colon in this?

Denotes "inner product"
That is to multiply the elements in the same position and then add them up
for example
A= 1 2
3 4
B= 5 6
7 8
A:B=1*5+2*6+3*7+4*8

Four problems are solved in mathematics
1.125x88+404x25=?
2.320x44+68x440=?
3.79x79-79+22x79=?
4.25x57+25x42+25=?

1. 125x88+404x25
=125x8x11+101x4x25
=11000+10100
=21100
2. 320x44+68x440
=44x(320+680)
=44x1000
=44000
3.79x79-79+22x79
=79x(79-1＋22）
=79x100=7900
4.25x57+25x42+25
=25x（57＋42＋1)
=25x100=2500

Let a be an invertible matrix, and prove: (a *) ^ - 1 = (a ^ - 1) *,

Because AA * = |a|e
So (a *) ^ - 1 = (1 / | a | a
A ^ - 1 (a ^ - 1) * = | a ^ - 1 | e
So (a ^ - 1) * = | a ^ - 1 | a = (1 / | a | a)
So: (a *) - 1 = (a ^ - 1) *

If the matrix A is invertible, it is proved that (a ') ^ - 1 = (a ^ - 1)'. A 'is the transpose matrix of A
AA^-1=A^-1A=E
Transpose on both sides, where (a ^ - 1)'a '= a' (a ^ - 1) = e '= e
So (a ^ - 1) '= (a ^ - 1)'

This is the answer, more complete

Let a.b.a + B be orthogonal matrices of order n, and prove that the negative power of (a + b) = the negative power of a + the negative power of B

Because a.b.a + B are orthogonal matrices of order n, the negative power of (a + b) = (a + b) transpose, the negative power of a = a transpose, the negative power of B = B transpose, so the negative power of (a + b) = (a + b) transpose = a transpose + B transpose = a negative power + B transpose