Using definition method to prove or solve the difference between sequence and function limit? The difference between the two is that the former n is related to $(she gei Ma can't write it) and the calculation is not unique. When solving the problem, it's not necessary to find the minimum value. In the latter, it's a bit difficult to understand whether it's necessary to find the minimum value when solving the problem. In my opinion, some proofs select the minimum value of the two values, and introduce a numerical value when solving the problem, so that half of the neighborhood length is less than or equal to it, How to introduce this value? What are the techniques?

Hello, you said the problem: I see that the minimum value of the two values selected in some proof questions is set to make the two inequalities established at the same time, and a numerical value will be introduced when solving, so that half of the neighborhood length is less than or equal to it. This is usually used with trigonal inequality, not necessarily half, also

Calculation of lim2n-1 / 4N + 3 with sequence limit
lim2n-1/n+3

If n approaches infinity, the result is 0.5 lobita rule
When it approaches 0, the result is - 1 / 3

Prove the following formula with sequence limit: lim2n-1 / 4N + 3 = 1 / 2 (n approaches infinity)

For any ε > 0, as long as n > 1 / ε, then | 2N-1 / 4N + 3-1 / 2 | = 5 / 2 (4N + 3) < ε〈 lim2n-1 / 4N + 3 = 1 / 2 (n approaches infinity)

Let a = {0 10} {1 00} {20 - 1}. I - {0 10}. How to calculate {3 41} {0 01} by finding the negative power of (I + a)

(I+A,I) =1 1 0 1 0 02 1 -1 0 1 03 4 2 0 0 1r2-2r1,r3-3r11 1 0 1 0 00 -1 -1 -2 1 00 1 2 -3 0 1r1+r2,r3+r2,r2*(-1)1 0 -1 -1 1 00 1 1 2 -1 00 0 1 -5 1 1r1+r3,r2-r31 0 0 -6 2 10 1 0 7 -2 -10 0 1 -5 1 1(I+...

If a = 1 / 2 (B + e), prove: A ^ 2 = a if and only if B ^ 2 = e, this is a proof of matrix, how to prove

From a = 1 / 2 (B + e)
A^2=A
1/4 (B+E)^2 = 1/2(B+E)
B^2 +2B +E = 2B +2E
B^2 = E
Every step is bidirectional, so a ^ 2 = a if and only if B ^ 2 = E#

Let n-order matrix a satisfy a ^ 2 = e, and | a + e ≠ 0, prove that a = E

Matrix A of order n satisfies that a ^ 2 = e, = = = "the Annihilation Polynomial of matrix A has no multiple roots, and the roots can only be positive or negative 1, = =" the minimum polynomial of matrix A has no multiple roots, and the roots can only be positive or negative 1, = = "matrix A can be diagonalized, and the eigenvalue of matrix A can only be positive or negative 1, and because | a + e | ≠ 0, the eigenvalue of matrix A is not negative 1, = = =

Let a be a matrix of order n, | e-A | ≠ 0, and prove that: (E + a) (e-A) * = (e-A) * (E + a)

Because (e-A) (E + a) = (E + a) (e-A) = E & sup2; - A & sup2; = e-A & sup2;
The inverse (A-E) and the right (A-E) = + A-E, respectively
(E + a) (e-A) inverse = (e-A) inverse (E + a)
Take e-A on both sides|
(E + a) (| e-A | (e-A) inverse) = (| e-A | (e-A) inverse) (E + a)
Namely: (E + a) (e-A) * = (e-A) * (E + a)
It's over

Let n-order matrix a satisfy a * a = A and E be n-order unit matrix. It is proved that R (a) + R (A-E) = n

From a & sup2; = a, a (e-A) = 0
We get R (e-A)

A is a matrix of order n, R (a + e) + R (A-E) = n, it is proved that a ^ 2 = E
Could you be a little more specific.

This. (a + E 0)
(0 A-E) make an elementary transformation. Go on. It's hard to play

Let a be a real number matrix of order n, if a ^ t * a = 0, it is proved that a = 0

If a ^ t * a = 0, then a * a = 0, so a = 0;

Calculation of lim2n-1 / 4N + 3 with sequence limit lim2n-1/n+3