Questions about the idea of using the definition of definite integral to solve the limit of sequence sum formula or definite integral problem, Which of the following ideas is right when using the definition of definite integral to solve the limit of sum of sequence or definite integral problem? 1. First write down the idea that "it has been verified that this limit exists or meets the existence condition of definite integral"; 2. This kind of problem has recognized limit or definite integral. There is no need to write anything. You can directly use the definition of definite integral to solve it. This idea is also clear (recognized!); 3. Isn't it circular logic to write that assumes existence or not and assumes existence by default? That is, when seeking a value, first assume its existence, and then use the existence to deduce the value, so as to obtain that the assumption is correct, which is similar to proving yourself?

Questions about the idea of using the definition of definite integral to solve the limit of sequence sum formula or definite integral problem, Which of the following ideas is right when using the definition of definite integral to solve the limit of sum of sequence or definite integral problem? 1. First write down the idea that "it has been verified that this limit exists or meets the existence condition of definite integral"; 2. This kind of problem has recognized limit or definite integral. There is no need to write anything. You can directly use the definition of definite integral to solve it. This idea is also clear (recognized!); 3. Isn't it circular logic to write that assumes existence or not and assumes existence by default? That is, when seeking a value, first assume its existence, and then use the existence to deduce the value, so as to obtain that the assumption is correct, which is similar to proving yourself?

First determine that f (x) is continuous in [a, b], so the definite integral exists
Since the definite integral exists, it can be solved by definition
When using the definition, choose a special division method: usually N equal parts interval [a, b], and then n tends to infinity (the maximum interval length 1 / n tends to 0)

Can definite integral and limit exchange order

I'm sorry to tell you, no! The limit cannot be calculated in the integral. Generally, there is a parameter in the definite integral to calculate the limit, which can be solved by using the integral mean value theorem or pinch criterion

Sequence limit problem If the sequence xn and yn satisfy If LIM (n approaches infinity) xnyn = 0 A. If xn is unbounded, yn must be bounded B. If 1 / xn is infinitesimal, yn must be infinitesimal Why do I think it's all right... And I can't give a counterexample!

A. do not choose. There is a counter example: xn = n [1 + (- 1) ^ n], yn = n [1 - (- 1) ^ n], are unbounded, but xnyn = (n ^ 2) [1 - (- 1) ^ (2n)] = 0, of course, LIM (n → inf.) xnyn = 0. B. choose. In fact, because 1 / xn is infinitesimal, xn is known to be infinite, so

A limit problem of number series in Senior Two In a regular hexagon with a side length of R, connect the midpoint of each side in turn to obtain a regular hexagon, and in this obtained regular hexagon, connect the midpoint of each side in turn to obtain a regular hexagon. In this way, let the sum of the side lengths of the first n regular hexagons be Sn, the sum of the side lengths of all these regular hexagons be s, and the sum of the areas of all these regular hexagons be t Find Sn, s, t

The side length of the nth regular hexagon is 6R * [(n-1) power of (2 / 2 root sign 3)]
Sn = 6R * [(2 / root 3) to the nth power - 1] / [(2 / root 3) - 1]
S = [(12 times root 3) + 24] * r
T = (6 times root 3) * r square

Solving sequence limit problem The limits of sequence xn and sequence yn are a and B respectively, and a is not equal to B, so what are the limits of sequence x1, Y1, X2, Y2, X3, Y3? To the specific process, huh

Prove that we take the sub columns xn and yn of the sequence x1, Y1, X2, Y2, X3, Y3
Because limxn = a, limyn = B, and a is not equal to B
So the sequence x1, Y1, X2, Y2, X3, Y3. Does not converge, that is, diverges. Then the limit does not exist
(Note: because of a convergent sequence, any subsequence converges and converges to the same limit)

Who can help me solve some limit problems? 1 find f (x) = sin2x + Tan (x / 2) period 2 LIM (x ^ n-1) / (x-1) (n is a positive integer) x-1 3 LIM (root (2x + 1) - 3) / (root (X-2) - root 2) x-4 4 LIM (root sign (x ^ 2 + X + 1) - root sign (x ^ 2-x + 1)) X-positive infinity 5 lim{root sign [(x + P) (x + Q)] - x} X-positive infinity 6 lim(x^2+1)(3+cosx)/(x^3+x) X-infinity 7 lim(1/(x+1)+1/(x^2-1)) x--1 8 lim(sinx^2-x)/[((cosx)^2)-x] X-infinity

1 2*pi
2 n
3 (2 root numbers) / 3
4 1
5 (p+q)/2
6 0
7 infinity
8 1