![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
X tends to 0, the limit of sin1 / x ^ 2-1 / sin2x (not SiNx ^ 2, sin2x)
Whether it is (SiNx) ^ 2 or sin (2x), the limit is ∞. Because 1 / sin2x is ∞ when x tends to 0, and sin1 / x ^ 2 is a bounded function, the difference must be ∞
When x tends to 0, why can't sin1 / X be equal to 1 / X in the limit of (square times sin1 / x) divided by SiNx?
Because when x tends to zero, SiNx can be equivalent to X
Here, 1 / X goes to infinity, so it doesn't work
Does the convergence function have bound and limit? Then does 1 / X converge? Why can X - > infinity get 0
The concept is vague, don't copy
The convergent sequence must be bounded
Read carefully, the book never said that the convergence function is bounded, only that the convergence function is locally bounded, the so-called locally bounded can be simply understood as bounded near the convergence point, away from it may be unbounded
RELATED INFORMATIONS
- 1. Functions are bounded, unbounded, convergent, divergent, with and without limits. What are the relations between these relations?
- 2. Find the left and right limit of function f (x) = [x] at x = 0
- 3. What function is f (x) = sgnx? What is the image like?
- 4. What is the intermediate value principle of continuous function?
- 5. The Weierstrass theorem (1) draw diagram of cases in which a feasible set (budget set) is not closed or not bunded,but a solution to the optimization problem exists. (in the case of drawing a graph, one of the feasible sets (budget set) is not closed or bunded, but there is a solution to the optimization problem.) (2)show f(x)=1,g(x)=x are continuous functions. It is shown that f (x) = 1, G (x) = x are continuous functions (3)Does the following function has a maximum on the inverval [-1,1]?If not,explan why. Does the following function have a maximum interval [- 1,1]? If not, please explain the reason f(x)= 1/x,x=/=0； 0,x=0.
- 6. How to explain the problem that spring force can't change suddenly
- 7. Can the spring force change suddenly?
- 8. Ln (1 + 2x ^ 2) / ln (1 + 3x ^ 3) Lim tends to be positive infinity. The limit of Ln (1 + 2x ^ 2) / ln (1 + 3x ^ 3) Lim is obtained by using the law of lobita
- 9. Finding the limit: x ^ - 1-e of LIM (x-0) (1 + x) divided by X
- 10. It is proved that limx approaches 0, the power of X + a of e minus the power of a of e divided by the power of a of x = E
- 11. (e ^ n times n!) / N ^ n how to find the limit x tending to infinity
- 12. Finding limit: when x tends to infinity, find the limit of (x + 1) &# e ^ X Limit: when x tends to infinity, find the limit of (x + 1) / e ^ X
- 13. One X of E, X tends to 0 - why is the limit 0?
- 14. How to find the sum of the first n terms of an = 1 / n
- 15. Prove the convergence of sequence √ 2, √ (2 + √ 2), √ (2 + √ (2 + √ 2)),. And find its limit
- 16. It is proved that if a sequence converges to a, then any of its subsequences converges and the limit is a Can that be expressed in mathematical language?
- 17. On N > N in sequence limit For example, if the sequence is n + 1 / N and the limit is 1, 1 / N can be calculated If you want the distance between the sequence and the limit to be less than 0.001, as long as n > 2000 In the concept of limit, there is an n > N, that is, 2001 > 2000 What does this n stand for?
- 18. Why convergence sequence must be bounded sequence? Don't go too far But I hope it makes me understand
- 19. Is the sequence with limit necessarily convergent? Is it not necessarily bounded
- 20. A question about the proof that the convergence of sequence of higher numbers must be bounded This theorem is proved in page 40 of the fourth edition of Tongji, because the sequence {xn} converges, let limxn = a, according to the definition of sequence limit, there exists positive integer n for ε = 1, such that for all xn when n > N, when the inequality | xn-a | n, | xn | = | (xn-a) + a | ≤ | xn-a | + | a|