Existence criteria of higher limit

1. Existence of left limit and right limit
2. The left limit is equal to the right limit

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1. f(x)=x^2+bln(x+1) f(x)=x^2+bln(x+1) (2) if B = 1, we prove that for any positive integer n, the inequality ∑ f (1 / k), 1 + 1 / 2 ^ 3 + 1 / 3 ^ 3 +. + 1 / N ^ 3 I think we should use mathematical induction, but I didn't try it out Is f (1 / 1) + F (1 / 2) + F (1 / 3) +... + F (1 / N)
2. One third minus one fourth bracket plus one fourth minus one fifth bracket plus bracket minus one fifth minus one sixth
3. Proof of the existence of limit for higher numbers Let a = max {A1, A2,... Am} (AI > 0, I = 1,2,..., m), then Lim [under n-th root sign (n-th power of a1 + n-th power of A2 +... + n-th power of AM)] = a n→∞
4. What is complex fraction
5. 4.6 minus bracket - 3 / 4 plus 1.6 minus bracket - 3 / 4
6. High number, use Taylor formula LIM (x + 1) ln (1 + 1 / x). X approaches positive infinity
7. Solving complex fraction How to simplify the fractions of fractions whose internal numerator and denominator contain unknowns one ___ +1 （1+x^2) ___________________ one ___ -1 （1+x^2) one ___ +1 （1+x^2) ___________________ one ___ -1 （1+x）^2 The question just now is wrong.
8. 5 out of 11 times 11 out of 15 times 11 out of 57 minus 3 out of 14 times 2 out of 3, 5 out of 7 times 14 out of 25 plus 1 out of 3 Tuoshi
9. A function limit problem in Advanced Mathematics Complete description of the title: Let y = sin1 / x, prove: for any number a ∈ (0,1), try to find the sequence {xn}, such that LIM (n →∞) xn → 0, and lim (n →∞) yn = LIM (n →∞) sin1 / xn = A. and give a geometric explanation for this conclusion
10. Are x + 1 / X and X / X fractions
11. 24 times bracket 3 / 4 plus 5 / 6 process
12. F (x) = x & # 178; ten 2x + L, then f (X-5)? Do you want to put X-5 as a whole in a question like this What does f (x) matter?
13. What are the "two criteria for the existence of limit" in mathematics
14. How much is 24 times bracket 2 minus one sixth?
15. High school mathematics f (x) = | lgx| What is his function image? I know that his domain of definition is x > 0. Should he be an increasing function? Why is he a decreasing function when I see the answer 0 < x < 1?
16. Higher number problems (limit existence criteria, two important limits) LIM (2 ^ n) (n times of SiNx / 2) X-infinity X is not equal to 0 Go for the limit lim[2^n*sin(x/2^n)] X is not equal to zero, and the limit is that n tends to infinity Proof by pinch theorem
17. Mathematical simplification ratio: 2.5:0.4 210:720 two fifths to three fourths 4:5 / 2 6.3:4 / 7 0.15:0.03 1.2:0.6 9 / 5:5 / 6 39 / 13 13 / 91 (is it better to simplify these
18. Given the fraction a + 1 / a = 3, what is the value of A-1 / a
19. Find the following limit in the high number - 2.6 2) LIM (x tends to 0) arcsinx / X Let t = arcsinx, then x tends to 0, which is equivalent to t tends to 0 LIM (x tends to 0) arcsinx / x = LIM (t tends to 0) t / Sint = 1 What I don't understand is why if t = arcsinx, then x equals Sint? I know that t = arcsinx, sin on both sides, x equals Sint But there is a theorem that SiNx is infinitesimal. Then isn't Sint sin (Sint)?
20. How much is eight ninths multiplied by nine plus three fourths minus two thirds?