Limx → 0 (x + sin2x) / (x-sin2x) = how many? No lobita rule

Divide up and down by 2x
=lim(1/2+sin2x/2x)/(1/2-sin2x/2x)
=(1/2+1)/(1/2-1)
=-3

RELATED INFORMATIONS

1. Limx → 0 {√ (x + 1) - 1} / sin2x
2. When x → 0, which of the following infinitesimals is (SiNx) / x, 2x-1, (1 / x) / ln (1 + x), x ^ 2 + simx?
3. When x approaches 0, the infinitesimals equivalent to sin3x are? A, 2x B, 3x C, 2x ^ 2 D, 3 (x-1)
4. When limx approaches 0, can (e ^ x-1-x) / x ^ 2 be equal to LIM (e ^ x-1) / x ^ 2-lim (x / x ^ 2) according to the four mixed operations of limit
5. Find the limit Lim [x tends to a] {e ^ a [e ^ (x-a) - 1]} / (x-a)
6. Given LIM (x - > 0) (2arctanx ln (1 + X / 1-x)) / x ^ n = C! = 0, find the values of constants C and N. the solution of this problem is done by using the law of Robida, My method is to split (2arctanx ln (1 + X / 1-x)) / x ^ n into (2arctanx / x ^ n) - (LN (1 + X / 1-x)) / x ^ n, and then use the equivalent infinitesimal to solve it. Why is the result different from the original solution? When is the appropriate time to use the equivalent infinitesimal
7. Does the limit of a function tend to infinity need to be equal when it tends to positive and negative infinity It seems that as long as the limit tends to be positive infinity, isn't it?
8. If x tends to 1, LIM (AX + b) / (x ^ 2-3x + 2) = 2, then what are a and B respectively
9. Why is f (x) = LIM (n →∞) (1-x ^ 2n) / (1 + x ^ 2n) x equal to - x when | x | 1? Is the independent variable x? What is n?
10. The order of 1-x and 1 / 2 (1-x ^ 2) infinitesimal when x tends to 1
11. Finding the limit process of (sin2x-1) / X when the limit x tends to 0 Find the limit of (sin2x-1) / X when x tends to 0 process
12. If the function f (x) is defined near x = 0, and f (0) = 0, f ′ (0) = 1, then limx → 0f (x) x = 1
13. Taking x as the base infinitesimal, finding the principal part of (x + SiNx ^ 2) ^ 3 Is [x + sin (x ^ 2)] ^ 3 There is another: sin (x + π / 6) - 1 / 2 is still principal
14. When x tends to zero, which is higher order infinitesimal compared with SiNx (TaNx + x ^ 2)
15. Try to determine the values of constants a, B and C such that e ^ x * (1 + BX + CX ^ 2) = 1 + ax + ο (x ^ 3), where ο (x ^ 3) is the infinitesimal of higher order than x ^ 3 when x → 0 There is an answer (e^x)*(1+Bx+Cx^2)=(1+x+x^2/2!+x^3/3!+o(x^3))*(1+Bx+Cx^2)=1+(1+B)x+(1/2+B+C)x^2+(1/6+B/2+C)x^3+o(x^3)=1+Ax+ο(x^3) So, there are 1 + B = a, 1 / 2 + B + C = 0, 1 / 6 + B / 2 + C = 0 The solution is: a = 1 / 3, B = - 2 / 3, C = 1 / 6 But I can't understand the second equal sign
16. Sum of infinitesimals and sum of infinitesimals The sum of infinitesimals is not necessarily infinitesimal. It may be infinitesimal, infinitesimal or bounded However, the sum of finite infinitesimals is infinitesimal. I am a little confused about these two problems. Can you give me a simple example to explain them?
17. Let's ask a limit problem. If a (x) is an infinitesimal of higher order of X, then when x approaches zero, a (x) / x = 0, and a (x) * x / x = 0, right?
18. What is higher order infinitesimal? How to apply it in finding limit? Give an example
19. Find the maximum and minimum values of the function f (x) = [(SiNx) ^ 4 + (cosx) ^ 4 + (sinxcosx) ^ 2] / (2-2sin2x), and point out the value of X when the maximum value is taken?
20. How to simplify SiNx ^ 4 + cosx ^ 4, What about SiNx ^ 4-cosx ^ 4