How to prove the equivalence of 2 / 3 (cosx-cos2x) ~ x (x → 0)

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1. Cosx + cos2x = 0, the value of X
2. The process of solving LIM (x → 0) Tan (2x ^ 2) / 1-cosx
3. . 2x + 3x-6
4. (3x + 2) ^ 2 = 16 find the value of X. 1 | 2 (2x-1) ^ 3 = - 4 find the value of X
5. Find the value of X: (3x + 2) &# 178; = 16 1 / 2 (2x-1) &# 179; = - 4
6. Calculation: (2x ^ 2) ^ 2 + (- 3x) ^ 3 · (- 2x)
7. (40-3x) (30-2x) = 198 * 2
8. How to solve 5 / 3x-3 = 3-3 / 2x
9. How to solve 3x-5 times 2x of 3 = - 1
10. Given the function f (x) = x ^ 3-x decreasing on (0, a) and increasing on [a, positive infinity), try to find the value of A
11. What is the infinitesimal order of x ^ 1 / 3 + x ^ 4 / 3, x ^ 1 / 2 and 1-cos x ^ 2 when the ball x approaches 0?
12. Given that the function f (x) is continuous on (- ∞, + ∞) and satisfies ∫ (0, x) f (x-u) e ^ UDU = SiNx, X ∈ (- ∞, + ∞), find f (x)
13. High number problem: when x tends to 0, if the formula of X contains 1 / x, can't we use the formula of equivalent infinitesimal? When x tends to 0, if the expression of X contains 1 / x, can we not use the formula of equivalent infinitesimal? When x tends to infinity, if the expression of X contains 1 / x, can we use the formula of equivalent infinitesimal? For example, e ^ [(1 / (x (x-1))] - 1
14. My freshman year. Our senior math teacher said that the infinitesimal substitution rule is not suitable for addition and subtraction, but I see that some problems also use the substitution rule? How do you understand the teacher's words? Under what circumstances does the infinitesimal substitution rule not apply? Can you give examples, thank you! If you are satisfied, there is an addition
15. Why can higher order infinitesimal be omitted
16. Can high order infinitesimal do four operations?
17. Can f (x) = g (x) + O (x) (higher order infinitesimal) be discarded in calculation? Another is the formula of Taylor series. As long as there is a point x0 in the interval (a, b) with n-order derivative, it can be transformed into the form of Taylor series. Does the whole interval (a, b) have n-order derivative? The content of this picture is very little, which is hard to understand, The problem I encountered is whether the higher order infinity of F (x) - f (x0) = the second derivative of F (x0) * (x-x0) ^ 2 + O ((x-x0) ^ 2) can be omitted Let me comment:
18. Which is higher order infinitesimal? When x tends to zero, which is higher order infinitesimal between 2x-x2 and x2-x3,
19. Taylor's formula for the problem of limit SiNx ^ (- 2) * x ^ (- 2) when x approaches 0, we use Taylor's formula of order 3 How do you calculate it?
20. Proof of Taylor formula Taylor Mean Value Theorem means that function f (x) is equal to the sum of polynomial PN (x) (that is, Taylor formula of order n of F (x)) and RN (x) (remainder of Taylor formula of order n of F (x)), and the remainder has the form [f (ξ) * (x-x0) ^ (n + 1)] / [(n + 1)!], so what needs to be proved is RN (x) = [f (ξ) * (x-x0) ^ (n + 1)] / [(n + 1)!].! why only need to prove RN?!