Which is higher order infinitesimal? When x tends to zero, which is higher order infinitesimal between 2x-x2 and x2-x3,

RELATED INFORMATIONS

• 1. 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:
• 2. Can high order infinitesimal do four operations?
• 3. Why can higher order infinitesimal be omitted
• 4. 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
• 5. 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
• 6. Given that the function f (x) is continuous on (- ∞, + ∞) and satisfies ∫ (0, x) f (x-u) e ^ UDU = SiNx, X ∈ (- ∞, + ∞), find f (x)
• 7. 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?
• 8. How to prove the equivalence of 2 / 3 (cosx-cos2x) ~ x (x → 0)
• 9. Cosx + cos2x = 0, the value of X
• 10. The process of solving LIM (x → 0) Tan (2x ^ 2) / 1-cosx
• 11. 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?
• 12. 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?!
• 13. Limit problems related to Taylor formula Find limit Lim [x-x ^ 2ln (1 + 1 / x)] (x → + ∞)
• 14. On finding limit by Taylor formula Why doesn't Taylor consider margin when he uses limit operation? Consider only polynomial of degree n?
• 15. When x → 0, (e ^ x-1) sin2x is equivalent to [(1 + x) ^ 1 / 2-1)] ln (1 + 2x) But the answer is the same level but not equivalent... Is I wrong or the answer is wrong? I'm not sure about the exam review
• 16. In using the Equivalent Infinitesimal Substitution to find the limit, 1: when x tends to 0, sin (f (x)) ~ f (x) 2: when f (x) tends to 0, sin (f (x)) ~ f (x) which is correct
• 17. When x → 0, the following functions are infinitesimal: A: SiNx / x, B: x ^ 2 + SiNx, C: ln (1 + x) / x, D: 2x-1
• 18. When x → 0, 1-cosx and axsinx are equivalent infinitesimals, then a=
• 19. The first higher number: infinitesimal comparison Higher Education Press: Advanced Mathematics (Volume I) P59 original sentence: the different results of the quotient of two infinitesimals reflect the differences in the "speed" of different infinitesimals tending to zero. Q: for example, if x / X indicates that x is of higher order, then x tends to zero faster than x, but when x belongs to 0 to 1 / 2, X falls faster than x under the same X difference,
• 20. Given that the point (3, 5) is on the straight line y = ax + B (a, B are constants, and a ≠ 0), then the value of ab − 5 is______ ．