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Can SiNx + cosx be replaced by X + 1 equivalently when x approaches 0? Can't addition and subtraction replace infinitesimal equivalently? Be sure. Can we replace the limit? How to find the limit of 1 / x power of this formula?
Addition and subtraction can not be replaced equivalently. It is said that if the whole of addition and subtraction is replaced, sometimes it is OK. The key depends on whether it is equivalent infinitesimal, that is, whether the replaced factor and the replaced factor are equivalent infinitesimal
For example, in this question, can SiNx + cosx be replaced by 1 + X? The judgment method is to divide the two and find the limit. If the limit value is 1, it depends on the situation. Sometimes it is OK to replace it as a whole
SiNx + cosx and 1 + X are equivalent factors, but whether they can be replaced depends on the situation
For example, your problem is the infinity limit of 1. Generally, we don't and can't use the equivalent infinitesimal in the base of index. There are two ways to solve this problem: one is to take logarithms on both sides, and then find the limit; the other is to change it into the exponential form with E as the base, and then find the limit
Original formula = (SiNx + cosx) ^ 1 / x = (1 + SiNx + cosx-1) ^ 1 / (SiNx + cosx-1) * (SiNx + cosx-1) * 1 / X
For (1 + SiNx + cosx-1) ^ 1 / (SiNx + cosx-1), we use two important limits and get that the limit is e
There are many ways to find the limit of (SiNx + cosx-1) * 1 / x, such as Taylor series expansion (expansion to the first order of X is OK, and the rest is replaced by O (x)), (I forgot the expansion) the limit is 1
So the answer is e
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______ ．
∵ point (3, 5) is on the straight line y = ax + B, ∵ 5 = 3A + B, ∵ B-5 = - 3a, then ab − 5 = a − 3A = − 13
Given that the point (2,6) is on the straight line y = ax + B (a, B are constants, and a is not equal to 0), then the value of a in B-6 is
Substituting point (3,5) into y = ax + B, we get: 5 = 3A + B, that is: B-5 = - 3a, so: a of B-5 = - 1 / 3
RELATED INFORMATIONS
- 1. 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______ ．
- 2. 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,
- 3. When x → 0, 1-cosx and axsinx are equivalent infinitesimals, then a=
- 4. When x → 0, the following functions are infinitesimal: A: SiNx / x, B: x ^ 2 + SiNx, C: ln (1 + x) / x, D: 2x-1
- 5. 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
- 6. 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
- 7. On finding limit by Taylor formula Why doesn't Taylor consider margin when he uses limit operation? Consider only polynomial of degree n?
- 8. Limit problems related to Taylor formula Find limit Lim [x-x ^ 2ln (1 + 1 / x)] (x → + ∞)
- 9. 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?!
- 10. 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?
- 11. Can we use the Equivalent Infinitesimal Substitution when the limit is exponentially calculated? For example, Lim [x - > 0, (1 + SiNx) ^ (1 / 2x)], can X in index 1 / 2x be directly replaced by SiNx? Can't SiNx be directly replaced by X?
- 12. F (x) is the fifth order infinitesimal of X?
- 13. The order of 1-x and 1 / 2 (1-x ^ 2) infinitesimal when x tends to 1
- 14. 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?
- 15. If x tends to 1, LIM (AX + b) / (x ^ 2-3x + 2) = 2, then what are a and B respectively
- 16. 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?
- 17. 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
- 18. Find the limit Lim [x tends to a] {e ^ a [e ^ (x-a) - 1]} / (x-a)
- 19. 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
- 20. When x approaches 0, the infinitesimals equivalent to sin3x are? A, 2x B, 3x C, 2x ^ 2 D, 3 (x-1)