![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
When x → 0, compare the following functions (infinitesimals) with X. which are the higher order infinitesimals of X? Which are the same order infinitesimals of X? Which are the lower order infinitesimals of X When x → 0, compare the following functions (infinitesimals) with X. which are the higher order infinitesimals of X? Which are the same order infinitesimals of X? Which are the lower order infinitesimals of X? Which are the same order infinitesimals? 1.tan^3 2.x^2(sin1/x)+x 3.cscx-cotx It's a process
1. Limtan ^ 3x / x = 0 infinitesimal of higher order
2. Lim [x ^ 2 (sin1 / x) + x] / x = 1 infinitesimal of the same order and equivalent infinitesimal
3. LIM (CSCX Cotx) / x = LIM (1-cosx) / xsinx = 1 / 2 infinitesimal of the same order
RELATED INFORMATIONS
- 1. 14. If the infinitesimal f (x) is an infinitesimal of higher order with respect to the infinitesimal g (x), then the limit of F (x) / g (x) is ()
- 2. On higher order infinitesimals o（x^2）+o(x^2)=?
- 3. Given that f (x) = a [(x-1) ^ 2] + B (x-1) + C - √ [(x ^ 2) + 3] is the infinitesimal of higher order of (x-1) ^ 2 when x → 1, find the values of constants a, B, C
- 4. X → 0, f (x) = x-sinx is the infinitesimal of higher order g (x) = xsinx We hope to divide f (x) and G (x) to get the form of the ratio of two infinitesimals, that is, the type of 0:0, and then judge their infinitesimal relationship from the simplified result, which may involve the equivalent infinitesimal transformation
- 5. What is the value of (2sinx-sin2x) / (x-sinx)? When I solve the problem, I first seek the derivative of the numerator denominator, the denominator is 1-cosx, and the numerator is 2cosx-2cos2x? Then I think if X -- > 0, the denominator is equal to 1, and the numerator is equal to 0, is this the answer? But if we expand cos2x into 2cos ^ 2x-1, the numerator is equal to 2. Strange, we can't expand it casually
- 6. What order of infinitesimal and high number is X-1
- 7. When x approaches 0, what order of infinitesimal is x ^ 2-sinx!
- 8. Is E2x power + 1 equivalent infinitesimal 2x or 2x + 2
- 9. Let f (x) be differentiable at x = 0 and f (0) = 0, then limx tends to 0, f (x) / x =?
- 10. If f '(0) = 1, then limx → 0f (x) - f (- x) / X=
- 11. How to prove that when p = (x ^ 2 + y ^ 2) ^ (1 / 2) - > 0, X * y is the infinitesimal of higher order of P?
- 12. α> How to prove that 1 / x ^ α is the infinitesimal of higher order of 1 / (㏑ x) ^ β
- 13. Find the maximum value of the second power - 2x + 3 of function y = x in the interval [0,3]
- 14. Find the extremum of the 2010 power of function (x-1) in [0,1]
- 15. Maximum and minimum values of function y = SiNx * cosx + SiNx + cosx
- 16. Find the function y = 2sin2x + SiNx cosx when x belongs to the maximum and minimum values of brackets - π / 2 to π / 2
- 17. How to simplify SiNx ^ 4 + cosx ^ 2
- 18. The x power of E plus x is equal to e, find X
- 19. If the x power of E is equal to x, what is x equal to
- 20. The x power of E is equal to one part of X to find X