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Does infinitesimal belong to limit existence
Generally speaking, it can be said that; strictly speaking, it can not be said that. 1. Infinitesimal is a process that tends to 0, which is the process of taking limit; and the process of taking limit can be a process that tends to any number, including the process that tends to infinity and the process that tends to infinitesimal. 2. If x tends to a certain number, it is
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- 1. Is the limit of infinitesimal zero?
- 2. Is it right to say that the limit of infinitesimal is 0?
- 3. Use the property of infinitesimal to calculate the following limit (1) Limx ^ 2cos1 / x where x tends to 0 (2) Lim [(arctanx) / x] where x tends to infinity
- 4. When x → 0, α (x) = kx2 and β (x) = 1 + xarcsinx − cosx are equivalent infinitesimals, then K=______ ．
- 5. Is the positive infinity power of a number less than one and greater than 0 equal to 0
- 6. What is the infinite power of E?
- 7. What is infinity plus infinitesimal For example, LIM (x →∞) (1 / x + e ^ x). It can be seen from the graph that it is infinite, or it can also be known that it is infinite by taking in the number to calculate, but how to solve this problem, In addition, LIM (x → - ∞) (1 / x + e ^ x)
- 8. What is infinity divided by infinitesimal
- 9. What is the power of infinitesimal to infinity? 0^∞ =0
- 10. Find the limit of function (x / x-1) - (1 / LNX) x tending to 1
- 11. Let f (x) have a first order continuous derivative, f (0) = 0, f ′ (0) ≠ 0, f (x) = ∫ x0 (x2 − T2) f (T) DT. When x → 0, f ′ (x) and XK are infinitesimals of the same order, and the constant k is obtained
- 12. If the derivative of F (x) is infinitesimal equivalent to the derivative of G (x), then are f (x) and G (x) infinitesimal equivalent
- 13. If the derivative of F (x) = ∫ x0 (x2-t2) f ′ (T) DT is infinitesimal equivalent to X2, then f ′ (0)=______ ．
- 14. If each bottle of purified water costs 2 yuan, the functional relationship between the amount of money spent on the purchase of purified water and Y (yuan) and the quantity purchased x bottles and the value range of the independent variable are given How much is it
- 15. The unit price of a notebook is 5 yuan. It takes y yuan to buy x (x ∈ {1,2,3,4,5} laptops. Try three expressions of the function y = f (x)
- 16. There are 500 notebooks for students, 5 for each, then the function between the remaining number of books y and the number of students x is______ The value range of the independent variable x is______ ．
- 17. Is the partial derivative of a function independent of the order of derivation
- 18. The relation between continuity and differentiability of binary function For example, if f (x, y) is continuous at point (0,0), then if x and y are all close to 0, f (XY) / (| x | y |) exists, is f (XY) differentiable at point (0,0) I know how to smoke The denominator is (| x | plus | y |)
- 19. If f (x) is a differentiable function, then dy is a linear function of △ X Why? Dy = f '(x) △ x, f (x) is a function of X, also called the linear function of △ x?
- 20. Let f (x) be differentiable, then when △ x → 0, △ y-dy is infinitesimal of higher order compared with X,