What is infinity divided by infinitesimal

-1, infinity is a positive number, infinitesimal is a negative number, these two are opposite numbers, the sum is 0, the division is negative 1

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1. What is the power of infinitesimal to infinity? 0^∞ =0
2. Find the limit of function (x / x-1) - (1 / LNX) x tending to 1
3. Limit: when x tends to positive infinity, does the limit of function f (x) = LNX ax tend to negative infinity;
4. What's the integral of 1 / X & sup2;? What's the integral of 1 / x square? What's the integral of 1 / X LNX? What's the integral of 1 / X & sup2? It's - 1 / x + C
5. lim(x→1)(x^2-2x+1)/lnx-x+1
6. LIM (x approaches infinity) √ (the square of x-3x) / 2x + 1 How to do it
7. On the theorem of infinitesimal and infinitesimal For example, theorem: the sum of finite infinitesimals is also infinitesimal Suppose that when x tends to x0, it is proved in the book that the sum of two infinitesimals when x tends to x0 satisfies the condition of infinitesimal But I think, why do two infinitesimals just tend to x0 when proving? The theorem says that two infinitesimals do not necessarily have the same x0? For example, the x power of (0.5) and the x power of 2 are infinitesimal. Although these two functions are not infinitesimal when they tend to finite values, their sum will not be infinitesimal Why?
8. Limx → 0sin3x / sin5x, find the limit
9. Find the limit: limx (1 + 2x) &# 185; divide by the square of X, when x approaches 0, how to find it,
10. It is proved that the function y = (1 / x) sin (1 / x) is unbounded in the interval (0,1], but it is not infinite when x tends to positive infinity
11. 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)
12. What is the infinite power of E?
13. Is the positive infinity power of a number less than one and greater than 0 equal to 0
14. When x → 0, α (x) = kx2 and β (x) = 1 + xarcsinx − cosx are equivalent infinitesimals, then K=______ ．
15. 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
16. Is it right to say that the limit of infinitesimal is 0?
17. Is the limit of infinitesimal zero?
18. Does infinitesimal belong to limit existence
19. 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
20. If the derivative of F (x) is infinitesimal equivalent to the derivative of G (x), then are f (x) and G (x) infinitesimal equivalent