LIM (x → 0 +) lncotx / LNX is used to find the limit

lim(x→0+) lncotx/lnx
=lim(x→0+) (1/cotx)*(-csc^2x)/(1/x)
=-lim(x→0+)x/sinxcosx
=-1

RELATED INFORMATIONS

1. Let f (x) be defined in a neighborhood of x = a, then a sufficient condition for f (x) to be differentiable at x = a is? A.lim (x approaches 0) [f (a + 2H) - f (a) Dlim (x tends to be 0) H [f (a + 1 / h) - f (a)] exists. Explain in detail why abd is not right (especially d)? A. LIM (H tends to 0) [f (a + 2H) - f (a + H)] / h exists, while LIM (H tends to 0) [f (a + H) - f (A-H)] / 2H exists C. LIM (H tends to 0) [f (a) - f (A-H)] / h exists. ABC option was forgotten just now, now add it. D is changed to dlim (H approaches infinity) H [f (a + 1 / h) - f (a)]
2. Given the function f (x) = 2ln3x + 8x, the value of LiMn →∞ f (1 − 2 △ x) − f (1) △ x is () A. 10B. -10C. -20D. 20
3. Given function, find Lim f (x) Given the function y = {x + 1, x < 1, Lim f (x) =? 1/x,x≥1 x→0 A. 1 b.0 C. No D.2
4. lim(x→0)[(secx)^2-1] /(1-cosx)
5. The limit of tanx-6 / secx + 5 when x tends to Π / 2
6. Is the square of LIM x → 0 (cosx-cos3x) / X equal to? Lim x → 0 (cosx-cos3x) / x square, please write the steps!
7. Find Lim x → 0 (Tan 2x SiNx) / X and lim x → 0 (COS x-cos 3x) / x ^ 2
8. Ln x = ax has several real roots (a > 0)
9. Given function f (x) = ln (AX) / (x + 1) - ln (AX) + ln (x + 1) Given the function f (x) = ln (AX) / (x + 1) - ln (AX) + ln (x + 1), (a is not equal to 0 and R) 1. Find the definition field of function f (x) 2. Find the monotone interval of function f (x) 3. When a > 0, if there is x such that f (x) ≥ ln (2a) holds, the value range of a is obtained
10. F (x) = x ^ 2 - ax + ln (x + 1), a belongs to R 0 F extremum when a = 2 If the function f (x) always has f prime (x) greater than x in the interval (0,1), find the value range of real number a The word "0" doesn't mean The speed of copying is fast
11. The derivative of F (x) = | LNX | at point (1,0) is The derivative of F (x) = | LNX | at point (1,0) is
12. Finding the derivative of F (x) = (x + 1) lnx-x + 1
13. F (x-1 / x) = LNX, find the derivative of F (x)
14. Ask What's the derivative of 1 / LNX
15. The derivative of LNX / A
16. [derivative] prove inequality in x < x < e ^ x, x > 0 by monotonicity It is proved that in x < x < e ^ x,
17. Proving: inequality 1 / lnx-1 / (x-1)
18. Proof: when x > 0, the inequality LNX > = 1-1 / X
19. Let g (x) = {① e ^ x, X ≤ 0, ② LNX, x > 0, then the solution set of inequality g (x) ≤ 1 about X is () A.（-∞,1] B.(-∞,e] C.[o,e] D.[0,1]
20. It is proved that the derivative of F (x) * LNX + F (x) * (2 / x) = 0