Detailed process of LIM (x → 1) lncos (x-1) / (1-sin (π X / 2))

lim(x→1) lncos(x-1)/(1-sin(πx/2))
Let X-1 = t, t → 0
The original formula = LIM (t → 0) lncost / (1-sin (π (T + 1) / 2))
=lim(t→0) lncost/(1-cos(πt/2))
=lim(t→0) -sint/cost/(π/2*sin(πt/2))
=-2/πlim(t→0) sint/sin(πt/2)
=-2/π*2/π
=4/π^2

RELATED INFORMATIONS

1. Find Lim sin (x-1) / (x ^ 2-1) where X - > 1
2. lim(x---1)[sin^2(x)-sin^2(1)]/[x-1]=? University Advanced Mathematics, seek advice
3. Find Lim X - > ∞ (xtan2 / x + (1 / x ^ 2) * (SIN) x ^ 2)
4. lim(x(sin)^2)
5. Lim sin (x-1) / X-1 x tends to infinity
6. How much is SiNx, sin (1 / x), sin (x ^ 2) equal when Lim x approaches zero? And how much are they equal when Lim x approaches infinity? And how much is cos Tan in this case?
7. lim(x->0)[(x^2)*sin(1/x)]/sinx I use the equivalent infinitesimal, because when (x - > 0), SiNx ~ x, so sin (1 / x) ~ 1 / x, Then the original formula = LIM (x - > 0) (x ^ 2) * (1 / x) / SiNx = 1, right
8. LIM (x tends to infinity) (sin n) / N =?
9. lim（x→2）x-2 /sin(
10. lim(sin√(x+1)-sin√x) x→+∞
11. Limit: LIM (x - > 4) (x ^ 2-6x + 8) / (x ^ 2-5x + 4)
12. Finding limit LIM (x ^ 2-6x + 8) / x ^ 2 + X-6
13. 1.5 find the limit LIM (x → 4) (x ^ 2-6x + 8) / (x ^ 2-5x + 4) 1.5 find the limit LIM (x → 4) (x ^ 2-6x + 8) / (x ^ 2-5x + 4)
14. Help find a limit: LIM (x ^ 2-6x + 8) / (x ^ 2-5x + 4) x → 4
15. lim x→∞ x^2-6x+8/x^2-5x+4 Wrong. It's not infinity. It's four
16. Prove LIM (X -- > x0) 2 ^ x = 2 ^ x0 by definition
17. LIM (x tends to positive infinity) cosx / [e ^ x + e ^ (- x)] =?
18. f(x)=ln(x+1),lim(x->0)
19. 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
20. 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