tentukan limit dari. 1. lim x mendekati π cos2x-1 / sin x 2. lim x mendekati π/3 x+π/3 / tan (x+π/3).
3. lim x mendekati 0 sin x / sin 2x 4. lim x mendekati 0 1-cos 2x / sinx
5. lim u mendekati π/2 tan u / u

LImit trigonometri

1.limx->π)  (cos 2x -1)/sin x
lim(x-> π)  (-2 sin² x)/ (sin x)
= lim(x->π)  -2 sin x
x= π --> limit  = -2 sin π  = - 2 (0)= 0

2.limit(x->π/3)  (x+π/3)/ tan (x+π/3)
= (x+π/3)/ (x+π/3)
= 1

3. limit (x->0)  sin x /sin 2x
= x/2x
= 1/2

4. lim(x->0) (1- cos 2x)/(sin x)
= lim(x->0) (2 sin² x)/(sin x)
= lim(x->0) 2 sin x
x  =0 --> 2 sin 0 = 2(0)+ 0

5. lim(u-> pi/2)   tan u/ u
= u/u = 1