tolong dibantu ^^ tentukan nilai limit berikut: Limit x mendekati 0 dengan 1 - cos x/ x sin 3x = ...?

jawab


lim(x->0) (1 - cos x). (x . sin 3x)

(1- cos x )/(x . sin x) = 
= ( 1 - {1- 2 sin² ¹/₂ x}) / (x . sin 3x)
= (2 sin² ¹/₂ x) /(x .sin 3x)


limit (x->0)  (2 sin² ¹/₂ x)/(x .sin 3x)
= 2 (¹/₂ x)²/ (x)(3x)
= 2 (1/4)/(3)
= 2/12
= 1/6

Langsung ya
1-cos x = 2sin²1/2x /X sin 3x
Jadi 2 ((1/2)x)/x) ((1/2)x/3x)
=2×½×1/6
=1/6