Lim x menuju 0 sin 2x – tan 2x per x^3…tolong lah

Limit Trigonometri

lim(x->0) ((sin 2x ) – tan(2x)) / (x³)

sin (2x) – tan (2x) =
=  sin (2x ) – (sin 2x)/(cos 2x)
= ( sin2x. cos 2x – sin 2x)/(cos 2x)
= sin 2x( cos 2x – 1) /cos 2x
=  tan 2x (2 sin² 2x) / cos 2x

limit (x ->0) (sin 2x – tan 2x) / (x³)
= limit (x -> 0) ( tan 2x )(2 sin² 2x) / (cos 2x) (x³)
= limit (x ->0)  (1 /cos 2x ) (tan 2x)/(x) . (2 sin² 2x) /(x²)
x = 0
= ( 1/ cos 0). (2x /x) (2)(2x)² /(x²)
= (1/1) (2)(2)(4x²/x²)
= 1 (2)(2)(4)
= 16