1. Lim x=0 (x2-4) tan 3x / x3+5x2+6x 2. Lim x=0 cos 4x-cos 6x / cos 2x.sin2 5x

limit trigonometri

1. lim(x->0)  { (x²-4) . tan 3x ] / (x³ + 5x² + 6x)
= lim(x->0) { (x+2)(x-2). tan 3x " / (x)(x+2)(x+3)
= lim (x->0)  (x-2) . tan 3x / (x+3). (x)
= lim (x->0)  (x-2)/(x+3) .  lim(x->0) tan 3x/ x
x= 0 --> (-2/3) . (3x/x) = - 2/3 .(3)
limit = -2

2. lim(x->0) {{ cos 4x - cos 6x)} / ( cos 2x. sin² 5x)
= lim(x->0) - {cos 6x - cos 4x) / (cos 2x. sin² 5x)
= lim(x->0) - (- 2 sin 5x. sin x)  (cos 2x . sin 5x. sin 5x)
= lim(x->0  2/cos 2x . lim (x->0) (sin 5x. sin x)/(sin5x. sin 5x)
x = 0
= (2/ cos 0) . (5x. x)/(5x.5x)
= (2/1).(1/5)
= 2/5