Question

Hitunglah lim tan x-sinx:x^3 dengan x→0

Answer 1

Lim (x → 0) (tanx - sinx) / x^3
= lim (x → 0) sinx / x * lim (x → 0) (1 - cosx) / (x^2 *cosx)
= 1*lim (x → 0) 1/cosx*lim (x → 0) (1-cosx) * (1+cosx) / [x^2*(1+cosx)]
= 1 * 1 * lim (x → 0) sin^2 x / x^2 * lim (x → 0) 1 / (1 + cosx)
= 1 * 1 * 1 * 1/2
= 1/2.