Question

lim a->0 
sin2a-tg2a/a^3
Помогите пожалуйста!

Answer 1

(sin2a-tg2a)/a^3 = sin2a(cos2a - 1)/(a^3*cos2a) = 
sin2a( - 2sin^2a)/(a^3*cos2a) = - 4cosa*sin^3a/(a^3*cos2a)
= ( - 4cosa/cos2a)*(sin^a/a^3)
lim(a->0)(sin2a - tg2a)/a^3 = - 4lim(a->0)(cosa/cos2a)*
lim(a->0)(sina/a)^3 = - 4*1 = - 4