Lim (4x+tg5x)/(x+sin2x) x->0

Question

Lim (4x+tg5x)/(x+sin2x) x->0

Answer 1

(4x+tg5x)/(x+sin2x)=(4+5*(sin5x/5x)*1/cosx)/1+2*(sin2x/2x))
lim(x->0)(4+5*(sin5x/5x)*1/cosx)/1+2*(sin2x/2x))=(4+5)/(1+2)=9/3=3