We can solve this using Lopital theorem.
lim x₋>0 (x+sinx)/6x = lim x->0 (x+sinx)'/ (6x)' = lim x->0 (1+cosx)/6 = (1+1)/6 = 2/6=1/3
lim x->0 (x cosx - sin2x)/x = lim x->0 (x cosx - sin2x)' / x' =
lim x->0( cosx -x sinx - 2 cos2x) / 1 = 1 - 0 -2 = -1
Good luck!!!
