Lim[ln(1+3X)]/sin4X
x->0
=
Lim{[ln(1+3X)]/3X}*[4X/sin4X]*(3/4)
x->0
=
Lim{[ln(1+3X)]/3X}*Lim[4X/sin4X]*(3/4)
x->0.x->0
=1*1*3/4
=3/4