On the top of the fraction, sin(3x) will keep going back and forth between -1 and 1.
On the bottom of the fraction, x+1 will keep getting larger, so ln(x+1) will keep getting larger, heading toward infinity.
The whole thing will keep going back and forth, above and below the x-axis, but it should gradually wiggle closer and closer to the x-axis. The limit should end up being 0.
You can see a graph of it by putting this in Google: plot((sin(3x)/(ln(x+1)))