lim x->0, (sin3x) / ln(x+1)

Question

Conjecture the correct answer for lim x -> 0 of sin3x / ln(x + 1), Support claim with best evidence.

Answer 1

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)))