Question

The limit of (1-cos3x)/x as x approaches 0

Answer 1

Use L'hopital's rule...

lim (1-cos(3x))/x = lim 3sin(3x) = 0
x->0 x->0

Answer 2

If you don't know L'Hopital's rule yet, use the known limit:
\[\lim_{x\to0}\frac{1-\cos ax}{ax}=0\]
Given function can be expressed as follows:
\[\lim_{x\to0}\frac{1-3\cos x}{x}\cdot\frac{3}{3}=3\lim_{x\to0}\frac{1-\cos3x}{3x}\]