By L'Hopital's rule, we need to find the lim as x approaches 0 of (cos x - 1)/(3x^2). (Note we take the derivative of the numerator and denominator.

We can repeat this again to find that this limit is equivalent to lim as x approaches 0 of (-sin x)/(6x) which is equal to lim as x approaches 0 of (-cosx)/6 = -1/6.