What is the lim as x approaches 0 of 3 times 1 - cosx divided by x?

First, you can take the constant factor 3 out, to obtain 3 times the limit of (1 - cos x) / x.

Since this is of the form 0/0, you can use L'Hôpital's rule, which states that in such cases, you can take the derivative of both numerator and denominator. This results in the limit (as x approaches 0) of sin x / x, that is, 1 / 1 = 1. So, the final result is 3 times the limit of 1 = 3.