Question

What is the limit as x approaches 0 of `tan(x)/(3x)`?

Answer 1

The limit should give a 0/0 indeterminate form but using de l'Hospital Rule you should get 1/3 as result.

You can derive the numerator and denominator and do the limit of the new fraction obtained
Deriv. Num = 1/ `cos^2(x)`

Deriv. Denom. = 3

Now you are left with:
Lim[( 1/ `cos^2(x)`)/3] when x->0
you get 1/3