Answer
$${\text{The limit does not exist}}$$
Work Step by Step
$$\eqalign{
& \mathop {\lim }\limits_{t \to 1/3} \frac{{t - 1/3}}{{{{\left( {3t - 1} \right)}^2}}} \cr
& {\text{Try to evaluate the limit}} \cr
& \mathop {\lim }\limits_{t \to 1/3} \frac{{t - 1/3}}{{{{\left( {3t - 1} \right)}^2}}} = \frac{{1/3 - 1/3}}{{{{\left( {3\left( {1/3} \right) - 1} \right)}^2}}} = \frac{0}{0} \cr
& {\text{Multiply the numerator and denominator by 3}} \cr
& \mathop {\lim }\limits_{t \to 1/3} \frac{{t - 1/3}}{{{{\left( {3t - 1} \right)}^2}}} = \mathop {\lim }\limits_{t \to 1/3} \frac{{3t - 1}}{{3{{\left( {3t - 1} \right)}^2}}} \cr
& {\text{Simplify}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{3}\mathop {\lim }\limits_{t \to 1/3} \frac{1}{{3t - 1}} \cr
& {\text{Evaluate the limit}} \cr
& \frac{1}{3}\mathop {\lim }\limits_{t \to 1/3} \frac{1}{{3t - 1}} = \frac{1}{3}\left( {\frac{1}{{3\left( {1/3} \right) - 1}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{0} \cr
& {\text{The limit does not exist}} \cr} $$
