Answer
$$2{\bf{i}} - 3{\bf{j}} + 4{\bf{k}}$$
Work Step by Step
$$\eqalign{
& \mathop {\lim }\limits_{t \to 2} \left( {t{\bf{i}} - 3{\bf{j}} + {t^2}{\bf{k}}} \right) \cr
& {\text{Evaluate the limit}} \cr
& \mathop {\lim }\limits_{t \to 2} \left( {t{\bf{i}} - 3{\bf{j}} + {t^2}{\bf{k}}} \right) = \left( 2 \right){\bf{i}} - 3{\bf{j}} + {\left( 2 \right)^2}{\bf{k}} \cr
& {\text{Simplifying}} \cr
& {\text{ }} = 2{\bf{i}} - 3{\bf{j}} + 4{\bf{k}} \cr} $$
