Answer
$$4{\bf{i}} + {\bf{k}}$$
Work Step by Step
$$\eqalign{
& \mathop {\lim }\limits_{t \to 4} \left( {t{\bf{i}} + \sqrt {4 - t} {\bf{j}} + {\bf{k}}} \right) \cr
& {\text{Evaluate the limit}} \cr
& {\text{As t approaches }}4,{\text{ the limit is}} \cr
& {\text{ = }}\left[ {\mathop {\lim }\limits_{t \to 4} t} \right]{\bf{i}} + \left[ {\mathop {\lim }\limits_{t \to 4} \sqrt {4 - t} } \right]{\bf{j}} + \left[ {\mathop {\lim }\limits_{t \to 4} \left( 1 \right)} \right]{\bf{k}} \cr
& = \left( 4 \right){\bf{i}} + \left( {\sqrt {4 - 4} } \right){\bf{j}} + \left( 1 \right){\bf{k}} \cr
& = 4{\bf{i}} + 0{\bf{j}} + {\bf{k}} \cr
& = 4{\bf{i}} + {\bf{k}} \cr} $$
