Answer
\begin{align}
\lim _{t \rightarrow 2}\left(3 t \mathbf{i}+\frac{2}{t^{2}-1} \mathbf{j}+\frac{1}{t} \mathbf{k}\right)=6 \mathbf{i}+\frac{2}{3} \mathbf{j}+\frac{1}{2} \mathbf{k}
\end{align}
Work Step by Step
Given $$\lim _{t \rightarrow 2}\left(3 t \mathbf{i}+\frac{2}{t^{2}-1} \mathbf{j}+\frac{1}{t} \mathbf{k}\right) $$
So, we get
\begin{align}
\lim _{t \rightarrow 2}\left(3 t \mathbf{i}+\frac{2}{t^{2}-1} \mathbf{j}+\frac{1}{t} \mathbf{k}\right)=6 \mathbf{i}+\frac{2}{3} \mathbf{j}+\frac{1}{2} \mathbf{k}
\end{align}
