\lim _{t \rightarrow 0} \mathbf{f}(t)=\left[\lim _{t \rightarrow 0} \frac{\sin t}{t}\right] \mathbf{i}+\left[\lim _{t \rightarrow 0} \ln (3+t)\right] \mathbf{j}=\mathbf{i}+(\ln 3) \mathbf{j}.