Chapter 12 - Vector-Valued Functions - 12.1 Exercises - Page 822: 63

$$\lim _{t \rightarrow \pi}(t \mathbf{i}+\cos t \mathbf{j}+\sin t \mathbf{k})=\pi \mathbf{i}-\mathbf{j}$$

Given $$\lim _{t \rightarrow \pi}(t \mathbf{i}+\cos t \mathbf{j}+\sin t \mathbf{k})$$ So, we get \begin{align} \lim _{t \rightarrow \pi}(t \mathbf{i}+\cos \pi \mathbf{j}+\sin \pi \mathbf{k})&=(\pi \mathbf{i}+\cos t \mathbf{j}+\sin t \mathbf{k})\\ &=\pi \mathbf{i}-\mathbf{j} \end{align}