# Question Find the limit.>3. $$\lim _{t \rightarrow 0}\left(e^{-3 t} \mathbf{i}+\frac{t^{2}}{\sin ^{2} t} \mathbf{j}+\cos 2 t \mathbf{k}\right)$$ 4. $$\lim _{t \rightarrow 1}\left(\frac{t^{2}-t}{t-1} \mathbf{i}+\sqrt{t+8} \mathbf{j}+\frac{\sin \pi t}{\ln t} \mathbf{k}\right)$$>5. $$\lim _{t \rightarrow \infty}\left\langle\frac{1+t^{2}}{1-t^{2}}, \tan ^{-1} t, \frac{1-e^{-2 t}}{t}\right\rangle$$ 6. $$\lim _{t \rightarrow \infty}\left\langle t e^{-t}, \frac{t^{3}+t}{2 t^{3}-1}, t \sin \frac{1}{t}\right\rangle$$

Find the limit.>3. $$\lim _{t \rightarrow 0}\left(e^{-3 t} \mathbf{i}+\frac{t^{2}}{\sin ^{2} t} \mathbf{j}+\cos 2 t \mathbf{k}\right)$$
4. $$\lim _{t \rightarrow 1}\left(\frac{t^{2}-t}{t-1} \mathbf{i}+\sqrt{t+8} \mathbf{j}+\frac{\sin \pi t}{\ln t} \mathbf{k}\right)$$>5. $$\lim _{t \rightarrow \infty}\left\langle\frac{1+t^{2}}{1-t^{2}}, \tan ^{-1} t, \frac{1-e^{-2 t}}{t}\right\rangle$$
6. $$\lim _{t \rightarrow \infty}\left\langle t e^{-t}, \frac{t^{3}+t}{2 t^{3}-1}, t \sin \frac{1}{t}\right\rangle$$
Transcribed Image Text: Find the limit.>3. $$\lim _{t \rightarrow 0}\left(e^{-3 t} \mathbf{i}+\frac{t^{2}}{\sin ^{2} t} \mathbf{j}+\cos 2 t \mathbf{k}\right)$$ 4. $$\lim _{t \rightarrow 1}\left(\frac{t^{2}-t}{t-1} \mathbf{i}+\sqrt{t+8} \mathbf{j}+\frac{\sin \pi t}{\ln t} \mathbf{k}\right)$$>5. $$\lim _{t \rightarrow \infty}\left\langle\frac{1+t^{2}}{1-t^{2}}, \tan ^{-1} t, \frac{1-e^{-2 t}}{t}\right\rangle$$ 6. $$\lim _{t \rightarrow \infty}\left\langle t e^{-t}, \frac{t^{3}+t}{2 t^{3}-1}, t \sin \frac{1}{t}\right\rangle$$
Transcribed Image Text: Find the limit.>3. $$\lim _{t \rightarrow 0}\left(e^{-3 t} \mathbf{i}+\frac{t^{2}}{\sin ^{2} t} \mathbf{j}+\cos 2 t \mathbf{k}\right)$$ 4. $$\lim _{t \rightarrow 1}\left(\frac{t^{2}-t}{t-1} \mathbf{i}+\sqrt{t+8} \mathbf{j}+\frac{\sin \pi t}{\ln t} \mathbf{k}\right)$$>5. $$\lim _{t \rightarrow \infty}\left\langle\frac{1+t^{2}}{1-t^{2}}, \tan ^{-1} t, \frac{1-e^{-2 t}}{t}\right\rangle$$ 6. $$\lim _{t \rightarrow \infty}\left\langle t e^{-t}, \frac{t^{3}+t}{2 t^{3}-1}, t \sin \frac{1}{t}\right\rangle$$