?Let \(\mathbf{r}(t)=e^{t} \mathbf{i}+\sin t \mathbf{j}+\ln t \mathbf{k}\). Find the

Chapter 3, Problem 7

(choose chapter or problem)

Let \(\mathbf{r}(t)=e^{t} \mathbf{i}+\sin t \mathbf{j}+\ln t \mathbf{k}\). Find the following values:

a. \(\mathbf{r}\left(\frac{\pi}{4}\right)\)

b. \(\lim _{t \rightarrow \pi / 4} \mathbf{r}(t)\)

c. Is \(\mathbf{r}(t)\) continuous at \(t=t=\frac{\pi}{4}\)?

Text Transcription:

\mathbf{r}(t)=e^{t} \mathbf{i}+\sin t \mathbf{j}+\ln t \mathbf{k}

a. \mathbf{r}\left(\{\pi}{4}\right)

b. \lim _{t \rightarrow \pi / 4} \mathbf{r}(t)

c. \mathbf{r}(t) continuous at t=t=\{\pi}{4}\)?