Chapter 13.2, Problem 6E

(a)

To determine

To sketch: The plane curve with the vector equation $\text{r}\left(t\right)=e^t\text{i}+2t\text{j},t=0$.

(b)

To determine

To find: The vector ${\text{r}}^{\prime }\left(t\right)$ from the vector function $\text{r}\left(t\right)=e^t\text{i}+2t\text{j},t=0$.

(c)

To determine

To sketch: The position vector $\text{r}\left(t\right)$ and the tangent vector ${\text{r}}^{\prime }\left(t\right)$ at $t=0$.