9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions

Defining And Differentiating Vector-valued Functions — Quiz

Test your understanding of defining and differentiating vector-valued functions with 5 practice questions.

Practice Questions

Question 1

A vector-valued function can be written as $\mathbf{r}(t)=\langle f(t),g(t)\rangle$. What does $\mathbf{r}(t)$ represent?

Question 2

If $\mathbf{r}(t)=\langle t^2,\sin t\rangle$, what is $\mathbf{r}'(t)$?

Question 3

For $\mathbf{r}(t)=\langle x(t),y(t)\rangle$, which expression gives the slope $\frac{dy}{dx}$ of the curve traced by the vector function?

Question 4

If $\mathbf{r}(t)=\langle 3t,4t\rangle$, what is the speed of the particle at any time $t$?

Question 5

Which of the following is the correct derivative of $\mathbf{r}(t)=\langle e^t,t^3\rangle$?