2. Vector-Valued Functions

Derivatives Of Vector Functions — Quiz

Test your understanding of derivatives of vector functions with 5 practice questions.

Practice Questions

Question 1

If $\mathbf{r}(t) = \langle t^2, \sin(t), e^{3t} \rangle$, what is the derivative $\mathbf{r}'(t)$?

Question 2

A particle moves along a path described by $\mathbf{r}(t) = \langle \ln(t), t^2, \frac{1}{t} \rangle$. At $t = 1$, what is the velocity vector $\mathbf{v}(1)$?

Question 3

Given $\mathbf{r}(t) = \langle e^t, \cos(t), \sin(2t) \rangle$, what is the speed $\|\mathbf{v}(t)\|$ at $t = 0$?

Question 4

If $\mathbf{r}(t) = \langle t^3, e^{-t}, \sin(t) \rangle$, at what value of $t$ is the acceleration vector $\mathbf{a}(t)$ equal to $\langle 6, -e^{-t}, -\sin(t) \rangle$?

Question 5

Let $\mathbf{r}(t) = \langle t, t^2, t^3 \rangle$. What is the curvature $\kappa(t)$ at $t = 1$?