Problem 1
Limits, derivatives and integrals of vector-valued functions are all evaluated __________ -wise.
Problem 1
How is velocity different from speed?
Problem 1
If \(\vec{T}(t)\) is a unit tangent vector, what is \(\|\vec{T}(t)\| ?\)
Problem 2
If \(\vec{N}(t)\) is a unit normal vector, what is \(\vec{N}(t) \cdot \vec{r}^{\prime}(t) ?\)
Problem 2
The definite integral of a rate of change function gives __________.
Problem 2
What is the difference between displacement and distance traveled?
Problem 3
Why is it generally not useful to graph both \(\vec{r}(t)\) and \(\vec{r}^{\prime}(t)\) on the same axes?
Problem 3
What is the difference between average velocity and average speed?
Problem 4
Describe in your own words what an "osculating circle" is.
Problem 5
Sketch the vector-valued function on the given interval. $$ \vec{r}(t)=\left\langle t^{2}, t^{2}-1\right\rangle, \text { for }-2 \leq t \leq 2 $$
