- Orthogonal, Perpendicular, Normal? Which is correct? You did (well/good)?
- "Exactly" (iɡˈzak(t)lē) and "Asymptote" (asɪm(p)təʊt)
- Consider the parametric curve $\vec r(t) = (3-2t^2,4t+5)$ for $-1\leq t\leq 2$.
- Draw the curve.
- Find $\frac{d\vec r}{dt}$. Then state $\frac{dx}{dt}$, $\frac{dy}{dt}$, and $\frac{dy}{dx}$, all in terms of $t$.
- Give a vector equation of the tangent line to the curve at $t=1$.
- Consider the curve $\vec r(t) = (2+4t,5-2t)$. Our goal is to visualize the difference quotient $\frac{\vec r(t+h)-\vec r(t)}{h}$.
- Draw the curve.
- When $t=0$ and $h=1$, add to your graph the vectors $\vec r(t+h)$ and $\vec r(t)$ based at the origin. Then add the difference vector $\vec r(t+h)-\vec r(t)$ by connecting the other two vectors.
- Repeat the previous when $t=0$ and $h=1/2$. In addition, draw the vector $\frac{\vec r(t+h)-\vec r(t)}{h}$.
- Repeat the previous when $t=0$ and $h=1/4$.
- Continue picking new values for both $t$ and $h$ until you can explain what the vector $\lim_{h\to 0}\frac{\vec r(t+h)-\vec r(t)}{h}$ represents.
- Repeat the previous problem with the curve $\vec r(t) = (t,t^2)$.
|
Sun |
Mon |
Tue |
Wed |
Thu |
Fri |
Sat |