- Zone of Proximal Development - Out of Class Group Study Suggestion - Your goal: Discover what your questions are. This requires we attempt something first so we know where our boundaries are. I highly recommend working with others, and as you do so, work on problems that no one yet has started. Each work on it by yourself, and then ask questions of each other as soon as you have them. If you meet during my office hour times, and you can't answer your questions together, invite me to join you.
Rapid Recall
- Draw $\ds \frac{x^2}{16}+\frac{y^2}{25}=1$.
- Draw $\ds \frac{x^2}{16}-\frac{y^2}{25}=1$.
- Draw $\ds -\frac{x^2}{16}+\frac{y^2}{25}=1$.
Group problems
- Draw $\ds \frac{(x-1)^2}{16}+\frac{(y-5)^2}{9}=1$ and then draw $\ds \frac{(x-1)^2}{16}-\frac{(y-5)^2}{9}=1$.
- Draw $\ds \frac{(x+2)^2}{9}+\frac{(y-4)^2}{25}=1$ and then draw $\ds -\frac{(x+2)^2}{9}+\frac{(y-4)^2}{25}=1$.
- Draw the parametric curve $x=2+3\cos t$, $y=5+2\sin t$ in the $xy$-plane. [Hint: Make a $t,x,y$ table of points, and then graph the $(x,y)$ coordinates.]
- Draw $x=3-2\cos t$, $y=4+5\sin t$ in the $xy$-plane.
- Draw the parametric curve $\vec r(t) = (2+t^2,3t-4)$ for $-2\leq t\leq 3$.
- Give $\frac{d\vec r}{dt}$. Then state $\frac{dx}{dt}$, $\frac{dy}{dt}$, and $\frac{dy}{dx}$.
- Give a vector equation of the tangent line to the curve at $t=2$.
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