You can access this page in I-Learn. It's the third bullet (Class Activities) on the home page.
- Alternate Possible Theme Song : The Power of Yet
Announcements
Hot-Chocolate Break Room
- Looking for SDL partners, or hoping to find a study group?
- Share anything with the class. This is one place you can share SDL's.
Self-Directed Learning Projects
- Have a specific plan that helps you develop deeper understanding. Think about Bloom's Taxonomy (see 1 and 2), and focus your efforts towards the highest levels.
- Carry out the plan, making modifications as needed (follow new leads, keep in the time constraints, etc.).
- Create something based on what you learned (Bloom's taxonomy).
- Share your work publicly.
- Complete a short steward report to reflect on your learning process.
Brain Gains
- Compute the derivative of the following functions:
- $f(x) = \pi^2$
- $\displaystyle g(x) = \frac{22}{7} x $
- $p(x) = x^3-2x^2+x+5$
Answer:
- $\displaystyle \frac{df}{dx} = 0$
- $\displaystyle g'(x) = \frac{22}{7}$
- $p'(x) = 3x^2-4x+1$
Where can I go for practice if my derivative skills are lacking? Thomas's calculus sections 3.3-3.6 are a great place to practice. You can use any calc text, if you had calculus at another school. In OpenStax, sections 3.3 - 3.6 are also a great place. https://openstax.org/books/calculus-volume-1/pages/3-3-differentiation-rules
- If a rover's motion on flat ground is described by $(x,y)=(3,4)t+(-2,5)$, what is its speed? Assume $x$ and $y$ are measured in meters and $t$ is given in minutes. (Hint: the rover's speed is constant in this situation.)
Answer:
When $t=0$, $(x,y) = (-2,5)$. When $t=1$, it is at $(1,9)$, so its position has changed by $\Delta x = 3$ and $\Delta y=4$. This means the rover has moved a total of $\sqrt{3^2+4^2}=5$ meters, so its speed is 5 meters/minute.
If we haven't had someone present 1.2 yet, let's do that now.
- Using the vectors on the screen, draw $\vec u+\vec v$ and $\vec u-\vec v$.
Answer:
We'll discuss this one.
If we haven't had someone present 1.6 yet, we'll have them share their work here.
- Give the component form of a vector of length 2 that is parallel to $\left<3,4\right>$.
Answer:
A unit vector is $\frac{1}{5}(3,4)$, so the desired vector is twice this, namely $$\frac{2}{5}(3,4) = \left(\frac{6}{5},\frac{8}{5}\right).$$
If we haven't had someone present 1.8 yet, we'll do that here.
- Draw and shade the region in space satisfying $0\leq z\leq 5$ with $x=2$.
Answer:
The region is an infinitely long sheet with $0\leq z\leq 5$, located 2 units out on $x$-axis, with the $y$ value taking on all possible values. The most common error here is to not let $y$ take on all possible values, in which case you'll end up with a short line segment at $y=0$ and $x=2$ running from 0 to 5 in the $z$ direction.
If we haven't had someone present 1.5 yet, we'll do that here.
Group Problems
Remember to pass the chalk between each problem.
- Give the component form of a vector that points from $(1,2,3)$ to $(-2,4,9)$.
- Give a vector equation of the line that passes through the point $(1,2,3)$ and $(-2,4,9)$ (all distances are in meters).
- An object starts at $P=(1,2,3)$ and each unit of time its displacement is $\vec v=(-4,5,1)$. Give an equation for the position $(x,y,z)$ at any time $t$.
- What is the speed of an object that follows the path described above?
- Use the law of cosines ($c^2=a^2+b^2-2ab\cos\theta$) to find the angle between the vectors $(-2,1)$ and $(1,3)$.
- Use the law of cosines to find the angle between the vectors $(1,2,3)$ and $(-2,4,9)$.
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