- No plans to Zoom, now that we've hit the
7th of February. But I can if it becomes medically necessary.
Here's a menu of our past zooms...
- I've graded your homework (1.1 and 1.2). A couple of comments:
- #8: the final point of this exercise was that we were creeping up on the instantaneous rate of change in population (the derivative!). It should have been around 728 people/year (units are important).
- #7: Limits must exist from both sides to exist at a point.
- You have a new assignment:
Read section 1.4, and to carry out the preview exercise. I'll have you upload your preview work to Canvas, so I can see it. This will be the pattern from now on.... I'll also have you turn in your handout work on Canvas, too. It will also be due by class-time on Wednesday.
You are free to ask questions, and work together on these! If you do work with someone, you might indicate that on your papers.
I've also assigned a couple of homework problems from section 1.3, which are due Monday.
- Your first exam is next Wednesday; it will cover material through section 1.4: the derivative function.
What are the units of "the slopes of these lines"?
In particular, last time I asked you to carry out the Section 1.3 Activity, Derivatives at a point:
I asked you to carry out this exercise, and when asked for a screenshot, capture that and then add it to an entry in a discussion on Canvas.
That seemed to go well, from my perspective -- except that there's a significant-sized group that didn't do it...:(
- We'll start by going over the results of our worksheet (the
algebraic parts); comparing them to our graphs in the
Discussion.
\[ 3. f(x)=3x-2; a=1 \]
\[ 4. f(x)=2x^2; a=2 \]
\[ 5. f(x)=x^3; a=1 \]
- Next we'll take a look at some slightly trickier algebraic expressions:
Exercise #9b,c in section 1.3.
\[ b. f(x)=\frac{1}{x}; a=1 \]
\[ c. f(x)=\sqrt{x}; a=1 \]
- Then we'll think about extending those beyond single points,
leading us to this important definition:
Definition 1.4.2. Let $f$ be a function and $x$ a value in the function's domain. We define the derivative of f, a new function called $f'$ by the formula \[ f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} \]