| Quiz 8 Solutions |
Mean score: 10/15. A handful of people wrote almost nothing for Problem 4. The title of the quiz was, in some way, a hint of what needed to be done there... Also, L'Hopital's Rule is NOT the quotient rule---please, please remember the distinction.
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| Quiz 7 Solutions |
Mean score: 10/15. Problem 2: many people forgot to cite MVT, or used it in a sort of hand-wavy way (some more hand-wavy than others). Problem 3: many people assumed the temperature would be of the form Ae^{kt}. This is true of the temperature relative to the fridge, but not of the actual temperature!
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| Wednesday 10/24 Handout |
Curve sketching and L'Hopital's rule. |
| Monday 10/22 Handout |
IVT, EVT, MVT. The problem is overkill. I overstated this course's expectations for your understanding of these theorems---sorry. |
| Quiz 6 Solutions |
Mean score: 10.3/15. Your score is curved by adding 2 to it (capped at 15).
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| Wednesday 10/17 Handout |
Logistic growth model (as an application of exponential growth), and max/min questions on second page. |
| Monday 10/15 Handout |
More miscellaneous differentiation stuff. |
| Quiz 5 Solutions |
Mean score: 11.6/15. The 11th derivative of a 10th degree polynomial is zero.
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| Wednesday 10/10 Handout |
Implicit Differentation |
| Monday 10/8 Handout |
Derivatives |
| Friday 10/5 Handout |
Derivatives |
| Wednesday 10/3 Handout |
Product and quotient rules, and trigonometric functions. |
| Monday 10/1 Handout |
Investigating subtleties of the power rule for derivatives. |
| Friday 9/28 Handout |
An application of polynomial derivatives: Descartes' rule of signs. |
| Wednesday 9/26 Handout |
More questions about the derivative. |
| Quiz 4 Solutions |
Mean score: 12.8/15. For problem 1, I used the same wording that showed up on HW4. Remember that being "continuous on an interval" has a very specific meaning! The question was not asking about the points at which f is continuous. For problem 2, I suggest reviewing the definition of continuity. For problem 3, a lot of people forgot to check that their choice of delta works. It's a pretty trivial check, but it should be done still. |
| Friday 9/21 Handout |
Questions on computing the derivative straight from the definition. |
| Wednesday 9/19 Handout |
Questions about limits at infinity, asymptotes, and sketching graphs.
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| Quiz 3 Solutions |
Mean score: 12.5/15. Problem 1 was mostly fine. In problem 2, a lot of people did not justify (a) why they could cancel out a common factor from the numerator and denominator, which is because the limit doesn't care about the specific value of a function at one point, and (b) why they could plug in the value of x after simplifying, which is because it's a rational function defined around 3 (direct substitution rule). In problem 3, many people forgot to consider what happens when x is negative. Also, many people "took the limit of an inequality" (don't do that; that's not how the squeeze theorem works).
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| Friday 09/14 Handout |
Handout for Friday 09/14. |
| Quiz 2 Solutions |
Median score: 11.5/15. Mean score: 10.3/15. Your score is curved by adding 2 to it (capped at 15). Quiz 2 from Friday 09/07. There was a very big spread of scores for this quiz.
In #2 a lot of people forgot to F.O.I.L. or something and made the so-called freshman's dream mistake. Unfortunately, if you expanded incorrectly, that set up the rest of the problem for disaster, so there was not much in the way of partial credit I could give you... Otherwise, points were assigned based on correct use of exponent laws, and getting the right answer.
If in #3 you miscalculated the range of f but correctly swapped the domain and range for f^{-1} (so your mistake carried over into (2)), you were only deducted for part (1), not for (2). For part (3), very few people realized that doing f^{-1} and then f is the same as doing nothing. You didn't HAVE to realize this to solve the problem, but it's something to be aware of. |
| Friday 09/07 Handout |
Handout for Friday 09/07. We'll continue thinking about problems from this handout on Monday. |
| Wednesday 09/05 Handout |
Handout for Wednesday 09/05 with problems about function manipulations, exponentials, and inverse functions. |
| Quiz 1 Solutions |
Median score: 13/15. Mean score: 12/15. The most common mistake was identifying g as tan(x) in Problem 1. Remember that tan(x) is periodic (with period pi). However, it was brought to my attention that Prof. Paulin drew only one period of tan(x) when he graphed it in class---I think because he was introducing inverse trigonometric functions at the time? |