# Problem sets and quizzes

Almost every Wednesday (before Thanksgiving) or Tuesday (after Thanksgiving), there will be an quiz during the last hour of the class period, closely based on an associated problem set. (However, there is no quiz in the first week of the course, and there is a final exam on Friday in the last week.) Unless otherwise specified, all problems are from the 3rd Edition of University Calculus: Early Transcendentals by Hass et al published by Addison–Wesley (Pearson).

Here are the quizzes and their associated problem sets (Quiz 1, Quiz 2, Quiz 3, Quiz 4, Quiz 5, Quiz 6, Quiz 7, Quiz 8, Quiz 9):

1. Continuity and limits:
• Date taken: October 12 Wednesday.
• Problems from Section 1.1 (pages 11–13): 7, 8, 13, 23, 25, 26, 71.
• Problems from Section 1.2 (pages 18–21): 5, 23, 24.
• Extra credit (essay): Explain your background in mathematics and what you are going to use this course for.
• Problems from Section 2.2 (pages 66–69): 1, 3, 9, 10, 15, 19, 25, 29, 35, 37, 43, 53, 57, 65.a.
• Problems from Section 2.3 (pages 75–78): 7, 9, 11, 13, 15, 17, 23, 27, 49.
• Problems from Section 2.4 (pages 83–85): 1, 3, 5, 11, 17, 23.
• Problems from Section 2.5 (pages 94–96): 1, 3, 5.d, 7, 9, 13, 15, 19, 21, 25, 27, 29, 39, 43, 77.
• Problems from Section 2.6 (pages 107–109): 1, 7, 9, 11, 15, 21, 25, 27, 29, 35, 41, 45, 49, 53, 57.
• Problems from Section 4.1 (pages 214–217): 1, 3, 5, 7, 9, 15, 17, 20.
2. Derivatives:
• Date taken: October 19 Wednesday.
• Problems from Section 2.1 (pages 56–58): 1, 3, 5.
• Problems from Section 3.1 (pages 117–119): 1, 2, 5, 11, 19, 23, 33, 34.
• Problems from Section 3.2 (pages 124–127): 1, 3, 5, 27, 28, 29, 30, 31, 34, 35, 37, 41, 45, 46, 47, 48.
• Problems from Section 3.3 (pages 135–137):
• 19, 20, 23, 61, 69;
• Extra credit: Show at least one intermediate step for each part: 74, and also show how the Reciprocal Rule is a special case of the Power Chain Rule.
• Problems from Section 3.6 (pages 158–161): 9, 11, 13, 83, 87, 104.
3. Differentiation:
• Date taken: October 26 Wednesday.
• Problems from Section 3.11 (pages 198–201): 19, 21, 23, 31, 33.
• Problems from Section 3.3 (pages 135–137): 1, 3, 5, 17, 25, 29, 31, 35, 41, 51.
• Problems from Section 3.6 (pages 158–161): 23, 31, 33, 35, 37.
• Problems from Section 3.7 (pages 164&166): 1, 3, 7, 21, 27, 29.
• Problems from Section 1.5 (pages 37&38): 11, 15, 19.
• Problems from Section 1.6 (pages 48–50): 43, 45, 47, 49, 51, 55, 57, 61, 63, 65.
• Problems from Section 3.8 (pages 174–176): 3, 21, 27, 39, 47, 51, 57, 65, 75, 89.
• Additional extra-credit problem: If f is a differentiable function, you can write y = f(x), so dy = f′(x) dx, which I'll call Equation 1. If f is also one-to-one, then you can rewrite y = f(x) as x = f−1(y), so dx = (f−1)′(y) dy, which I'll call Equation 2. Use Equations 1 and 2 to derive the rule that (f−1)′ = 1/(f′ ∘ f−1).
4. Quiz 4:
• Date taken: November 2 Wednesday.
• Problems from Section 1.3 (pages 27–29):
• 5, 6, 9, 11, 31, 33;
• These really use the Half-Angle Formulas: 47, 49.
• Problems from Section 3.11 (pages 198–201): 25, 27, 29, 37.
• Problems from Section 3.5 (pages 151–153): 1, 3, 5, 9, 11, 13, 15, 19, 23, 31, 35, 61.
• Problems from Section 3.6 (pages 158–161): 27, 29, 39, 43, 47, 65, 97, 98.
• Problem from Section 3.7 (pages 164&166): 11.
• Problems from Section 3.8 (pages 174–176): 63, 93.
• Problems from Section 1.6 (pages 48–50): 67, 69.
• Problems from Section 3.9 (pages 180&182):
• 1, 7, 9, 11, 13–20, 21, 23, 25, 31, 35, 37, 39;
• Extra credit: Show at least two intermediate steps: 52.
• Problems from Section 3.4 (pages 144–147): 1, 3, 5, 7, 9, 13, 17, 18, 21, 25.
• Problems from Section 3.10 (pages 187–190): 1, 2, 3, 6, 12, 13, 15, 23, 27, 29, 31, 41.
5. Quiz 5:
• Date taken: November 9 Wednesday.
• Problems from Section 3.11 (pages 198–201): 1, 2, 3, 4, 5, 6, 7, 10, 11, 13, 14, 15, 16, 51, 52, 53, 57.
• Problem from Section 3.4 (pages 144–147): 30.
• Problems from Section 4.2 (pages 222–224):
• 1, 5, 9, 11, 13, 15, 21, 25, 29, 31, 39, 43, 48;
• Extra credit: 62.
• Problems from Section 4.3 (page 228): Assume that the graphs include all unmarked endpoints but do not extend beyond the portion shown (so the functions' domains are [−4, 4]): 15, 16, 17.
• Problems from Section 4.5 (pages 248&249): 1, 3, 5, 11, 13, 15, 21, 27, 37, 43, 51, 55, 59, 60, 78.a.
6. Quiz 6:
• Date taken: November 16 Wednesday.
• Problems from Section 4.1 (pages 214–217): 11, 12, 13, 14, 23, 27, 37, 39, 41, 55, 61, 71.
• Problems from Section 4.3 (pages 228–230): 1, 3, 5, 7, 13, 19, 23, 29, 33, 43, 47.a&b, 49.a&b, 55.a&b, 67.
• Problems from Section 4.4 (pages 238–241):
• 1, 3, 5, 7, 11, 19, 23, 27, 43, 53, 81, 82, 83, 84, 85, 87, 101, 103, 104, 107, 108.
• Extra credit: Assume that the second derivative is also defined everywhere, and give reasons for your conclusion: 114.
• Problems from Section 1.4 (page 33): Optional: 1, 2, 3, 4.
7. Quiz 7:
• Date taken: November 29 Tuesday.
• Problem from Section 3.4 (page 146): 23.
• Problems from Section 4.6 (pages 255–260): 1, 3.c, 7, 9, 11, 13, 15, 29, 31, 37, 39, 43.a, 51, 53.a.
• Problems from Section 4.7 (pages 264&265): 1, 3, 5, 9, 10, 13, 21, 23.
• Additional extra-credit problem: Newton's Method is guaranteed to work under certain conditions given by the Kantorovich Theorem: If f is differentiable at x0, f(x0) and f′(x0) are nonzero, f is twice differentiable strictly between x0 and x0 − 2f(x0)/f′(x0), and |f′‍′(x)| ≤ ½|f′(x0)|2/|f(x0)| whenever x is strictly between x0 and x0 − 2f(x0)/f′(x0). Of the 4 applications of Newton's Method in Exercises 4.7.1, 4.7.9, and 4.7.10, which of these does Kantorovich's Theorem apply to and why?
• Problems from Section 5.2 (pages 299&300): 1–6, 7, 9, 11–16, 17, 19, 23, 29, 31, 33, 35, 39, 43.
• Problems from Section 5.1 (pages 291–293): 1–19 odd.
• Problems from Section 5.3 (pages 308–315): 9, 11, 13, 15, 17, 27, 35, 43, 49, 71.
8. Quiz 8:
• Date taken: December 6 Tuesday.
• Problems from Section 4.8 (pages 271–275):
• 1–24, 27, 29, 35, 39, 41, 45, 49, 51, 55, 61, 65, 75, 77, 81, 83;
• Note that the book is conflating the function y with its output y(x) at the input x: 95, 97, 105.
• Problems from Section 5.4 (pages 320–323): 1–15 odd, 23, 29, 39, 43, 47, 51, 57, 59, 61, 77, 78, 79.
• Problems from Section 5.5 (pages 329–330):
• 1–7 odd, 15, 17, 21, 25, 27, 31, 35, 39, 47, 55, 57, 61;
• Note that the book is conflating the function s with its output s(t) at the input t: 73, 75.
• Problems from Section 5.6 (pages 337–340): 1–9 odd, 13, 19, 25, 31, 37, 41, 45.
• Problems from Section 4.2 (pages 222–224): 40, 45, 47.
• Additional extra-credit problem: A positive quantity undergoes exponential growth if its rate of change with time is also positive and proportional to the size of the quantity (so a constant multiple of that size). If t stands for time and A stands for a quantity undergoing exponential growth, then write down a differential equation involving A and t to say that the rate of change of A with time is a positive constant k times A. If the value of A is a when t = 0, then solve this initial-value problem using separation of variables; you should be able to see why this is called ‘exponential’ growth. (The unspecified constants k and a should both appear in your answer.)
9. Quiz 9:
• Date taken: December 13 Tuesday.
• Problems from Section 5.6 (pages 337–340): 47, 51, 55, 57, 59, 67, 69, 75, 81, 87, 99.
• Problems from Section 6.3 (pages 376&377):
• 1, 3, 7, 9, 13, 15.a, 19.a;
• Extra credit: Show at least two intermediate steps (hint: implicit differentiation): 30.
• Problems from Section 6.1 (pages 361–364): 1, 5, 7, 13, 15, 17, 21, 23, 25, 35, 45, 51.
• Problems from Section 6.2 (pages 369–371): 1, 3, 5, 9, 15, 21, 25, 27, 31, 39.
• Problems from Section 6.4 (pages 381–383): 1–7.a odd, 13–21 odd.
That's it!
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