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):

- 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.

- 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.

- 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 d*y*=*f*′(*x*) d*x*, 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 d*x*= (*f*^{−1})′(*y*) d*y*, which I'll call Equation 2. Use Equations 1 and 2 to derive the rule that (*f*^{−1})′ = 1/(*f*′ ∘*f*^{−1}).

- 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.

- 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.

- 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.

- 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*x*_{0},*f*(*x*_{0}) and*f*′(*x*_{0}) are nonzero,*f*is twice differentiable strictly between*x*_{0}and*x*_{0}− 2*f*(*x*_{0})/*f*′(*x*_{0}), and |*f*′′(*x*)| ≤ ½|*f*′(*x*_{0})|^{2}/|*f*(*x*_{0})| whenever*x*is strictly between*x*_{0}and*x*_{0}− 2*f*(*x*_{0})/*f*′(*x*_{0}). 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.

- 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.)

- 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.

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