# Homework

In case you miss a homework assignment in class, you can find it below. Unless otherwise specified, all problems are from the 2nd Edition of University Calculus: Early Transcendentals published by Addison Wesley (Pearson). When I return graded homework, I may post some solutions here too; see the downloading help if you have trouble reading them. (See the grading policies for general instructions on doing homework and how it will be graded.)
1. Introduction and review:
• Date assigned: October 6 Monday.
• Date due: October 7 Tuesday.
• Problems from Section 1.1 (pages 11–13):
• No additional work needed: 7, 8;
• Show at least one intermediate step: 13;
• No additional work needed: 23, 25, 26;
• Show a formula for x as a function of h as an intermediate step: 71.
• Problems from Section 1.2 (pages 18–21):
• Show at least one intermediate step: 5;
• No additional work needed: 23, 24.
• Extra credit (essay): Explain your background in mathematics and what you are going to use this course for.
2. Continuity:
• Date assigned: October 7 Tuesday.
• Date due: October 9 Thursday.
• Advice: Refer to the lecture notes on continuity for definitions and basic principles, but also look at the examples in the textbook.
• Problems from Section 2.5 (pages 95–97):
• Note: Since we define continuity before limits, do not use limits in any of your answers. You only need to know how to recognize continuity from an unbroken graph or from an analytic formula.
• No additional work needed: 1–4, 5.d, 6.d, 7.b, 8, 9, 10;
• Show what equations or inequalities you solve (unless the function is continuous everywhere and there is nothing to solve): 13, 15, 19, 21, 25, 27;
• Show the simplified form of g: 29, 39;
• Show what equation you solve for a: 43.
• Some answers: DjVu format, PDF format.
3. Epsilontics:
• Date assigned: October 8 Wednesday.
• Date due: October 13 Monday.
• Advice: Refer to the lecture notes on continuity for definitions and basic principles, but also look at the examples in the textbook.
• Problem from Section 2.5 (pages 95–97): Show why the Intermediate Value Theorem applies, but skip the part that requires a graphing calculator: 77.
• Problems from Section 2.3 (pages 76–79):
• Note: In all of these problems, we always have L = f(c). So although the book intends these problems to be about limits, they are all really about continuity, specifically that f is continuous at c.
• No additional work needed: 7–14;
• Show what equation or inequality you solve to find the interval or to find δ, or show a graph similar to the book's graphs for the previous problems: 15, 17, 23, 27;
• Show what equation or inequality you solve to find δ: 37, 39, 41, 49.
• Extra credit: Use the epsilontic definition to show why
{  x sin (1/x) for x ≠ 0 0 for x = 0
is continuous in x at x = 0. (Hint: For every real number t, −1 ≤ sin t ≤ 1.)
4. Limits:
• Date assigned: October 10 Friday.
• Date due: October 15 Wednesday.
• Problems from Section 2.2 (pages 67–70):
• No additional work needed: 1–4, 9, 10;
• Show at least what numerical calculations you make: 15, 19, 25, 29, 35, 37, 43, 53, 57;
• No additional work needed (but be sure to do all that the books asks!): 65.a.
• Problems from Section 2.4 (pages 84–86):
• No additional work needed: 1–6;
• Show at least what numerical calculations you make: 11, 17, 23.
5. Limits involving infinity, derivatives as limits:
• Date assigned: October 12 Tuesday.
• Date due: October 17 Friday.
• Problems from Section 2.6 (pages 108–110):
• No additional work needed: 1, 2;
• Show at least what numerical caclulation you make involving only finite numbers: 7, 9, 11, 15, 21, 25, 27, 29, 35;
• Show at least one intermediate step addressing the sign of the result: 41, 45, 49, 53, 57.
• Problems from Section 2.1 (pages 57–59): Show what numerical calculations you make: 1, 3, 5.
• Problems from Section 3.1 (pages 119&120):
• No additional work needed: 1, 2;
• Show what limits you evaluate, as well as their results: 5, 11, 19, 23, 31, 33, 34.
6. Derivative functions, basic rules:
• Date assigned: October 16 Thursday.
• Date due: October 21 Tuesday.
• Problems from Section 3.2 (pages 125–129):
• Show what limits you evaluate, as well as their results: 1, 3, 7, 9;
• No additional work needed: 27–30, 31, 35;
• Show what limits you evaluate, as well as their results: 37, 41;
• No additional work needed: 45–48.
• Problems from Section 3.3 (pages 137–139): Do the first derivatives only, showing at least one intermediate step for each: 1, 3, 7, 9.
• Problems from Section 3.6 (pages 161–164): Show at least one intermediate step for each derivative: 1, 87.a,b,e.
7. Calculating derivatives and differentials:
• Date assigned: October 20 Monday.
• Date due: October 23 Thursday.
• Problems from Section 3.3 (pages 137–139): Show at least one intermediate step for each derivative: 11, 15, 17, 21, 25, 41, 49.
• Problems from Section 3.11 (pages 203–205): Show at least one intermediate step for each that is not simply dy/dx (in fact, you never need to find dy/dx at all): 21, 24.
• Problems from Section 3.6 (pages 161–164): Show at least one intermediate step for each derivative: 33, 83, 87.f,g,h.
8. Implicit differentiation, exponential functions:
• Date assigned: October 22 Wednesday.
• Date due: October 27 Monday.
• Problems from Section 3.7 (pages 168&169): For each derivative, show an equation after differentiating but before solving: 1, 3, 7, 21.
• Problems from Section 1.5 (pages 38&39): Show at least one intermediate step for each: 11, 15, 19.
• Problems from Section 3.3 (pages 137–139): Show at least one intermediate step for each derivative: 5, 29, 31, 35, 51.
• Problems from Section 3.8 (pages 178&179): Show at least one intermediate step: 67.
• Problem from Section 3.11 (pages 203–205): Show at least one intermediate step that is not simply dy/dx (in fact, you never need to find dy/dx at all): 31.
• Problems from Section 3.6 (pages 161–164): Show at least one intermediate step for each derivative: 35, 77.
9. Trigonometric functions:
• Date assigned: October 24 Friday.
• Date due: October 29 Wednesday.
• Problems from Section 1.3 (pages 27–29):
• No additional work needed: 6;
• Show at least one intermediate step: 9, 11.
• Problems from Section 3.5 (pages 153–156): Show at least one intermediate step for each derivative: 1–15 odd, 19, 23, 31, 33, 35.
• Problem from Section 3.11 (pages 203–205): Show at least one intermediate step for each that is not simply dy/dx (in fact, you never need to find dy/dx at all): 25.
• Problems from Section 3.6 (pages 161–164): Show at least one intermediate step for each derivative: 3, 17, 27, 29, 39, 43, 47, 65, 73, 86, 89.
• Problems from Section 3.7 (pages 168&169): For each derivative, show an equation after differentiating but before solving: 11, 27, 29.
10. Inverse functions:
• Date assigned: October 28 Tuesday.
• Date due: October 31 Friday.
• Problems from Section 1.6 (pages 49–51): No additional work needed: 43, 45, 65, 67.
• Problems from Section 3.8 (pages 178&179): Show at least one intermediate step for each derivative: 13, 21, 27, 39, 47, 51, 57, 63, 65, 75, 89, 93.
• Problems from Section 3.9 (pages 185&186): Show at least one intermediate step for each derivative: 1, 7, 9, 11, 13–19 odd, 21, 23, 25, 31, 35, 37, 39.
• Problems from Section 3.11 (pages 203–205): Show at least one intermediate step for each that is not simply dy/dx (in fact, you never need to find dy/dx at all): 33, 35, 38.
11. Basic applications of derivatives:
• Date assigned: October 30 Thursday.
• Date due: November 5 Wednesday.
• Problems from Section 3.4 (pages 146–149):
• Show at least one intermediate step for each result: 1–7 odd, 9, 13;
• Show what numerical calculation you make for the second half of part g: 17;
• No additional work needed: 18, 21;
• Show at least what numerical calculations you make: 23, 25.
• Problem from Section 3.5 (pages 153–156): Show at least what numerical calculations you make: 61.
• Problems from Section 3.6 (pages 161–164): Show at least one intermediate step for each result: 97, 98.
• Problems from Section 3.10 (pages 191–195): As intermediate steps, show at least every equation that you differentiate (unless it is given in the problem statement) and the resulting equation immediately after differentiating (regardless of what is given in the problem statement): 1, 2, 3, 6, 12, 13, 15, 23, 24, 27, 29, 31, 38, 41.
• Problems from Section 3.11 (pages 203–205):
• Show f(a) and f′(a): 1–7;
• Show the chosen integer, the value of the function at that integer, and the value of its derivative at that integer: 10, 11, 13, 14;
• Show f(0) and f′(0): 15;
• Show at least one intermediate step for each part except part a: 16;
• Show at least a relevant approximate equation for each result: 51, 52, 53, 57.
12. Mean-value theorems:
• Date assigned: November 3 Monday.
• Date due: November 6 Thursday.
• Problems from Section 4.2 (pages 228–230):
• Show what equation you solve to find c: 1, 5;
• No additional work needed (but give reasons as directed): 9, 11, 13, 15;
• Show the zero (root), and indicate what calculation (using Rolle's Theorem!) shows that there is not another one: 21, 25;
• Extra credit (give reasons!): 54.
13. L'Hôpital's Rule:
• Date assigned: November 7 Friday.
• Date due: November 11 Tuesday.
• Problems from Section 4.5 (pages 253&254): Use L'Hôpital's Rule instead of algebraic manipulation; each time it is used (which may be never or more than once in a problem), show at least the expressions immediately before and after its application: 1, 3, 5, 11, 13, 15, 21, 27, 37, 43, 51, 55, 59, 60.
14. Extrema:
• Date assigned: November 10 Monday.
• Date due: November 13 Thursday.
• Problems from Section 4.1 (pages 219–222):
• No additional work needed: 1–14, 15, 17, 20;
• Show what equations or inequalities you solve and what numerical calculations you make: 55, 61, 71.
• Problems from Section 4.3 (pages 233–235):
• Show what equations or inequalities you solve, what numerical calculations you make, and what limits you evaluate (if any), without using a graph: 1, 3, 5, 7, 13;
• No additional work needed: 15–18;
• Show what equations or inequalities you solve, what numerical calculations you make, and what limits you evaluate (if any), without using a graph: 19, 23, 29, 33, 43, 47.a&b, 49.a&b, 55.a&b;
• No additional work needed: 67.
15. Graphing:
• Date assigned: November 12 Wednesday.
• Date due: November 18 Tuesday.
• Problems from Section 1.4 (page 33): Optional, no additional work needed: 1–4.
• Problems from Section 4.4 (pages 243–246):
• Show what equations or inequalities you solve, what numerical calculations you make, and what limits you evaluate (if any): 1–7 odd, 11, 19, 23, 27, 43, 53;
• No additional work needed: 81–84;
• Show what equations or inequalities you solve, what numerical calculations you make, and what limits you evaluate (if any): 85, 87, 101;
• No additional work needed: 103–106.
16. Applied optimization:
• Date assigned: November 14 Friday.
• Date due: November 20 Thursday.
• Problems from Section 4.1 (pages 219–222): Show what equations you solve and what numerical calculations you make: 23, 27, 37, 39, 41.
• Problems from Section 4.6 (pages 260–266): Show what equations you use, both before and after differentiating: 1, 3.c, 7, 9, 11, 13, 15, 29, 31, 37, 39, 43.a.
17. Summation notation:
• Date assigned: November 20 Thursday.
• Date due: November 24 Monday.
• Problems from Section 5.2 (pages 304&305):
• No additional work necessary (but be sure to do everything asked for): 1–6;
• No additional work necessary: 7, 9, 11–16;
• Show at least one intermediate step: 17, 19, 23, 29.
18. The Riemann integral:
• Date assigned: November 24 Monday.
• Date due: December 2 Tuesday.
• Problems from Section 5.1 (pages 296–298): Show what numerical calculations you make (except perhaps for calculating values of Δx): 1–19 odd.
• Problems from Section 5.2 (pages 304&305):
• Show what numerical calculations you make (except perhaps for calculating values of x and Δx): 33, 35;
• Show at least what limits you take: 39, 43.
• Problems from Section 5.3 (pages 313–317):
• No additional work needed: 1–14;
• Draw or explain what geometric area you used: 15, 17, 27;
• Show what numerical calculations you make: 35, 43, 49;
• Show a graph or an inequality that explains your answer: 71.
19. Indefinite integrals:
• Date assigned: November 25 Tuesday.
• Date due: December 4 Thursday.
• Problems from Section 4.2 (pages 228–230): No additional work needed: 33.
• Problems from Section 4.8 (pages 277–281):
• No additional work needed: 1–24;
• Show at least one intermediate step for each: 27, 29, 35, 39, 41, 45, 49, 51, 55, 61, 65, 75, 77, 81, 83.
• Problems from Section 5.5 (pages 333–335): Show at least one intermediate step for each: 1–7 odd, 15, 17, 21, 25, 27, 31, 35, 39, 47, 55, 57, 61.
20. Evaluating definite integrals:
• Date assigned: December 3 Wednesday.
• Date due: December 8 Monday.
• Problems from Section 5.4 (pages 325–328):
• Show at least one intermediate step involving the result of an indefinite integral: 1–15 odd, 23, 29;
• Show at least one intermediate step each way: 39, 43;
• Show at least one intermediate step: 47, 51;
• Show what definite integrals you evaluate: 57, 59, 61.
• Problems from Section 5.6 (pages 341–344): Show the integrals you have after substitution: 1–9 odd, 13, 19, 25, 31, 37, 41, 45.
21. Differential equations:
• Date assigned: December 5 Friday.
• Date due: December 10 Wednesday.
• Problems from Section 4.2 (pages 228–230): Show at least one intermediate step: 39.
• Problems from Section 4.8 (pages 277–281):
• Show at least one intermediate step: 95, 97, 105;
• Show what numerical calculations you make, or show what direct integral you evalute: 119.A.
• Problems from Section 5.5 (pages 333–335):
• Show at least one intermediate step: 71, 73;
• Show at least one intermediate step: 77.
22. Two-dimensional geometric applications:
• Date assigned: December 9 Tuesday.
• Date due: December 12 Friday.
• Problems from Section 5.6 (pages 341–344): Show what definite integrals you evaluate: 47, 51, 55, 57, 59, 67, 69, 75, 81, 87, 99.
• Problems from Section 6.3 (pages 376&377):
• For each problem, show what definite integral you evaluate and at least one intermediate step on the way to that integral: 1, 3, 7, 9, 13;
• Show at least one intermediate step: 15.A;
• Extra credit (hint: implicit differentiation): Show at least two intermediate steps: 30.
23. Three-dimensional geometric applications:
• Date assigned: December 12 Friday.
• Date due: December 18 Thursday.
• Problems from Section 6.1 (pages 361–364):
• Show at least what definite integrals you evaluate: 1, 5, 7;
• Show at least what definite integrals you evaluate, or give an explanation in words: 13;
• Show at least what definite integrals you evaluate: 15, 17, 21, 23, 25, 35, 45, 51.
• Problems from Section 6.2 (pages 369–371): Show at least what definite integrals you evaluate: 1, 3, 5, 9, 15, 21, 25, 27, 31, 39.
• Problems from Section 6.4 (pages 381–383):
• No additional work necessary: 1.A, 3.A;
• Show at least what definite integrals you evaluate: 13, 19, 23.
24. Extra credit: Newton's Method:
• Date assigned: December 12 Friday.
• Date due: December 18 Thursday.
• Problems from Section 4.7 (pages 269–271):
• For each iteration, show what numerical calculation you make to get the next result: 1, 5;
• Show what calculations you make: 9&10;
• Use Newton's Method to at least three decimal places; show an integer as your initial guess, then show what numerical calculation you make to get each result: 13;
• Use Newton's Method to find a positive solution to at least three decimal places; show an integer as your initial guess, then show what numerical calculation you make to get each result: 23.
That's it!
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This web page and the files linked from it were written between 2003 and 2014 by Toby Bartels, last edited on 2014 December 12. Toby reserves no legal rights to them.

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