# Homework

In case you miss a homework assignment in class, you can find it below. Unless otherwise specified, all problems are from the 13th Edition of Calculus for Business, Economics, Life Sciences, and Social Sciences written by Barnett et al and published by Prentice Hall (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.

You can always do more homework problems! You may need to practise the material if you want to remember it for the final exam, a subsequent course, or the rest of your life. If you bought MyMathLab access with your course textbook (or separately), then you can find supplementary problems through the Moodle page. (However, MyMathLab is not required for this section.)

Here is the assigned homework:

1. Introduction:
• Date assigned: July 14 Tuesday.
• Date due: July 16 Thursday.
• Extra-credit essay question: Explain your background in mathematics and what you are going to use this course for.
2. Review; continuity and smoothness:
• Date assigned: July 16 Thursday.
• Date due: July 21 Tuesday.
• Pages to read in the textbook: 121&122, 125–128.
• Problems from Chapter 1 Review (pages 87–92):
• Show what numerical calculations you make: 5;
• No additional work needed: 9&10;
• Show at least one intermediate step for each part: 11;
• No additional work needed: 13–16;
• Show what numerical calculation you make on a calculator: 20–23;
• No additional work needed: 24;
• Show what calculations you make: 46–49;
• No additional work needed: 62&63;
• Show what equations you solve or what numerical calculations you make: 83;
• No additional work needed: 86.A&B.
• Problems from Section 2.3 (pages 128–132):
• Note: Solve the problems marked ‘no additional work needed’ directly by looking at the relevant graphs; do not bother with any limits yet!
• No additional work needed: 19.E, 22.E, 28.E, 29.E, 30.E;
• Show a sign chart: 47–53 odd;
• No additional work needed: 69, 71, 73, 89, 93;
• No additional work needed: Referring to Exercise 2.3.93 again, is S smooth at 50?
3. Differences and differentials:
• Date assigned: July 21 Tuesday.
• Date due: July 23 Thursday.
• Problems from the handout (DjVu, PDF):
• Show what numerical calculations you make: 1, 3, 5.
• No additional work needed: 7–10.
4. Differentials:
• Date assigned: July 23 Thursday.
• Date due: July 28 Tuesday.
• Problems from the handout (DjVu, PDF):
• Show at least one intermediate step (for each problem): 11, 13, 15, 16, 17, 19, 25, 27.
• No additional work needed: 29, 30.
• Show at least one intermediate step: 33, 37, 39, 43, 45, 47, 55, 61, 65.
5. Derivatives:
• Date assigned: July 28 Tuesday.
• Date due: July 30 Thursday.
• Problems from the handout (DjVu, PDF):
• No additional work needed: 67.
• Show at least one intermediate step: 69.
• Problems from Section 2.5 (pages 153–156):
• No additional work needed: 9, 11, 13, 17.
• Show at least one intermediate step: 19, 21, 25, 33, 36, 41, 45, 50, 51.
• Problems from Section 3.4 (pages 211–213): Show at least one intermediate step not shown in the answers in the back of the book: 17, 21, 22, 29, 47.
• Problems from Section 3.3 (pages 201–203): Show at least one intermediate step not shown in the answers in the back of the book: 13, 15, 25, 29, 89.
• Problems from Section 3.5 (pages 218–220): Find dy/dx at the given value of (x, y); show at least one intermediate step not shown in the answers in the back of the book: 15, 17, 21, 23, 24.
• Problems from Section 4.2 (pages 266–271): Show the first derivative as an intermediate step: 17, 19.
6. Applications of derivatives:
• Date assigned: July 30 Thursday.
• Date due: August 4 Tuesday.
• Pages to read in the textbook: 163–170.
• Problems from Section 2.5 (pages 153–156): Show what calculations you make or what equations you solve: 61, 63, 95, 97.
• Problems from Section 3.4 (pages 211–213): Show what calculations you make or what equations you solve: 92.
• Problems from Section 3.3 (pages 201–203): Show what calculations you make or what equations you solve: 98.
• Problems from Section 2.7 (pages 170–173):
• No additional work needed: 9–16.
• Show at least one intermediate step: 17–20.
• No addtional work needed if you do them all in order: 21–28.
• Show what numerical calculations you make: 39, 43, 45.
7. Related rates:
• Date assigned: August 4 Tuesday.
• Date due: August 6 Thursday.
• Pages to read in the textbook: 220–223.
• Problems from Section 3.6 (pages 224&225):
• Show at least two intermediate steps: 9, 11, 13.
• Show what equation you differentiate, as well as at least one more intermediate step: 17, 25, 26, 27, 29.
8. Limits from graphs:
• Date assigned: August 6 Thursday.
• Date due: August 11 Tuesday.
• Pages to read in the textbook: 95–99, 109, 112.
• Problems from Section 2.1 (pages 105–108): No additional work needed: 9–16.
• Problems from Section 2.2 (pages 117–121): No additional work needed: 9–16.
9. Calculating limits:
• Date assigned: August 11 Tuesday.
• Date due: August 13 Thursday.
• Pages to read in the textbook: 100–104, 113&114.
• Problems from Section 2.1 (pages 105–108): For each limit, show what numerical calculation or calculation with infinities you make and show one intermediate step whenever you use an algebraic simplification (or L'Hôpital's Rule): 29, 31, 35, 37, 40, 42, 51, 54, 60, 61, 62.
• Problems from Section 2.2 (pages 117–121): For each limit, show what numerical calculation or calculation with infinities you make and show one intermediate step whenever you use an algebraic simplification (or L'Hôpital's Rule): 17–23 odd, 43, 45, 89, 91.
• Problems from Section 4.3 (pages 279&280): For each limit, show what numerical calculation or calculation with infinities you make and show one intermediate step whenever you use L'Hôpital's Rule (or an algebraic simplification): 9, 17, 33, 35, 45, 47, 49, 51.
10. Optimization:
• Date assigned: August 13 Thursday.
• Date due: August 18 Tuesday.
• Extra-credit problem about limits: Assuming that f is a fixed differentiable function and c is a fixed real number in the domain of f, use L'Hôpital's Rule (showing at least two intermediate steps) to find limh → 0 ((f(c + h) − f(c))/h).
• Problems from Section 4.5 (pages 299–301):
• No additional work needed: 9–12.
• Show what equations you solve and what numerical calculations you make (without using a graph): 19, 25, 26, 27, 31, 35, 37, 43, 47, 51, 55, 67, 69, 71.
• Problems from Section 4.6 (pages 310&313): Show what equations you solve and what numerical calculations you make: 19, 21, 25, 31, 32, 46, 49.
11. Tangent lines and local extrema:
• Date assigned: August 18 Tuesday.
• Date due: August 20 Thursday.
• Problems from Section 2.5 (pages 153–156): Show what calculations you make or what equations you solve: 57, 59.
• Problems from Section 3.4 (pages 211–213): Show what calculations you make or what equations you solve: 39, 41.
• Problems from Section 3.3 (pages 201–203): Show what calculations you make or what equations you solve: 61, 63.
• Problems from Section 3.5 (pages 218–220): Differentiate with respect to x, and show what calculations you make or what equations you solve: 41, 45.
• Problems from Section 4.1 (pages 249–253):
• No additional work needed: 9–16, 19–26;
• Show what equations or inequalities you solve: 33, 37, 41, 45;
• No additional work needed: 69–74.
12. Concavity and inflections:
• Date assigned: August 20 Thursday.
• Date due: August 25 Tuesday.
• Problems from Section 4.2 (pages 266–271):
• No additional work needed: 9, 10;
• Show what equations or inequalities you solve: 25–35 odd.
13. Graphs:
• Date assigned: August 25 Tuesday.
• Date due: August 27 Thursday.
• Problems from Section 2.2 (pages 117–121):
• Show what equations or inequalities you solve to find what limits to take and show what limits you take and their results: 33, 35, 39, 52, 54, 55, 60, 64;
• Show what limits you take and their results: 66, 70, 74.
• Problems from Section 4.4 (pages 289–293):
• No additional work needed: 9, 10;
• Use a graphing calculator if you like, but calculate the window size first and make sure that all intercepts, local extrema, inflections, and asymptotes appear: 19, 21, 31, 37, 39.
14. Exponents and logarithms:
• Date assigned: September 1 Tuesday.
• Date due: September 3 Thursday.
• Problems from Section 3.2 (pages 194&195): No additional work needed: 9, 11, 13, 15, 43–53 odd.
• Problems from Section 3.4 (pages 211–213): Show at least one intermediate step not shown in the answers in the back of the book: 25, 27, 35, 37, 51, 53, 55, 83–89 odd.
• Problems from Section 3.3 (pages 201–203): Show at least one intermediate step not shown in the answers in the back of the book: 17, 19, 31, 33, 85, 91.
• Problems from Section 3.5 (pages 218–220): Find dy/dx at the given value of (x, y); show a general formula for dy/dx as an intermediate step: 25, 27, 29.
• Problems from Section 4.3 (pages 279&280): For each limit, show what numerical calculation or calculation with infinities you make and show one intermediate step whenever you use L'Hôpital's Rule (or an algebraic simplification): 25–31 odd, 37–43 odd, 53–61 odd.
15. Applications involving exponents and logarithms:
• Date assigned: September 3 Thursday.
• Date due: September 8 Tuesday.
• Problems from Section 3.2 (pages 194&195): Show what calculations you make or what equations you solve: 27, 29, 65, 67.
• Problems from Section 3.4 (pages 211–213): Show what calculations you make or what equations you solve: 93, 97.
• Problems from Section 4.5 (pages 299&301): Show what equations you solve and what numerical calculations you make (without using a graph): 23, 59, 63, 65.
• Problems from Section 4.2 (pages 266–271): The graphs are optional, but show what equations or inequalities you solve: 89.
16. Integration:
• Date assigned: September 10 Thursday.
• Date due: September 15 Tuesday.
• Problems from Section 5.1 (pages 328–331):
• No additional work needed: 9–23 odd.
• Show at least one intermediate step for each: 43, 45, 47, 51, 65, 67, 69.
• Problems from Section 5.2 (pages 340–342): Show what substitution you make: 21, 25, 29, 33, 37, 41, 59, 63, 65, 67.
• Problems from Section 5.5 (pages 371–375):
• Show at least what numerical calculation you make for each: 13, 17, 21, 25, 29, 33, 35, 37, 39, 43.
• This is a trick question, so explain why: 47.
• Show at least what numerical calculation you make for each: 57, 59, 61.
17. Differential equations:
• Problems from Section 5.3 (pages 349–352):
• Show what integrals you evaluate: 9, 11, 13;
• Interpret ‘y(0)’ as y|x=0, and either show what definite integrals you evaluate or show what indefinite integrals you evaluate and what algebraic equation you solve to find the constant: 15, 17, 19;
• Show what algebraic equation you check: 25;
• Show what integrals you evaluate and what algebraic equation you solve: 39, 43;
• Show what equation you solve: 89, 91.
• Extra credit: Show what integrals you evaluate and what algebraic equations you solve: If I borrow P = \$150,000 at r = 3% annual interest, compounded continuously, and also continuously pay back I = \$12,000 per year, then the amount A that I owe after t years will satisfy dA/dt = rA − I, where A|t=0 = P. Solve this differential equation, and then find out how long it will take me to pay off this loan (which will be finished when A = 0.)
That's it!

We didn't get to the following material, but you can look at it if you want.

• Integration by parts:
• Problems from Section 6.3 (pages 407–409): Show u, du, v, and dv for each application of integration by parts: 9, 11, 15, 19, 23, 27, 37, 41, 45, 51, 55.
That's it!
Go back to the the course homepage.

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