Differential Calculus (Chapters 1-4)

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Section 2.6

Homework: p. 144; 1-4, 7,9-19 odd, 25,27,35,37,38,39

Note: I am adding numbers 18 and 26 to this assignment.

In class, homework discussion topics:



  • #17: since the limit was of the form \lim_{x \to \infty}f(x), we used \sqrt{x^2} \Rightarrow x. If the limit had been to negative infinity, as in \lim_{x \to -\infty}f(x), we would have said \sqrt{x^2} \Rightarrow -x.

Section 2.7

Homework: p. 154; 1-9 odd, 15,17,22,23,25


Section 2.8

Homework: p.161; 1,3,5,7,19,21,23,27,29,31,33,34


Section 2.9

Homework: 1,4,5,8,9,11,12,14,15,19,25,31,33,34,37 a) b) c)

Optional: 41,43

Chapter 2 Review:

p.175: 1,3,7,13,15,23,35,36,37,39,41


Chapter 3

Section 3.1

Videos and Resources

Note: As you work through these problems, try to memorize the differentiation rules.

Homework: p.189; 3,5,7,17,19,25,37,39,43,47,49,53

optional: 57,59


Section 3.2

Videos and Resources

Note: As you work through these problems, try to memorize the differentiation rules.


Homework: p.195; 1,3,5,7,11,17,21,31,35,37,38

Optional: 41,42


Section 3.3

Homework: 1,9,11,12,13,15,17,18,19,32,33


Section 3.4

Videos and Resources

Homework: 1,3,5,9,13,14,15,25,31,33,35,39,47


Section 3.5

Video lecture and Resources

Homework: 1,3,5,19,21,23,25,46,53,55a,57a,b,59,65


Section 3.6

Videos and Resources

Examples of Implicit Differentiation


Optional: 69 (Use a computer algebra system such as Sage Math to solve the system of equations that you develop).


Section 3.7

Videos and Resources

Homework: p.237 #1,3,5,7,9,45,49,55


Section 3.8


Homework: p.245 #3,5,25,27,35,37,45


Section 3.9

Feel free to skim/read this section. We’re not going to cover this stuff.


Section 3.10

Videos and Resources

Homework: p.257 #1,3,4,5,7,

Optional extra practice: 8,9,17,29


Section 3.11


Homework: p.264 #3,5,9,11,15,17,21,25,27,39 (see example 5, p.263)

Linear Approximations Videos and Resources

Differentials Videos and Resources


Chapter 3 Review:

p.268 #29,49,53,55,61,66,85,90


Chapter 3 Study Suggestions:

  • Be confident on problems like:
    • p. 189 #5,25,43,44
    • p.195 #3,7,31
    • p.213 #3,11,25
    • p.222 #36,37
    • p.232 #55,56
    • p.238 #29
    • p.238 #45
    • p.257 #7,17
    • p.265 #9,10,15-19

Chapter 4

Section 4.1:

p.284; #1-7,11 all, 35, 39,45,57,59,71,75


Section 4.2:


p.293; #5,6,7,11


Section 4.3:


p.303; #1 c,d,e (a and b are optional)


optional extra practice: #6,47



Section 4.4:

p.311 #1,2,3,7,9,29,45,47

-Take a crack at #73, but feel free to just review the solution in the solution manual. Mostly, I just want you to see this.


Section 4.5:

p.321 #9,25,47 (If this looks short it is because these problems are pretty tedious).



Section 4.6:

Read pages 322 to 328. The skills in this section basically repeat those from 4.5, but with a little extra skepticism about what graphing utilities (or calculators) show us. As such, there is no exercise set for this section. Just read it carefully and ask me if you have any questions.



Section 4.7:

p. 334 #1 (consider making your table for part a.) by writing some code, 9, 11,15,17,23,33


Section 4.8:

This section discusses a couple of concepts from economics. It is worth reading the section, just for exposure to more applications to derivatives, but I am not going to assign problems from this section. I can’t find any evidence that these concepts will be referenced on the AP tests, but as we review for the tests, if we learn otherwise, it will be easy to just learn the vocab and formulas then. Again, this stuff is just applications of basic calculus concepts to some ideas in economics.


Section 4.9:

p. 349 #1,2,3,5,9,13,29

Related Resources:

Newton’s method in python Video


Section 4.10:

p. 356 : 1, 5,9,13,18,43,45-47, 49, 53,63