Problem sets
I will assign problem sets that will be listed below.
Unless otherwise specified,
all readings and exercises
are from the 2nd Edition
of University Calculus: Early Transcendentals
by Hass et al published by Addison Wesley (Pearson).
You can always do more homework problems!
You may need to practise the material
if you want to remember it
for the quizzes,
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 are the assigned problems:
- General review:
- Date assigned: October 5 Monday.
- Date done in class: October 6 Tuesday.
- Date due in final form: October 7 Wednesday.
- Reading: Pages 1–11, pages 14–18.
- 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.
- Continuity:
- Date assigned: October 6 Tuesday.
- Date done in class: October 7 Wednesday.
- Date due in final form: October 8 Thursday.
- Reading:
Page 86,
page 87 through the end of Example 1
(but ignore the discussion of limits
and just compare the answers with the graph),
all of page 89, page 90 from Example 6 onwards,
page 91 through Example 8, Example 12 on pages 92&93,
page 1 of the handout on continuity,
the very top of page 2 of the handout (finishing the paragraph).
- Problems from Section 2.5 (pages 95–97):
- Note:
Since we're covering continuity before limits,
do not use limits in any of your answers.
You only need to know how to recognize continuity
from a graph or from a formula.
- No additional work needed: 1–4, 5.d, 6.d, 7–10;
- 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 to find a:
43.
- Limits:
- Date assigned: October 7 Wednesday.
- Date done in class: October 8 Thursday.
- Date due in final form: October 9 Friday.
- Reading:
From page 59 to the very top of page 66;
the top half of page 1 of the handout on limits.
- 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, 57;
- Epsilontics:
- Date assigned: October 9 Friday.
- Date done in class: October 12&13.
- Date due in final form: October 14 Wednesday.
- Reading:
Pages 66&67,
pages 70–76,
from the bottom of page 87 through page 88,
from Theorem 10 on page 91 through page 93,
page 2 of the handout on continuity.
- Problems from Section 2.2 (pages 67–70):
- Show at least what numerical calculations you make: 53;
- No additional work needed (but be sure to do all that the book asks!):
65.a.
- 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;
- 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.
- Extra credit:
Use the epsilontic definition of continuity from the handout
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.)
- Additional limits:
- Date assigned: October 13 Tuesday.
- Date done in class: October 14 Wednesday.
- Date due in final form: October 15 Thursday.
- Reading:
Pages 79–84, pages 97–108,
the remainder of the handout on limits.
- 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.
- Problems from Section 2.6 (pages 108–110):
- No additional work needed: 1, 2;
- Show at least what numerical caclulations 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 each result:
41, 45, 49, 53, 57.
- Derivatives as limits:
- Date assigned: October 14 Wednesday.
- Dates done in class: October 15&16.
- Date due in final form: October 19 Monday.
- Reading: Pages 52–57, 116–118.
- 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, 33, 34.
- Derivative functions:
- Date assigned: October 16 Friday.
- Date done in class: October 19 Monday.
- Date due in final form: October 20 Tuesday.
- Reading: Pages 120–125.
- Problems from Section 3.2 (pages 125–129):
- Show what limits you evaluate, as well as their results: 1, 3, 5;
- No additional work needed: 27–31, 34, 35;
- Show what limits you evaluate, as well as their results: 37, 41;
- No additional work needed: 45–48.
- Basic rules:
- Date assigned: October 19 Monday.
- Date done in class: October 20 Tuesday.
- Date due in final form: October 21 Wednesday.
- Reading:
Paying particular attention to the statements in function notation
(f′(x) and the like)
and the proofs:
page 129 through Example 4 on page 132,
page 134 through Example 9 on page 136,
page 156 through the end of the proof on page 158,
the handout
on an alternative definition of derivative.
- Problems from Section 3.3 (pages 137–139):
- Show at least one intermediate step for each derivative:
19, 20, 23;
- Show what equation you solve: 61, 69.
- Problems from Section 3.6 (pages 161–164):
- State clearly what functions
f, g, f′, and g′ are
(as well as the final answer):
9, 11, 13;
- Show what numerical calculation you make: 83, 87.a–e.
- No additional work needed: 104.
- Differentials:
- Date assigned: October 20 Tuesday.
- Date done in class: October 21 Wednesday.
- Date due in final form: October 22 Thursday.
- Reading:
The handout on differentials through page 3,
the definition and Example 4 on page 198.
- Problems from Section 3.11 (pages 203–205):
- No additional work needed: 19;
- 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, 23.
- Problems from Section 3.3 (pages 137–139):
Show at least one intermediate step for each derivative:
1, 3, 17, 25, 41.
- Problems from Section 3.6 (pages 161–164):
Show at least one intermediate step for each derivative:
23, 31, 33.
- Exponential functions:
- Date assigned: October 21 Wednesday.
- Dates done in class: October 23&26.
- Date due in final form: October 27 Tuesday.
- Reading:
Bottom of page 33 through page 38,
bottom of page 132 and page 133.
- 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.
- 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, 37.
- Implicit differentiation:
- Date assigned: October 26 Monday.
- Date done in class: October 27 Tuesday.
- Date due in final form: October 28 Wednesday.
- Reading:
Page 4 and the top half of page 5
of the handout on differentials,
pages 164–166 of the textbook.
- Problems from Section 3.7 (pages 168&169):
For each derivative,
show an equation after differentiating
but before solving:
1, 3, 7, 21, 27, 29.
- Trigonometric functions:
- Date assigned: October 27 Tuesday.
- Date done in class: October 28&29.
- Date due in final form: October 30 Friday.
- Reading: Pages 21–27, pages 149–153.
- Problems from Section 1.3 (pages 27–29):
- No additional work needed: 5, 6;
- Show at least one intermediate step: 9, 11, 31, 33;
- Show at least one intermediate step
(using the half-angle formulas,
not the double-angle formulas as the header implies):
47, 49.
- Problems from Section 3.5 (pages 153–156):
Show at least one intermediate step for each derivative:
1–5 odd, 9–15 odd, 19, 23, 31, 35.
- 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):
25, 27, 29.
- Problems from Section 3.6 (pages 161–164):
Show at least one intermediate step for each derivative:
27, 29, 39, 43, 47, 65.
- Problem from Section 3.7 (pages 168&169):
Show an equation after differentiating but before solving algebraically:
11.
- Logarithms:
- Date assigned: October 28 Wednesday.
- Date done in class: October 29&30.
- Date due in final form: November 2 Monday.
- Reading: Pages 39–45, pages 170–178.
- Problems from Section 1.6 (pages 49–51):
No additional work needed: 43–51 odd, 55, 57, 61–65 odd.
- Problems from Section 3.8 (pages 178&179):
- Show at least one intermediate step for each derivative:
13, 21, 27, 39;
- Show at least ln y and its derivative or differential
as intermediate steps:
47, 51;
- Show at least one intermediate step for each derivative: 57;
- Show an equation after differentiating but before solving algebraically:
63, 65;
- Show at least one intermediate step for each derivative: 75;
- Show at least ln y and its derivative or differential
as intermediate steps:
89, 93.
- 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):
33.
- Inverse trigonometric functions:
- Date assigned: October 29 Thursday.
- Date done in class: November 2 Monday.
- Date due in final form: November 3 Tuesday.
- Reading: Pages 45–49, pages 180–184.
- Problems from Section 1.6 (pages 49–51):
No additional work needed: 67, 69.
- Problems from Section 3.9 (pages 185&186):
- No additional work needed: 1, 7, 9, 11, 13–20;
- Show at least one intermediate step for each derivative:
21, 23, 25, 31, 35, 37, 39.
- 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):
37.
- Derivatives with respect to time:
- Date assigned: November 2 Monday.
- Date done in class: November 3 Tuesday.
- Date due in final form: November 4 Wednesday.
- Reading:
Page 139 through the end of Example 4 on page 144,
online video.
- 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: 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.
- Related rates:
- Date assigned: November 3 Tuesday.
- Date done in class: November 4 Wednesday.
- Date due in final form: November 5 Thursday.
- Reading:
Page 186–191,
the bottom half of page 5
of the handout on differentials.
- 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, 27, 29, 31, 41.
- Sensitivity and linear approximation:
- Date assigned: November 4 Wednesday.
- Date done in class: November 5 Thursday.
- Date due in final form: November 9 Monday.
- Reading:
Bottom half of page 145,
page 195 through the top of page 201,
page 203,
page 6 of the handout on differentials,
the handout on linear approximation.
- Problem from Section 3.4 (pages 146–149):
Show at least what numerical calculations you make: 28.
- Problems from Section 3.11 (pages 203–205):
- Show f(a) and f′(a): 1–6;
- Show the chosen integer (which is not a exactly),
the value of the function f at that integer,
and the value of its derivative f′ at that integer:
7, 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.
- Mean-value theorems:
- Date assigned: November 6 Friday.
- Date done in class: November 9 Monday.
- Date due in final form: November 10 Tuesday.
- Reading:
Pages 222–226 (nothing about the laws of logarithms),
pages 251&252
(just Theorem 7 and the discussion after it,
nothing about L'Hôpital's Rule yet).
- 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.
- Problems from Section 4.5 (pages 253&254):
Show what equation you solve to find c: 78.a,c.
- L'Hôpital's Rule:
- Date assigned: November 9 Monday.
- Date done in class: November 10 Tuesday.
- Date due in final form: November 11 Wednesday.
- Reading:
Page 246 through Example 8 on page 251, proof on the bottom of page 252.
- Problems from Section 4.5 (pages 253&254):
- When you use L'Hôpoital's Rule,
show at least the expressions immediately before and after its application;
when you use algebraic manipulation,
show at least the expression after the manipuliation:
1, 3, 5;
- 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:
11, 13, 15, 21, 27, 37, 43, 51, 55, 59, 60.
- Absolute extrema:
- Date assigned: November 10 Tuesday.
- Date done in class: November 11 Wednesday.
- Date due in final form: November 12 Thursday.
- Reading: Pages 214–219.
- Problems from Section 4.1 (pages 219–222):
- No additional work needed: 1–14, 15, 17, 20;
- Show what equations you solve and what numerical calculations you make:
23, 27, 37, 39, 41.
- Local extrema:
- Date assigned: November 11 Wednesday.
- Date done in class: November 12 Thursday.
- Date due in final form: November 13 Friday.
- Reading: Pages 230–233,
middle of page 238
(the paragraph before Theorem 5, Theorem 5 and its proof,
and the first paragraph after the proof).
- Problems from Section 4.1 (pages 219–222):
- 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.
- Concavity:
- Date assigned: November 12 Thursday.
- Date done in class: November 13 Friday.
- Date due in final form: November 16 Monday.
- Reading:
From page 235 to the top of page 238,
online notes.
- Problems from Section 4.4 (pages 243–246):
- Show what equations you solve and what numerical calculations you make:
1–7 odd;
- No additional work needed: 81–84, 103, 107, 108.
- Extra credit (give reasons): 114.
- Graphing:
- Date assigned: November 16 Monday.
- Date done in class: November 16&17.
- Date due in final form: November 18 Wednesday.
- Reading:
Pages 29–33 (optional, if you want to use a graphing calculator),
from the bottom of page 238 to page 243,
online notes.
- 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):
11, 19, 23, 27, 43, 53;
- 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: 104, 105, 106.
- Applied optimization:
- Date assigned: November 17 Tuesday.
- Date done in class: November 18 Wednesday.
- Date due in final form: November 19 Thursday.
- Reading:
Pages 255–260, online notes.
- Problems from Section 4.6 (pages 260–266):
Show what equations you use, both before and after differentiating:
1, 3.c, 7, 9–15 odd, 29, 31, 37, 39, 43.a.
- Summation notation:
- Date assigned: November 18 Wednesday.
- Dates done in class: November 19&20.
- Date due in final form: November 23 Monday.
- Reading:
Pages 299–301, online notes.
- 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 for each sum:
17, 19, 23, 29, 31.
- Riemann sums:
- Date assigned: November 20 Friday.
- Date done in class: November 23 Monday.
- Date due in final form: November 24 Tuesday.
- Reading:
Pages 289–296, from the middle of page 301 through page 304.
- 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.
- Riemann integrals:
- Date assigned: November 23 Monday.
- Date done in class: November 24 Tuesday.
- Date due in final form: November 30 Monday.
- Reading:
From the bottom of page 301 to the middle of page 302,
the handout on integrals
(for the big picture).
- Problems from Section 5.2 (pages 304&305):
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.
- Antidifferentiation:
- Date assigned: November 24 Tuesday.
- Date done in class: November 30 Monday.
- Date due in final form: December 1 Tuesday.
- Reading: Page 271 through the top of page 274, pages 276&277.
- Problems from Section 4.8 (pages 277–281):
- No additional work needed: 1–24;
- Show at least one intermediate step for each:
75, 77, 81, 83.
- Integration by substitution:
- Date assigned: November 30 Monday.
- Date done in class: December 1 Tuesday.
- Date due in final form: December 2 Wednesday.
- Reading: Pages 328–333.
- 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.
- The Fundamental Theorem of Calculus:
- Date assigned: December 1 Tuesday.
- Date done in class: December 2&3.
- Date due in final form: December 4 Friday.
- Reading: Pages 317–323, page 335 through the top of page 338.
- 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.
- 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.
- Differential equations:
- Date assigned: December 2 Wednesday.
- Date done in class: December 3&4.
- Date due in final form: December 7 Monday.
- Reading:
the middle section of page 226, pages 274&275,
online notes on semidefinite integrals.
- 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;
note that the book is conflating the function y
with its output y(x) at the input x:
95, 97, 105;
- Show what numerical calculations you make,
or show what direct integral you evaluate:
119.a.
- Problems from Section 5.5 (pages 333–335):
- Show at least one intermediate step;
note that the book is conflating the function s
with its output s(t) at the input t:
71, 73;
- Show at least one intermediate step: 77.
- Planar area:
- Date assigned: December 4.
- Date done in class: December 7 Monday.
- Date due in final form: December 8 Tuesday.
- Reading: From the bottom of page 323 to page 325.
- Problems from Section 5.4 (pages 325–328):
Show what definite integrals you evaluate: 57, 59, 61.
- 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.
- Arclength:
- Date assigned: December 7 Monday.
- Date done in class: December 8 Tuesday.
- Date due in final form: December 9 Wednesday.
- Reading: Pages 372–376.
- 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, 19.a;
- Extra credit (hint: implicit differentiation):
Show at least two intermediate steps: 30.
- Volume of revolution:
- Date assigned: December 8 Tuesday.
- Date done in class: December 9&10.
- Date due in final form: December 11 Friday.
- Reading: Pages 353–360, 364–369.
- 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.
- Surface area of revolution:
- Date assigned: December 10 Thursday.
- Date done in class: December 11&14.
- Date due in final form: December 15 Tuesday.
- Reading: Pages 378–381.
- Problems from Section 6.4 (pages 381–383):
- Show at least one intermediate step: 1–7.a odd;
- Show at least what definite integrals you evaluate:
13–21 odd.
- Newton's Method:
- Date assigned: December 11 Friday.
- Date done in class: December 14&15.
- Date due in final form: December 16 Wednesday.
- Reading: Pages 266–269.
- Problems from Section 4.7 (pages 269–271):
- For each iteration,
show what numerical calculation you make to get the next result:
1, 3, 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;
- Show an integer as your initial guess,
then show what numerical calculation you make to get each result:
21;
- 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!
Go back to the the course homepage.
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last edited on 2015 December 11.
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