Errata list / things to fix for Version 5.

1. Constant appearing in 6.5, #17. It's an integration problem, so it isn't technically *wrong*.

2. In Section 8.2, n^th partial sums need better definition. The formula implies that

S_n will add up terms r^0 + r + r^2 + ... + r^n, but this actually adds up n+1 terms.

The geometric series portion should be rewritten. Not really used in the text, but it

influences answers at the back. (See email from Chuck Cusack.)

3. Page 6, line 3: refers to $\sin(x)/x$ when it should refer to $\sin(1/x)$.

pA.1 1.1#17: In the solution, the limit should seem to be exactly $-7$.

p74 02_01_exset_05: the enum counter resets (you \setcounter the wrong enum level?). also, inequalities 4 & 5 should be switched.

p74 2.1#34 solution: g’=0 at x=0

pA.4 2.1#37: The solution should be negated.

p82 2.3 para 2 line 2: “linear function” should be pluralized

p98 2.4#24: The solution should not have parts (b) or (c) (and no label ``(a)''). (I don’t think we added that in, but it’s not easy to check through your source for the exercises.)

p98 2.4#34: The solution should use $h’$, not $f’$.

pA.6 2.6#29b solution: $+\sqrt[4]{108}$ should be $-\sqrt[4]{108}$.

p141 3.2 #3-10: In order to match Rolle's Theorem, the final $[a,b]$ should be $(a,b)$.

pA.6 3.2#23: 0 should not be included in the solution.

p173 4.1#15: The given problem has a unique solution at $x=0$. The given solution works for $g(x)=\cos x+1$.

p179 4.2#4: ``circular'' should be ``spherical''.

p194 4.4#30 you probably want y instead of f(x)

pA.9 5.2#23 solution: The answer should be 22.

pA.9 5.2#25 solution: The answer should be 0.

p258 Example 5.5.8, Figure 5.5.14: Since you measured every 30 seconds, the time column should be labeled “Measurement #”. Or you can leave it as time, but, e.g., change 7 to 3.5 min.

p281 6.1#36 solution: For $\abs x<1$, we need $\frac12 \ln\abs{\ln \left(x^2\right)}+C$ (absolute values).

pA.11 6.4#23 solution: $\tan^{-1}\left(\frac{x+2}2\right)$ should be $\tan^{-1}\left(\frac{x+2}3\right)$.

pA.12 6.7#13 Solution: Should be $2x\sech^2(x^2)$.

pA.12 6.8#3 Solution: Should have $\le10$ instead of $<10$.

p361 7.1#27-30: ``area triangle'' should be ``area of the triangle''.

p361 7.1#29: The solution should be 0, or a $(3,3)$ should become $(-1,3)$.

p361 7.1#30 solution: The area should be $\frac{21}2$.

p388 Example 7.5.1 solution line 2: ``it is'' should be ``is it''.

pA.13 7.5#5b solution: The answer is a length, so the units should just be ft.

p417 8.1#13-16: $a_n$ is multiply defined

p433 8.2#34a solution: should have the negative with $n$ odd, not $n$ even.

p433 8.2#36 solution: the series started at $n=1$, so it should be (a) $S_n=\dfrac{e^{-1}-e^{-n-1}}{1-e^{-1}}=\dfrac{1-e^{-n}}{e-1}$, (b) $\dfrac{e^{-1}}{1-e^{-1}}=\dfrac1{e-1}$.

p433 8.2#38a solution: $a_n = \frac12\left(\frac{1}{2n-1}-\frac{1}{2n+1}\right)$, so that $S_n=\frac12\left(1-\frac1{2n+1}\right) = \frac{n}{2n+1}$.

p441 8.3#22 solution: should specify $n\geq 3$ at the end, not $n\geq 2$.

pA.15 8.3#41a solution: $a_n/n<n$ should be $a_n/n<a_n$

pA.15 8.4#21 solution: $e^2$ should be $e^{-2}$.

p483 8.7#29-34 might want to ask for the $x^n$ term, since Taylor polynomials start with the 0th term.

pA.17 8.8#11 solution: The Taylor Series should be $\frac12+\sum_{n=1}^\infty$.

pA.19 9.2#45 solution: should be $t=k\pi$ for integral $k$.

pA.19 9.3#11 solution: a: The second term in the numerator should be doubled; b: The normal line is $y=-x$.

pA.19 9.3#29 solution: The intervals should be: concave up: $(-\pi/2,0)$; concave down: $(0,\pi/2)$.

p545 9.4#50 solution: $P(-1/2,\pi/3)$ should be $P(-1/2,2\pi/3)$

pA.20 9.4#53 solution: the origin is also a point of intersection

pA.34 14.3#17c solution: -1t should be t-1

p869 14.3#20d solution: 250 should be 0

pA.46 In Algebra / Factoring by Grouping, $(cs+d)$ should be $(cx+d)$.

pA.47 In Algebra / Taylor Series: should end with $+ . . .$ and pA.47 In Algebra / Maclaurin Series: same

You mentioned that all exercise sets now start with an odd and end with an even. There are a few sets with an odd number of problems:

01_04_exset_03

02_06_exset_02

04_04_exset_03

05_01_exset_01

05_01_exset_02

06_02_exset_03

06_03_exset_02

07_04_exset_04

08_07_exset_06

09_02_exset_09

10_04_exset_01

10_05_exset_05

also:

2.3#26 doesn’t seem to belong to that instruction set, leaving the set with an odd number of problems

7.1#19,20: These don’t really belong to their exercise set

10.2#21 throws off the parity

Grammar:

p423 8.2 just before Thm 8.2.2: $p$ is not in math mode % fixed

p496 8.8#12 solution: an open quote is never closed % fixed

p793 Def&Thm 13.4.2: (x_2,y_2) should have a comma after it % fixed

Misspellings. The good news is I figured out how to spell check in my editor (and from the command line:

cat text/*tex | aspell list -t --ignore=3 --ignore-case | sort | uniq > misspell.txt

The bad news is I figured out how to spell check.

Multiple places: The units Newtons and Joules should be capitalized

p292 6.2#4: original is misspelled.

p557 9.5#34 solution: Pythagorean is misspelled

p583 Example 10.2.6 solution para -2 line -3: unknown is misspelled

p607 Example 10.4.6 statement line 1: parallelepiped is missing its second “le”

p698 12.2 line -1: Multivariable is misspelled

p723 12.5 Examples 2, 4, 5 title: Multivariable is misspelled

p788 Definition 13.4.1: Variable is misspelled

p829 13.7 Figure 13.7.2 caption: canonical is misspelled

p841 14.1 para before Definition 14.1.1 line 3: definition is misspelled

p851 14.2 para 3 line -2: circle is misspelled

p865 para 2 line -3: continuously is misspelled

p884 Example 14.5.5 title: cylindrical is misspelled

p895 Example 14.6.3 statement line -2: positive is misspelled

You tend to omit the second e in parameterize (and its relatives). You can try searching for “arametriz”:

Section 9.2

Section 9.3

Section 10.5 x2

Section 11.1

Section 11.5 x5

Section 12.7

Section 14.1 x13 (plus two more commented out)

Section 14.3 x20

Section 14.4 x12

Section 14.5 x44 (I think)

Section 14.6 x6

Section 14.7 x8

solution to 12.2.20 b as -1, I think it should be 1.

I had forgotten a subtle point about l'Hopital's rule that is not mentioned in the book that stumped me for a while. I was trying to take the \lim x-->\infty (x^2+sin x)/x^2 as a student might (l'Hopital instead of algebra) and was confused when after the second application it failed to exist. I had forgotten that l'Hopital's rule only applies if the limit on the right exists. This is not stated in book and that can certainly cause misunderstandings since a student could draw the wrong conclusion (that the original limit does not exist). I would suggest maybe adding a phrase such as "assuming the limit on the right exists" in the two theorems.

In page 136, problem 14: The graph and the given function do not match! Please fix this in the next version! Yes, the inside function is supposed to be x^4 - 2x^2+1. Somehow that mistake has lived on for a very long time.

6.4 #23 has (x+2)/2 in the arctan, but it should be (x+2)/3.

5.2. Number 23 and 25 answers in the back are off.

The solutions to 8.2 #31, 35, and 37 have r^n, but Theorem 8.2.1 has r^{n+1} , so one of these appears to be incorrect. I think the problem is Theorem 8.2.1 since the sum of the first n terms would be the sum from 0 to n-1, making r^n correct.

6, line 3, it is said that the function in figure 1.1.13(c) is sin(x)/x when the function is sin(1/x).

01_Limits_Involving_Infinity, line 238: I've added the following

modifier at the end of the line: "for any positive integer $n$" since

the statement is false for n less than or equal to zero.

03_Extreme_Values: when defining critical point, the text suggests that

critical number and critical value are synonymous. Maybe I've done too

much differential topology/geometry, but I consider critical number to

be the x coordinate, while the critical value (i.e. function value) is

the y coordinate.

03_Mean_Value_Theorem, line 104: there's a bit of awkwardness with the

parenthetical remark and the preposition: "parallel with" makes sense,

but between these two words there's (i.e. have the same slope), and I

expect the next word to be 'as' rather than 'with'.

I've changed it to "parallel with (i.e. have the same slope as) the

dashed line" in my version.

05_Riemann_Sums, line 59: "these rectangle" (missing an s at the end)

05_Definite_Integrals, line 144: "viewed a merely a" (first 'a' should

be 'as')

06_Trigonometric integrals, line 152: "vise-versa" rather than vice-versa

07_Work, line 143: "peformed"

07_Work, line 199: "empyting"

10_Vector_Introduction, line 203: "nonvector"

10_Vector_Introduction, line 300: "unkown"

10_Vector_Introduction, line 388: "text" should be "texts"

11_Vector_Tangent_Normal, line 79: reference fig:tannorm3 (in the

figure) should be ex_tannorm3

13_Center_of_Mass, line 39: "Vairable"

13_Cylindrical_Spherical, line 3: "desribing"

13_Cylindrical_Spherical, line 51: "canoncial"

14_Line_Integral_Intro, line 84: "defintion"

14_Line_Integral_Vector, line 163: "continously"

14_Vector_Fields, lines 156 and 181: the figures refer to parts (a),

(b),... of the Example, but the parts are numbered 1, 2,... in the

Example itself.

14_Parameterized_Surfaces, line 158: "cylinderical"

14_Surface_Integral, line 131: "postive"

Page 415, Section 8.1, Part of Example 8.1.7: combined fraction should not have $n^2+4n+1$ but $n^2+3n$ in the numerator.