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82 | 82 | The following errors exist in the in June 2021 printed version of Apex LT Calculus II: |
83 | 83 | \begin{enumerate} |
84 | 84 | \item \S7.1\#5 p348: The solution's line segment should go through $(5,-2)$. |
| 85 | +\item \S7.3 Example 7.3.3\#3 p361: The $C$ disappears at the end. |
| 86 | +\item \S7.4 Key Idea 7.4.4\#1 p371: $\cosh^{-1}$ is only defined for positive arguments, so we don't need the absolute value. % todo |
| 87 | +\item \S7.5 Example 7.5.1\#3 p377: We need to have a $\lim_{x\to 0}$ in front of the $\frac2{\cos x}$. |
| 88 | +%\item \S8.2 p397: ``only by a constant ... $+C$ for some constant $C$.'' Check the spacing between ``C'' and ``for''. % todo |
85 | 89 | \item \S8.2 Key Idea 8.2.2\#4 p400: $\tan^{m-2}x$ is missing its $x$. |
| 90 | +\item \S8.3 Example 8.3.2 p409: ``Key Idea 8.3.1(b)'' should be ``8.3.1(2)''. % todo |
| 91 | +\item \S8.3 Example 8.3.3 p410: ``Key Idea 8.3.1(c)'' should be ``8.3.1(3)''. % todo |
| 92 | +\item \S8.3 Example 8.3.5 p412: ``Key Idea 8.3.1(b)'' should be ``8.3.1(2)''. % todo |
| 93 | +\item \S8.6 p436: ``An improper integral is said to \textbf{converge} if its corresponding limit exists'' \emph{and is finite}. |
86 | 94 | \item \S8.7 p456 Theorem 1: The variable $n$ is representing two different things. For that matter, so is $M$. |
| 95 | +%\item \S9.1 p464: From Larry, at bottom of page: you could put in a sentence that says that theorems on limits at infinity from Calculus I have obvious analogues that apply to sequences. (But we need to state the theorems on limits at infinity.) |
| 96 | +\item \S9.1 p466: We haven't stated a Squeeze Theorem for sequences. % todo (but see previous note from Larry). |
| 97 | +\item \S9.2 Theorem 9.2.1 p479: We need to specify that $a\neq 0$. |
| 98 | +\item \S9.3 p490: $[n,\infty]$ should be $[n,\infty)$. |
| 99 | +\item \S9.4 p497: ``For $n\ge N$, We're now'' should be lowercased. % p496? |
| 100 | +\item \S9.4 Example 9.4.2 p498: The stated inequality should be for all $n\ge 2$. |
| 101 | +\item \S9.4 Example 9.4.3 p500: ``Harmonic Sequence'' should be ``Harmonic Series''. |
| 102 | +\item \S9.7 p523 \#6: If the terms contain a factorial, then the divergence test might work. (The root test is also a possibility, if you believe Knewton.) % todo |
| 103 | +\item \S9.9 p546: ``pattern that make their formation'' should be ``makes''. |
| 104 | +\item \S9.9 Theorem 9.9.1 p549: The theorem defines $R_n(x)$ and should be stated as such. % todo |
| 105 | +\item \S9.9 Example 9.9.3\#1 p550: The seventh derivative is $y=+6!/x^7$. |
| 106 | +\item \S9.9 Example 9.9.3\#2 p550: ``[1,2] again'' should be ``[1,2] is again''. |
| 107 | +\item \S9.9 Example 9.9.3\#2 p550: $720/5040\approx1/7$, with subsequent changes. % todo |
| 108 | +\item \S9.9 Example 9.9.4 p552: ``guarantee'' should be ``guarantees''. |
| 109 | +\item \S9.10 p557: ``not the case'' should be ``not necessarily the case''. |
| 110 | +\item \S9.10 Example 9.10.6 p562: The Taylor expansion for $\ln x$ given in Key Idea 9.10.1 is centered at $x=0$. We can use Theorem 9.10.2 with $h(x)=x-1$. % todo |
| 111 | +\item \S10.1 p580: The surface area approximation is not actually a Riemann Sum, because we use two different points in the same interval. % todo: omit or look into the gory details |
| 112 | +\item \S10.2 Example 10.2.13 p594: ``on a wheel of radius $r$ as starts rolling" should be ``as it starts rolling''. |
| 113 | +%\item \S10.3 p605: There's some bad spacing on $f'$ (twice). |
| 114 | +\item \S10.3 p608: ``the parametric equation defining these curves'' should be ``equations''. |
| 115 | +\item \S10.4 Figure 10.4.4: A ray for $-\pi/4$ should be in the fourth quadrant. % todo |
| 116 | +\item \S10.4 Example 10.4.3 p615: $\tan\pi/4$ should be $\tan(\pi/4)$. |
| 117 | +%\item \S10.4 Figure 10.4.7: move this outside of the example. % todo |
| 118 | +%\item \S10.4 Example 10.4.6\#2 p617: There's a space in front of ``This function is valid only when''. % todo? |
| 119 | +\item \S10.5 Example 10.5.2 p627: ``in polar,'' should be ``in polar coordinates,''. |
| 120 | +\item \S10.5 Example 10.5.7 p632: $1+2\cos\theta+\cos\theta$ should have $\cos^2\theta$. |
87 | 121 | \item At the back of the book, integration rule \#2 should enclose its integrand in parentheses, and \#23 should have $a>0$ or use $|a|$. |
| 122 | +%\item We should include $\int\sec^3xdx$ in the table of integration rules. % todo (or $\int\sec^{2k+1}xdx$) |
88 | 123 | \label{2021-06-00II} |
89 | 124 | \end{enumerate} |
90 | 125 |
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91 | 126 | \noindent |
92 | 127 | The following error exists in the in June 2021 printed version of Apex LT Calculus III: |
93 | 128 | \begin{enumerate} |
| 129 | +\item \S12.1 p717 Example 3: In the last displayed equation, ``Multiplying $\vec r(t)$ by 5'' should produce $5\vec r(t)=\langle5\cos t+t,5\sin t+\frac32t\rangle$. |
94 | 130 | \item \S13.5 p815 Example 6: In the final fraction, the ``$+3y^2$'' should be in the denominator, not the numerator. |
| 131 | +\item \S14.7 p931 Example 4: We need to divide by $M$. It also turns out that we can compute these integrals exactly. |
| 132 | +\item \S15.1 p951 Example 3: $\sqrt{1+t^2}$ should be $\sqrt{1+4t^2}$. The final answer is correct. |
95 | 133 | \item \S15.4\#27 p 989: $\vec f$ should be $\vec F$. |
96 | 134 | \item \S15.7 p 1021 Key Idea 15.7.1: In the $\mathbb{R}^2$ Divergence Theorem, the left hand side should have $\oint_{\partial R}$, not a double integral. In Green's Theorem, $\vec F$ is missing its vector arrow. |
97 | 135 | \item At the back of the book, integration rule \#2 should enclose its integrand in parentheses, and \#23 should have $a>0$ or use $|a|$. |
98 | 136 | \label{2021-06-00III} |
99 | 137 | \end{enumerate} |
100 | 138 |
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101 | | -\end{document} |
| 139 | +%\end{document} |
102 | 140 |
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103 | 141 | \startMarkdownTable |
104 | 142 | \begin{table}[ht] |
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