# Errata

Despite numerous sets of eyes examining the text, APEX Calculus contains errors. This page lists ** some **errors in Version 3.0.

**Important:**this page is no longer updated. Submissions of errors and other suggestions are always welcome; while errors will be addressed, they likely won't appear on this page. Version 4.0 is due to appear Fall '18 and will address all errors submitted.

I am greatly indebted to the many users who have read the text very closely and uncovered a number of errors. If you find an error, please let me know. This page *used* to keep a running tally of all known errors, but the list grew long and I fell behind in the editing/updating process.

I am currently (November, 2017) fixing all known errors. Version 4 of the test is planned to be released in Spring, 2018, ready for the 2018/19 academic year. At that time, this page will be restarted afresh.

**Errors in Accuracy:**

**Page 68, Section 2.1:**The displayed equations at the top of the page should have the limit as "h→0", not as "x→0".**Page 73, Section 2.2:**The next to last sentence on the page should end "... figure that v(0) = 52 ft/s.", and not "v(0) = 42 ft/s."**Page 416, Section 8.2:**In Example 239, part 5, the summation shouldn't start at n=10 as that makes the denominator of the summand 0.**Page 432, Section 8.3:**In Example 249, the series index is n but the summand is given in terms of x. All the x's should be n's.**Page 29, Section 1.3:**Exercise 36 should have the limit as "x→3", not "x→3+", and the interval [0,3] should not be given.**Page 548, Section 9.5:**Exercises #21-23 should be given in terms of θ, not t.**Page 84, Section 2.3:**Exercise #37 has wrong answers in the back of the book. The slope of the tangent line should be \(\sqrt{2}\) instead of \(\sqrt{2}/2\), and the slope of the normal line should be \(-1/\sqrt{2}\) instead of \(-2/\sqrt{2}\).**Page 624, Section 11.1:**Figure 11.3 has the wrong caption. A vector-valued function is shown, as well as the value of the function at a particular point. The derivative is*not*shown (nor has the derivative been defined yet).**Page 694, Section 12.3:**Example 405 has two errors in the answer to Part 3. It should read: \[\begin{align*} f_x(x,y) &= e^{x^2y^3}(2xy^3)\sqrt{x^2+1} + e^{x^2y^3}\frac12\big(x^2+1\big)^{-1/2}(2x) \\ &= 2xy^3e^{x^2y^3}\sqrt{x^2+1}+\frac{xe^{x^2y^3}}{\sqrt{x^2+1}}. \end{align*}\]**Page 718, Section 12.5:**The computation of \(f_y(x,y)\) is wrong in Example 421; it is missing a \(+3y^2\) term. This error carries over into the denominator of the final answer of the example.**Page 681, Section 12.1:**The answer to #19 should list the radius as \(r=\sqrt{2/c^2-1}\).**Page 319, Section 6.6:**In Key Idea 19, the third column of #3 should be \(\frac{1}{2a}\ln\left|\frac{a+x}{a-x}\right|\); the text is missing the "\(a\)" in the coefficient of \(\ln\). This error also exists in the Integration Rules table in the back of the text.**Page 65, Section 2.1:**In Example 36, the limits should be as "h→0", not "x→0".**Page 3, Section 1.1:**The caption for Figure 1.4 should say "for x near 0", not "x near 1."**Page 41, Section 1.5:**The caption should refer to "Example 24(1)", not "24(a)".**Page 18, Section 1.3:**The Composition Rule of Theorem 1 is incorrect. In short, we need to require that the function g(x) be continuous at L, hence we need to add the requirement that "g(L)=K."

As a result, the answer to part 4 of Example 12 should change to reflect checking for this new condition. Also, problems 10, 11, 12 and 17 in the Exercise section, which involve the Composition Rule, should all technically be answered with "one cannot know with the given information." These latter issues will be fixed for future editions of the text.**Page 35, Section 1.4:**The answer to #6f should read, in part, "x>2", not "x<0".**Page 620, Section 10.6:**The -6's in the displayed equations should be +6's; the resulting dot product has a value of 14, not -16, giving a final answer of about 1.74, not 1.98**Page 653, Section 11.3:**The graph of the solution in the back of the book for #13 should reference the vectors \(\vec v(1)\) and \(\vec a(1)\); instead, the t-value they reference is \(\pi/4\).**Page 578, Section 10.2:**The answer in the back of the book for problem #21 should be \(\langle 3/\sqrt{58},7/\sqrt{58}\rangle\).**Page 129, Section 3.1:**The answer to #6 should list B as both a relative and absolute maximum.**Page 304, Section 6.4:**The answer to #6 should have \(x^2+4\) under both square roots, instead of \(x^2+1\) under one square root.**Page 425, Section 8.2:**The answer to #38 should state that \(a_n = \frac12\left(\frac{1}{2n-1}-\frac{1}{2n+1}\right)\), and hence \(S_n = \frac{n}{2n+1}\).

**Errors in Grammar:**

**Page 56:**The third sentence of Section 2.1 should read "Students of physics...", not "Student of physics..."**Page 85:**The last sentence of the page should refer to the "Product Rule" and not the "Produce Rule." The Produce Rule is something else entirely.**Page 89:**The last paragraph of Example 55 should start "This is a beautiful result.", and not "This is beautiful result."**Page 98:**The first sentence of the second paragraph after Theorem 19 should read "... then rewrite the ..." instead of "the rewrite the".**Page 736:**Example 432 should read "Find the equation*of the*tangent ..."; "of the" is missing.**Page 37:**The end of the third sentence on the page should read "of what f(1) actually*is*." In the text, the word "is" is "this".