Calculus:Error log

Did you find something that looks like an error (or possible error) to you? Report the error quickly here (anonymous, does not require login, but you can optionally provide an email ID to be notified of the fix).

We have just started logging errors. On this page, you will find information about all errors that persisted on the site for more than one month on any page. Note: This applies only to errors that were not fixed by December 18, 2011. Errors fixed before then are not being logged on this page.

We are only required to include here errors that were present for at least 24 hours before being fixed; however, we may optionally include errors that were present for anywhere between 3 hours and 24 hours, generally to provide insight about the nature of errors that might happen. Errors that were present for fewer than 3 hours should not be included.

Page	Error description	Version where it was introduced	Version where it was corrected	Why error? Why not caught? ("I" refers to Vipul)
Practical:Chain rule for differentiation (< 24 hours to fix)	My example for evaluation at a point for the chain rule for differentiation was incorrect; it confused the role of $g$ and $g'$.	December 4, 2023	December 5, 2023	The error lasted about 10 hours. I actually remembered about this within a few hours -- I made the edit shortly before sleeping and spontaneously noticed the error (even without actively trying to review it) the next morning right after waking up. The reason for the original error was a hasty attempt to modify a similar example for the product rule, without thinking about the modification as its own example. Something about it must have made me uneasy enough to spontaneously remember it and notice the error upon waking up the next morning.
Existence of directional derivatives in every direction not implies differentiable	Two errors: the actual limit in the counterexample was incorrect (missing a square) and a superfluous statement in the proof was incorrect.	April 13, 2012	December 13, 2022 (two edits)	Single edit creating the full proof; not enough proofreading after the creation
Parametric derivative	The final expression had a missing prime symbol.		September 24, 2021	carelessness
Derivative	The final form of for left-hand derivative and right-hand derivative missed the $\{\}_{0}$ subscript at the end.		September 24, 2021	carelessness
Logistic function	The derivative expression in the "Key data" table had an extra minus sign. The derivative in the section that actually computed it was correct		July 6, 2019
Second derivative test for a function of multiple variables	wrote that the derivative must be $(-1)^{r}$, where the intended statement was that the sign of the derivative must be $(-1)^{r}$		July 4, 2015	carelessness
Limit	In a discussion of the relation between one-sided and two-sided limits, forgot an "and are equal" (not in the main definition, but in an aside)		May 16, 2015	carelessness, insufficient review
Derivative of differentiable function satisfies intermediate value property	at one stage in an explanation, used two-sided derivative notation where only one-sided derivatives are guaranteed to exist.		January 20, 2013	minor issue
inverse function theorem	omitted a continuity condition/constraint		January 20, 2013	genuine conceptual misunderstanding; didn't think through proof clearly and didn't rack brains for counterexample.
first derivative test	omitted continuity from "succinct version" (now "short version") of test; it was included in the lengthier description		May 3, 2012	error in judgment, not so much in fact (because continuity assumption was stated in the longer version)
second derivative test	Didn't state that the point of concern must be a critical point in the "What the test states" section though it was stated in the "What the test is for" section	September 19, 2011	May 2, 2012	didn't review, revisit page
point of local extremum implies critical point	Fact numbers in the Explanation column for the local minimum case were somewhat messed up (although fact numbers in the Facts used column were correct), also used "maximum" instead of "minimum" at a couple of places in the "Given data used" column	October 20, 2011	April 25, 2012 and May 4, 2012	copy-paste error from maximum to minimum. I should really have caught the second error at the time I caught the first ... it just goes to show that one has to be doubly, triply careful when reading tabular proofs and check that all columns are correct and up to date.
first derivative test	had "right" in place of "left" for one of the case rows	September 19, 2011	April 24, 2012	didn't review, revisit page
product rule for partial differentiation	directional derivative instead of gradient at one place, and a bunch of minor typos, missing open parenthesis, use of $\cdot$ for function product at one place (might confuse with dot product), and extraneous statements like "let ${\overline {u}}$ be a unit vector" in definition components where no unit vector was needed.		April 2, 2012	didn't revisit page often enough
partial derivative	Had "x" in place of "y" in one of the derivative descriptions/definitions.	December 17, 2011	April 1, 2012	Didn't revisit page often enough