Calculus:Error log

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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.

Page Error description Version where it was introduced Version where it was corrected Why error? Why not caught? ("I" refers to Vipul)
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