# Errata for MTH 132 Course Videos

## Chapter 1

• Section 1.4 Video 2 -- Example 4.7 (10:39) -- Dropped a 2. This alters the solution for all the parts!
• Section 1.6 Video 1 -- Theorem 6.3 (7:38) -- The hypothesis should really be "if a is in the interior of the domain of f..." otherwise the two sided limit may not exist (such as in the sqrt(x) at x=0).
• Section 1.8 Video 1 -- Theorem 8.4 (4:24) -- First off, this is quite informal so it should just be a remark. Also there is a subtle consistency issue. It claims that various types of functions are continuous at all points of their domain but in the videos I never state that in the case of endpoints in a domain if a function, if the endpoint is left (or right) continuous it is considered continuous (it does state this in the book). So bottom line, sqrt(x) is continuous at x=0. I should have spent another minute or two to specify this in the video.
• Section 1.8 Video 2 -- Definition 8.14 (10:00) -- Types of discontinuities are defined in an awkward way. I define jump discontinuities as the complement of the set of removable and infinite discontinuities. This is somewhat forgivable because in this class we do not cover oscillating essential discontinuities but it could have been done much better and more clearly by just defining jump discontinuities as ones where the left and right limits exist by don't agree.

## Chapter 2

• Section 2.5 Video 2 -- Example 5.9(b) (11:13) -- There is an interesting issue here. Even if the derivative of the inside function DNE, it is possible for the derivative of the composition to exist (take |x|^3 at 0). It really means the chain rule cannot be applied to calculate the derivative with those choices of functions. Still though the answer in this case is DNE.

## Chapter 3

• Section 3.1 Video 2 -- Example 1.12 (10:00) -- Mistakenly evaluate f(1)=-12 when it should be f(1)=-10.