The explanation of the average value function was very good. Images for some of the properties of definite integrals could be helpful. The media links I was able to open I thought were very good. Most references to individuals seems neutral. I didn't find any instances of culturally insensitive or offensive text. I did have trouble with some media links but I'm attributing that to the work computers and blocking access to some sites. I was curious why delta x(sub i) was not included in the definition of a Riemann sum but this was later explained in 5.2. Yes, the text is nicely broken into manageable sections that could be rearranged if necessary. The limit rule for sinx/x as x approaches 0 is explained in 2.3, but I would like this to have it's Theorem or Rule box. This would include many of the functions mentioned in chapter 1 (they could be included in the Precalculus review), the existence of a limit, the compound formula and continuous compound formula. There were some bold terms that I would have like to see get a boxed definition. It was formal when necessary but otherwise friendly or not stuffy. I thought the writing was very accessible. Many chapter openers and student projects involve situations that would interest students. I appreciate the informal proofs about limits at infinity along with the formal proofs. It provides greater accuracy but uncertainty about if it's an upper or lower sum. I would also say that about the midpoint rule for finding area under a curve, not necessary but gives the alternative to an upper sum and lower sum.
This isn't required but is nice to get exposure to in Calculus 1. The text covers all topics I was expecting except for a discussion about normal lines.
Reviewed by Pat Miceli, Associate Professor, City Colleges of Chicago on 4/10/23
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