1. The problem statement, all variables and given/known data I've been reviewing some Taylor polynomial material, and looking over the results and examples here. https://math.dartmouth.edu/archive/m8w10/public_html/m8l02.pdf I'm referring to Example 3 on the page 12 (page numbering at top-left of each page). The question is asking about an upper bound on the error. 2. Relevant equations 3. The attempt at a solution I was able to get the result in the PDF, but in the discussion of the example, the authors mention that there is a logical issue with using an exact value of e^(0.2) while we're approximating f(x) = e^x . As an alternate bound the authors propose using f(5)(c) < 2 . Can anyone tell me where the justification for this value of 2 comes from? Why is this a proposed value for an upper bound?