Adapting 2021 BC 6

Nine of nine. We continue our look at the 2021 free-response questions. We will look at ways to adapt, expand, and explore this question to help students better understand it and look at other questions that can be asked based on a similar stem. 2021 BC 6 This is a Sequence and Series (Type 10)…

Adapting 2021 BC 5

Eight of nine. We continue our study of the 2021 free-response questions. We will look at ways to adapt, expand, and explore this question to help students better understand it and look at other questions that can be asked based on a similar stem. 2021 BC 5 This is a Differential Equation (Type 6) with…

A Curiosity

Thoughts on the power series for  , which I found curious. Last week someone asked me a question about the Maclaurin series for  .  Finding the Maclaurin series is straightforward:   Substituting for x gives   We can find the radius and interval of convergence by using the Ratio test: This indicates that Maclaurin series…

What’s the “Best” Error Bound?

A know a lot of people like mathematics because there is only one answer, everything is exact. Alas, that’s not really the case. Numbers written as non-terminating decimals are not “exact;” they must be rounded or truncated somewhere. Even things like  and 5/17 may look “exact,” but if you ever had to measure something to…