Some Notes

I didn’t come across anything calculusy to write about this week, so here are a few other items you might be interested in. Two Explorations Two explorations previously posted on topics that come up this time of year. Differential Equations. An exploration in Differential Equations is a summary/review exploration in which students will work 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…

Good Question 17

A common question in (older?) textbooks is to give students a function or relation and have them graph it without technology (because in the old days technology was not available). Students had to find all the appropriate information without hints or further direction: they were supposed to know what to do and do it. AP…

Quadratic Formula or Not?

There was a very interesting post in the AP Calc TEACHERS – AB/BC Facebook page last week. It discussed an apparently new method for solving quadratic equation without guess-and-check factoring, completing the square, or the quadratic formula. It was discovered by Dr. Po-Shen Loh of Carnegie Mellon University. The full article is here. The article…