tag:blogger.com,1999:blog-2750355884816556227.post3973294320438984381..comments2023-04-15T06:16:25.962-05:00Comments on Long tails of \int_e^r est: King Mao: Power RuleCalcDavehttp://www.blogger.com/profile/14039458440867020542noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-2750355884816556227.post-63070864311054412662010-09-13T21:02:07.797-05:002010-09-13T21:02:07.797-05:00Well, here's how it went in the one class wher...Well, here's how it went in the one class where we had enough time for them to actually get anywhere with it:<br /><br />They started with throwing out really long problems. So, I had to reassure them that this wasn't a challenge to get my to show some "math magic." Even problems like 2x^2 + 3x - 4 at x = 5 has like 9 different "variables" that could each factor in to the answer (each of the coefficients, each x, each + or -, and the 5). So, treat it like a science experiment and start small and only change one thing at a time.<br /><br />Then, they thought they got it too early when they threw out y = x + c at various x-values and various constants (since they are all 1 for the slope of the tangent). They also assumed the linearity of the operator pretty quickly--which is ok in this case because derivatives work like that, but it's something to keep an eye on later.<br /><br />They only needed to get to cubics to think they knew the pattern and it checked out. Then I proved it using synthetic division for (x^n - a^n)/(x-a). They weren't so interested in that since they already knew the "trick" and don't care where it comes from. (perhaps another blog post there)CalcDavehttps://www.blogger.com/profile/14039458440867020542noreply@blogger.comtag:blogger.com,1999:blog-2750355884816556227.post-62226821392393931972010-09-12T10:42:11.675-05:002010-09-12T10:42:11.675-05:00Oooh, damn. About halfway through the post my head...Oooh, damn. About halfway through the post my head was screaming, "USE WOLFRAM ALPHA!! USE WOLFRAM ALPHA!!" Do your kids have internet at home? Maybe you could make a widget and have them explore on their own the night before? <br /><br />In summer school I used Wolfram Alpha a couple of times for some exploration stuff, and its great. I was actually planning on doing exactly what you are doing, but with Wolfram. Let us know how they deal with it.Anonymousnoreply@blogger.com