tag:blogger.com,1999:blog-7806043650549721218.post4550067329864183587..comments2021-01-20T22:36:58.627-06:00Comments on EPSILON-DELTA: Continuity and IVTRebecka Petersonhttp://www.blogger.com/profile/12227797437296056645noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-7806043650549721218.post-64934900633391982312014-08-09T04:45:22.222-05:002014-08-09T04:45:22.222-05:00Ask the students if the IVT is true for functions ...Ask the students if the IVT is true for functions in the rational plane. x, x^2, and root x on [0, 4] are good enough to really cause the students to crane their necks. This question requires the students to consider continuity and what that definition really means.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7806043650549721218.post-61304036923284531942013-09-08T21:05:38.005-05:002013-09-08T21:05:38.005-05:00Ohhhh!! Love it. Will add this for next time. Than...Ohhhh!! Love it. Will add this for next time. Thanks!Rebecka Petersonhttps://www.blogger.com/profile/12227797437296056645noreply@blogger.comtag:blogger.com,1999:blog-7806043650549721218.post-66705913344253799872013-09-04T15:18:00.050-05:002013-09-04T15:18:00.050-05:00You should also try "The height of a plane fr...You should also try "The height of a plane from a few minutes before take-off to a few minutes afterwards." You'd be surprised at the interesting conversations concerning whether there is a "first moment" when you are in the air or a "last moment" on the ground. briehttps://www.blogger.com/profile/18102587900266610644noreply@blogger.comtag:blogger.com,1999:blog-7806043650549721218.post-79814204197631178352013-09-02T19:29:36.496-05:002013-09-02T19:29:36.496-05:00Yes! That's exactly how I feel my students vie...Yes! That's exactly how I feel my students view IVT, too. They can "work" the trite textbook problems, but do they REALLY understand the theorem? <br /><br />I'd be really interested to hear more about your school's approach to calculus. So, do first year calc students take AP Calc AB, or do they take a non-AP calc course?Rebecka Petersonhttps://www.blogger.com/profile/12227797437296056645noreply@blogger.comtag:blogger.com,1999:blog-7806043650549721218.post-52273257903064194102013-09-02T05:11:17.863-05:002013-09-02T05:11:17.863-05:00Rebecka
I really like the questions you posed her...Rebecka<br /><br />I really like the questions you posed here - especially as a follow up to Kate's questions. I find that students 'get' the IVT but only in the context of 'Oh, that's the one where I identify roots between consecutive integers' or some other forced context from Precalculus or Calculus. I am teaching AP Calc BC (we do it as a second year of Calculus at our school) and many of my students remembered both IVT and MVT but most confused their names. This was interesting to me as, in my mind, the names of these theorems reveal quite a bit about what the theorem says.Anonymousnoreply@blogger.com