tag:blogger.com,1999:blog-15868947.post6193136473059423664..comments2022-11-28T01:53:13.499-08:00Comments on Halfway There: Even lotteries have winnersZenohttp://www.blogger.com/profile/09058127284297728552noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-15868947.post-45993800514580785522012-04-28T01:34:39.528-07:002012-04-28T01:34:39.528-07:00Simply shocking. It seems, that your students'...Simply shocking. It seems, that your students' basic problem is to determine the linear function, whyich are, subsequently f(x)=-x=3, f(x)=3x-5 and f(x)=3. This should be have done a way long before the elementary integrating was introduced (as I remember, in Poland children are taught this in the age of 12), Let alone the Pytagorean theorem if you really did not bother about the method.. Greetings from Bridgwater.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15868947.post-64842563130088052222011-12-24T13:42:23.539-08:002011-12-24T13:42:23.539-08:00This is awesome!This is awesome!ivonoreply@blogger.comtag:blogger.com,1999:blog-15868947.post-36199309039190269192011-12-17T17:34:56.615-08:002011-12-17T17:34:56.615-08:00If it makes you feel any better, I solved a univer...If it makes you feel any better, I solved a university calculus problem by taking the average of two infinities. It was a bogus problem, anyway.Lightning Rosehttps://www.blogger.com/profile/09287732852487842915noreply@blogger.comtag:blogger.com,1999:blog-15868947.post-40696679388720464872011-12-16T22:18:51.199-08:002011-12-16T22:18:51.199-08:00Du hast recht, Daniel. Amusing, isn't it? If o...Du hast recht, Daniel. Amusing, isn't it? If only I hadn't used the function I used, <i>or</i> the intervals I chose. Weird, weird coincidence.Zenohttps://www.blogger.com/profile/09058127284297728552noreply@blogger.comtag:blogger.com,1999:blog-15868947.post-37202548442704822922011-12-16T16:59:40.453-08:002011-12-16T16:59:40.453-08:00The geometric reason why this allegedly "stup...The geometric reason why this allegedly "stupid" calculation actually works is of course the fact that your blue curve is - at least in the relevant range between x=1 and x=5 - perfectly symmetrically aligned with respect to the curve y=x, so the two curves give the same integral value.<br /><br />Greetings from Bonn (in Germany),<br />DanielAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-15868947.post-32781729896220393832011-12-16T07:41:33.118-08:002011-12-16T07:41:33.118-08:00No, Tualha, she wasn't messing with me. I'...No, Tualha, she wasn't messing with me. I'm quite certain she had no idea her calculations were invalid. Joshing around with coincidentally correct bogus math would have been completely uncharacteristic of her.Zenohttps://www.blogger.com/profile/09058127284297728552noreply@blogger.comtag:blogger.com,1999:blog-15868947.post-6688763197004760532011-12-16T06:31:19.905-08:002011-12-16T06:31:19.905-08:00...Do you suppose she was messing with you?
Perha......Do you suppose she was messing with you?<br /><br />Perhaps while doing homework earlier in the term, she used this bogomath by mistake and noticed that it worked under certain circumstances. So she decided to have a little fun with you on the exam.<br /><br />Prudence would dictate doing it on homework instead, with less of the grade at stake, but maybe she was doing well enough that she could afford to risk some points on this exam.<br /><br />Are the rest of her grades consistent with this interpretation?Tualhanoreply@blogger.comtag:blogger.com,1999:blog-15868947.post-69416538935650816982011-12-15T22:36:30.183-08:002011-12-15T22:36:30.183-08:00This teaches us one thing: when in doubt, integrat...This teaches us one thing: when in doubt, integrate y dx! HeheeAnnienoreply@blogger.comtag:blogger.com,1999:blog-15868947.post-44204726826056212242011-12-15T16:04:47.707-08:002011-12-15T16:04:47.707-08:00Some of the other problems were just a bit more ch...Some of the other problems were just a bit more challenging, Sophia.Zenohttps://www.blogger.com/profile/09058127284297728552noreply@blogger.comtag:blogger.com,1999:blog-15868947.post-13078734648001484982011-12-15T13:21:38.192-08:002011-12-15T13:21:38.192-08:00I wish my calculus professor would ask me question...I wish my calculus professor would ask me questions as easy as these.<br />Or maybe not, I would drive myself crazy looking for the catch...Sophianoreply@blogger.comtag:blogger.com,1999:blog-15868947.post-4510498576550510742011-12-15T07:53:16.305-08:002011-12-15T07:53:16.305-08:00It's hard for a smart person to anticipate the...It's hard for a smart person to anticipate the vast potential for stupidity.Kathienoreply@blogger.comtag:blogger.com,1999:blog-15868947.post-85866528437469399522011-12-15T07:01:26.711-08:002011-12-15T07:01:26.711-08:00hahahahaha *takes breath* hahahaha!
...
*Stops,...hahahahaha *takes breath* hahahaha! <br /><br />...<br /><br />*Stops, realizes her students are taking a final, and she shouldn't tempt fate right now*Laurahttps://www.blogger.com/profile/11687460104635611761noreply@blogger.comtag:blogger.com,1999:blog-15868947.post-22144819680426222682011-12-15T06:39:44.378-08:002011-12-15T06:39:44.378-08:00Full disclosure, Simon: Two of my students fell do...Full disclosure, Simon: <i>Two</i> of my students fell down this particular rabbit hole on this particular problem. The guy's "solutions" consisted solely of the bogus definite integrals. He got very little credit. (<i>Perhaps</i> he also eyeballed the graphs and saw that his answers were consistent with them, but he did not say so.) The gal accompanied her bogus integrals with notes that pointed out the simple geometric computations as an alternative. She earned most of the points, with a few deducted for the calculus bogosity.Zenohttps://www.blogger.com/profile/09058127284297728552noreply@blogger.comtag:blogger.com,1999:blog-15868947.post-1725302857464084402011-12-14T22:51:33.593-08:002011-12-14T22:51:33.593-08:00That's hilarious!
Your graph and chosen integ...That's hilarious! <br />Your graph and chosen integration regions match up perfectly to your student's consistent misunderstanding. Also, it's possible that the student noticed that their answers matched the number of squares, which is what you were looking for, but they didn't bother writing down the observation since they "answered" the problem with the more mathsy calculus.<br />So how did you mark it?Simonhttps://www.blogger.com/profile/05928042944229954890noreply@blogger.com