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Some books require it to be smooth as well, and your example qualifies for this, so is not too controversial. However other examples where it is not smooth at (a,b) may also change concavity at (a,b). This is where it gets controversial. Some books still call it an inflection, others don't...

It changes concavity at (0,0), so this is an inflection. But all the derivatives of order greater than 1 do not exist at (0,0).

This is incorrect. e = 2 + 1/2! + 1/3! + 1/4! + ............ This is because e = 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + ............ Anyway, I wrote some notes on e at http://www.angelfire.com/planet/threeunit/factsaboute.pdf http://www.angelfire.com/planet/threeunit/e.pdf

Yes there is. And it was reviewed <a href="http://www.maa.org/reviews/GreatPieDebate.html">here</a>.

Have you guys seen the video The Great Pi/e debate before you voted? You can get it at https://www.maa.org/EbusPPRO/Bookstore/ProductDetail/tabid/170/Default.aspx?ProductId=1440

The same can be said of MANSW's recommendations from yesterday's meeting.

Why don't you write a submission? I did. Here it is: http://www.angelfire.com/ab7/fourunit/submission3.pdf

I don't want to reveal too much at this stage, but I can say that if they adopt the IEU's recommendations, the final syllabus will look very different from the draft.

Have MC like the AMC? Is the HSC a competition? If so then how are results reliable and valid in the context of standards referencing? They aren't. So here's a MC for you. Vested interests are at play here. Choose which of the following are correct. A. Cost cutting. Thousands of tax-payer...

The President of MANSW has proclaimed in the June 2008 Secondary Newsletter that "MULTIPLE-CHOICE QUESTIONS WILL BE PART OF ALL THREE CALCULUS COURSES". MANSW is also holding a meeting on June 14 at 1:30 – 4:30pm, Kent Road Public School, Eastwood, for their submission to the Calculus courses...

Why? ..............

There is a meeting next Tuesday to be held by the NSW/ACT Independent Education Union at 4.30pm-5.30pm at the IEU Head Office at 176-182 Day St, Sydney. Members of the Board of Studies Mathematics Curriculum Committee will be present to receive a submission from the IEU which will be based on...

The IMO for 2008 was held in Madrid, Spain, July 16-17. Question paper: http://www.angelfire.com/ab7/fourunit/imo2008.pdf Website: http://www.imo-2008.es The Australian team is Paul Cheung, Sydney Technical High School, NSW Andrew Elvey Price, Brunswick Secondary College, Vic Giles Gardam...

For 4 unit, you can obtain a copy of <a href="http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths4u_syl.pdf">the syllabus</a> to see if you have covered the requirements of Component A. You can use <a href="http://users.tpg.com.au/nanahcub/texts.pdf">textbooks</a> to assist you in...

Other AMC papers with solutions for 1978-2007 are available from http://www.amtt.com.au

It shouldn't have the 0.5 5x32=160 Thanks for the correction. But the correct answer is still C.

Pederson, D.G. & Sommariva, H.M. (eds), AMC Solutions & Statistics 2002, AMT Publishing, 2002, pp. 42-46. And just so it's fair for others on this thread, I've also attached questions 21-30 here:

Official solutions attached.

Terry Tao has just won the $500,000 Waterman Award. http://www.eurekalert.org/pub_releases/2008-04/nsf-ntb040908.php