Carrotsticks
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As the name suggests, 'harder' applications of topics in 2U.My 4U tutoring class teacher says that mechanics / Harder 3U (referring back to Carrotstick's comment on Harder 2U) is the hardest o-o What's with all this 'harder' stuff?
For example in the 2002 Extension 1 HSC, they asked a question which required the construction of an Upper and a Lower bound rectangle, then using them to bound the integral of 1/x between n and n+1. The next part essentially got you to prove that lim as n -> infinity of (1+1/n)^n approaches e using the Squeeze Law. However, they just got you to establish the bounds, not actually take the limit. But this was not really fully done in the HSC until the 2009 Extension 2 Question 7 (b) and (c), but for 1/e instead of e.
The question uses nothing except the ability to integrate y=1/x and the ability to do a bit of algebra manipulation... all of which are taught in 2U extensively. It uses no concepts from the Extension 1 course and hence, goes under 'Harder 2U'.
Here is the Extension 1 2002 HSC version:
Here is the Extension 2 2009 HSC version:
Even so, the Extension 2 (Question 8, can you believe it!?) version did not even require anything from the Extension 1 or 2 course, only 2U skills.