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Re: HSC 2012 Marathon :) %5Cfrac%7Bd%7D%7Bdx%7Dln%28%5Cfrac%7B1%7D%7B%5Csqrt%7Bsinx%7D%7D%29=%28%5Csqrt%7Bsinx%7D%29%28%5Cfrac%7B-cosx%7D%7B2%28sinx%29%5E%7B3/2%7D%7D%29%5C%5C%20=%5Cfrac%7B-cosx%7D%7B2sinx%7D%5C%5C%20=%5Cfrac%7B-cotx%7D%7B2%7D <a...

Can you type out the question or scan it? I don't have a copy of the book...

The first statement isn't true. A counterexample is Liouville's constant: http://mathworld.wolfram.com/LiouvillesConstant.html

There's no stationary point on y=e^x- the curve is increasing for all values of x as the derivative is also e^x which is >0 for all x. Are you sure you wrote the question out properly?

Quite interesting- thanks Carrot :)

What is your school rank?

You should do whatever your teachers want. I know at Tech, we can't write alt. ∠s, // lines, but rather have to write alternate angles on parallel lines. If we wrote the former, we'd lose marks so basically check with your school. Do whatever in the HSC though.

Re: I got 97 for my economics exam, the next highest mark was 78. Will I get scaled d No. Having said this, if you consistently score 50's, I wouldn't be expecting a very high mark unless your school is EXTREMELY ruthless in marking.

How did you get a much higher mark for MX1 than 2U? Was the 2U test really hard or did you just have a bad day?

Actually you have no idea. Most people doing standard think that if they write the same thing in standard or advanced, they'll end up with the same mark, just with standard you avoid Shakespeare. Very few people actually understand how the HSC works- really no one at a selective school should do...

Try doing HSC 2010 Q28. Look at the marking guidelines and sample answer if you need help with it...

Re: HSC 2012 Marathon :) Yep, whoops didn't think of that. Why then does wolfram show the curve continuous at 0?

Re: HSC 2012 Marathon :) Consider the straight line y=x. You can multiply the RHS by x/x without changing its value. Thus the straight line becomes y=x^2/x which suddenly can't have a value of 0, even though the line hasn't changed and its still defined at x=0

Re: HSC 2012 Marathon :) http://www.wolframalpha.com/input/?i=y%3Dx^3%2Fx

Re: HSC 2012 Marathon :) Your are right. There is no 'hole' at x=0

Re: HSC 2012 Marathon :) Sorry, what do you mean? The question is saying that when a rectangle is a square, that is the shortest possible diagoncal length- i.e. as you stretch a square out into a rectangle, the diagonal becomes longer. Now you have to prove that.

Re: HSC 2012 Marathon :) This was from our last 3U test- Prove that the smallest diagonal of a rectangle occurs when the rectangle is a square (medium?- I'm not very good at estimating, maybe someone else can give a judgement)

Yeah, I was thinking about doing it like that (its essentially the same thing) but I try to minimise the number of terms I have to write out in latex because I'm pretty slow haha.

I don't think they would- I've never seen anything this hard in any HSC paper (the fact that I got it by trial was a fluke pretty much). Where did you get this question from OP?

I don't think you can do it with substitution or by parts or any 'normal' means. The way I did it was trial and error- working out what you need to differentiate to give that as the answer. I can post the answer though if you guys want (but that might spoil it...)