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Can inverse functions intersect at points not on the line y=x?

In this question, when it says 'let M be the maximum value of |a_n-1|, |a_n-2| ...' EDIT: is it saying M is equal in magnitude to the highest coefficient?

Hi, I was wondering which HSC years have had the more challenging exams, as I'd like to have a go at them at some stage. I only really know that 2003 was supposed to be very difficult. (If you'd like to say which years have had easier and moderate papers, that would be great as well.)

For this proof, can I do what I did from lines 3 to 4? \sum_{n=0}^{\infty }\frac{x^{2^{n}}}{1-x^{2^{n+1}}}\\=\lim_{N\rightarrow \infty }\frac{1-x^{2^{N+1}}-1+x}{(1-x)(1-x^{2^{N+1}})}\\=\lim_{N\rightarrow \infty }\frac{x(1-x^{2^{N+1}-1})}{(1-x)(1-x^{2^{N+1}})}\\=\frac{x(1-x^\infty...

How did your trials go?

If I don't know the states of matter for a question should I write them or not (ie. do you lose marks for incorrect states if the marking for that question doesn't actually require states?)

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Hi, Seeing as how economics majors at university don't require HSC economics as a prerequisite, I was wondering how long it would typically take for universities to cover the Yr11-12 content? A semester? A year?

Hey so I was wondering if anyone could say whether or not I can do the working out that I do for volumes questions... Eg Q. Consider a shell of inner radius x, outer radius x + δx, and height y. In textbooks, I see them go: δV=pi( (x+δx)^2 -x^2)y and then by expanding and 'ignoring' the (δx)^2...

Hi. So our class is getting close to finishing all the content and I was just wondering what people did after they finished it in previous years? Should I be looking to do questions out of another textbook, go through end of chapter questions, etc? Or should I just be doing past papers (and if...

Could someone possibly explain to me the steps of this from how they converted the sum into the sum product thingy up until they get 1/n?

Hi, Can anyone explain what the redistribution effect on a tariff graph is and how to understand it by looking at the graph?

Hi, Can anyone help me with this question? It asks to find 1+2w+3w^2 and 1+3w+2w^2, where 1,w,w^2 are cube roots of unity. I've found that they equal (-3+-isqrt(3))/2, but I can't figure out which answer (positive or negative) matches which expression. Thanks

Hi guys, can anyone help me with this integral? I=\int \sqrt{16+x^2}dx I know that there would be easier ways to solve it but can anyone see where I've gone wrong? I use a trigonometric substitution and then integration by parts. Assuming my other steps are right, I get to...

Hey So I trying to come up with other forms of creative writing to use instead of a short story and when I had a look at a few of the previous SecII questions that have been on the exams, a lot of them say 'compose an imaginative piece of writing...'. I was wondering whether a form like a...

Hi, I was just wondering in regards to conics questions in exams that require you to find the tangent/normal/chord of contact etc, do you need to prove them from scratch for any question or are there some questions where you can just write the formula down or whatever? Thanks

Hi, I was just wondering what half yearly 4U papers are good to practice on? Or are they all good? Thanks

Hi can someone please help me with these two textbook questions about the CAD. 1. Explain two ways in which a CAD can be financed. 2. Explain three possible effects of an increase in CAD on economic and trade performance. For 1, I thought that the CAD is financed by the capital and...

Hey. So just like the title says, in what ways are voltage transformations related to the law of conservation of energy? Thanks. :santa:

How does the equivalence of energy and mass (E=mc^2) really fit in to the topic of special relativity? Is it to do with mass dilation?