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Ahhhhh now i see it, thanks!

Hey guys, I am attempting to prove a question that I found from a problem set from Stanford Uni on series and sequences, however I'm having a little bit of difficulty. I've been at it for a while and so finally i've resorted to looking at the provided solution. The question and solution are...

I'm not sure if there's a flaw in this or not, but here's my attempt: The person who can see 99 hats (ie the 100th person) should inspect all the hats in front of them. If there is an even number of red hats, they should say "red". If there is an odd number of red hats, they should say "blue"...

Re: HSC 2013 4U Marathon Slightly advanced for 3U students + 3U marathon forum seems to be dead so i'll just post it here: \\ $ Prove by Mathematical Induction that for all positive values of $ n, \\\\ \tan^{-1}(\frac{1}{2}) + \tan^{-1}(\frac{1}{8}) + \tan^{-1}(\frac{1}{18}) +...+...

lol

http://www.coroneos.com.au/shop-online/hsc-past-papers/hsc-extension-2-mathematics-past-papers-1990-2011-worked-solutions-2012-

Re: HSC 2013 2U Marathon Fixed: \int \frac{x^3}{x^2+1} dx I put a space between the "tex" wraps and the code itself and it worked.

Re: HSC 2013 4U Marathon You copied the wrong code, swing me a PM so we aren't spamming this thread and i'll teach you how to do it.

Re: HSC 2013 4U Marathon http://www.codecogs.com/latex/eqneditor.php Use this website, then simply copy and paste the code generated and wrap it around [ tex ] "CODE" [ / tex ] (without the spaces).

Re: MX2 Integration Marathon \\ $ Let $ u = \sqrt{\tan x} \\\\ \Rightarrow u^2 = \tan x \\\\ \Rightarrow 2udu = \sec^2xdx \\\\ \Rightarrow dx = \frac{2udu}{\sec^2x} \\\\ \Rightarrow dx = \frac{2udu}{1 + \tan^2x} = \frac{2udu}{1 + u^4} .'. \int \sqrt{\tan x}dx = \int \frac{2u^2du}{1 + u^4}...

Re: HSC 2013 3U Marathon Thread Well done, was quiet a straight forward question i must admit and the only reason i posted it was because i was hoping someone would post a non-calculus solution. It can be done very elegantly as follows: Note that the shortest distance between 2 points is a...

Re: HSC 2013 3U Marathon Thread $ Island 1 and Island 2 are positioned as such that there perpendicular distances from a straight shore line are 1km and 2km respectively, and along the shore line these two islands are 6km apart. A pier is to be built on the shore of the lake and a straight...

Re: HSC 2013 4U Marathon \\ $Find $ \\\\ \int\frac{x^3 e^{x^2}}{(x^2+1)^2}dx

Re: HSC 2013 4U Marathon My apologies. Should simply read "if f(x)" not if and only if. I was in the middle of doing another question when i posted that one up haha; fixed it now.

Re: HSC 2013 4U Marathon Your logic and method is correct Sy, but you've made a mistake with your algebra. \\ $ To begin with we must suitably split up the integrand so that it is easily integratable via IBP. $ $ Thus the simplest way is to re-write $ I $ as \int f'(x)*[f'(x)f(x)^{n}]dx...

Re: HSC 2013 4U Marathon \\ $ For any given function $f $ let, $ \\ \\I = \int [f'(x)]^2 [f(x)]^n dx; $ \\ \\ where n is a positive integer. Show that, if $ f(x)$ satisfies $ \\ f''(x)= kf(x)f'(x)$, for some constant $ k$, then $ I$ can be integrated to obtain an expression in terms of $ f(x)...

Re: HSC 2013 4U Marathon Nice job Sy. Alternatively, from the line you posted instead of simplifying down to cotangents and using the fact cot is periodic by pi, you can cross-multiply the sin's on the denominators and then bring everything to the one side to make the equation = 0. This...

Re: HSC 2013 4U Marathon \\$ The points P, Q, R and S lie on an ellipse and have coordinates $ \\ (a $ cos $ p, b $ sin $ p), (a $ cos $ q, b $ sin $ q), (a $ cos $ r, b $ sin $ r) $ and $ (a $ cos $ s, b $ sin $ s) $ respectively; where $0 \leq p < q < r < s < 2\pi $; and a and b are both...

Re: HSC 2013 3U Marathon Thread \\ $Use Mathematical induction to show that:$ \\ \\ x^n $ + $ y(2x+y)^{n-1} $ is divisible by $ (x+y); $ where n, x and y are positive integers.$

Bachelor of Engineering/BSc(Mathematics Major) @ University of Queensland