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I don't think the roots of the derivative having opposite signs would imply the original function having 3 real roots, It should be the stationary points with the y-values being opposite in signs giving 3 roots. EDIT: besides the better method is to draw the graph k/x, one case where k>0...

Re: HSC 2015 3U Marathon pi*e = \pi e

Re: HSC 2015 3U Marathon Using the symmetrical properties, find \int_{-a}^{a} cos^{-1}x \ \ dx \ \ \ \ \ \ -1\leq\ a \leq 1

you'll adapt to it don't worry. :)

wut, I'm asian and I've made white friends. and I make friends so that I know there's help when I need it, (like my math problems)

I can't wait to see how it turns out :D

Lel I make friends with people I regularly see at my uni classes, regardless of their nationality (and yes that includes the international one). But sure you would get along better with people who are of the same race.

Oh yeah I remember back in my yr 7 science class, we would basically throw shit around and not listen to the teacher. She got fired in the end like holy shit karma failed.

Re: MX2 2015 Integration Marathon I'm assuming k is just a constant, using by parts u = ln(x+\sqrt{x^2+k^2}) \ \ \ \ \ v' = 1 \\ \\ \\ u' = \frac{1}{\sqrt{x^2+k^2}} \ \ \ \ \ v = x \Rightarrow xln(x+\sqrt{x^2+k^2}) - \int\frac{x}{\sqrt{x^2+k^2}} \ \ dx and yeah just...

And also the period for tan functions are pi/b where b is whatever pho just said

The syllabus hasn't really changed in a long time haha. Yeah it's good to practice the 84 marker question, since the difficulty is pretty similar. I remember learning something in the 2007 Q7, and actually applied that idea in my 2013 paper Q14 (best feels ever when I solved it)

The log law doesn't apply to complex numbers :P

The line is actually y = 4-4x, so the answer is A

well it's good to know that no one is hurt.

sorry mate, not even wolfram alpha can give you a simple answer.

yup you're right, the question probably needs more information since the polynomial is in the form -(x-\beta)(x-1)^2 and there's nothing in the question that would restrict beta to be greater than 1 and now we know why Math in focus is unreliable :P

Re: MX2 2015 Integration Marathon is I_n Suppose to have limits or not?

Q6 you're solving sinx = +-(1/root2) Q7 limiting sum question with 3/5 as the ratio (also be wary of the 2 in the front) Q8 PUQ and PRT are similar triangles, use that to find the length x (i.e UT) and add 8 and 6 to get PS

Ya Clilic had an ankle injury sadly, but ofc Djoker was in a supreme form. But holy shit I didn't expect Federer to win in straight sets.