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I reckon the 'e' method makes life easier. Luthian, in your first post it's just subbing in e^ln2 for 2 because 2^x = e^x.ln2 so your working is: y = 2^x = (e^ln2)^x = e^x.ln2 dy/dx = ln2.e^x.ln2 =...

I might not call you pedantic but I would certainly dare you to draw x²/1000 + y²/900 = 1 to 'scale' on A4 paper.

I would if I had the time at the moment (HSC and whatnot). If you're cool with posting your questions on the board then there are more than enough people to tackle them. I geuss right now the board is good because we can be selective in what we do.

I remember debating this some time ago and the conclusion we ended up with was that you can safely treat undefined x values of f(x) as zeros of 1/f(x). Examples exist where this is not the case but I don't think we have to worry about it for the level we're working at and given the kind of...

Haha, yeah, except for the fact that I got nothin' when it comes to circle geometry and conics. Those two topics, along with my stupid mistakes, kill me.

The resistive force gives you the equation of motion which is: acceleration = v(dv/dx) = -v√(1 - v²) dv/dx = - √(1 - v²) dx/dv = -1/√(1 - v²) then integrate w.r.t. v to get x = cos^-1v + c ... when x=0, v=R so c =...

From the Wolfram site: "A function is monotonic if its first derivative (which need not be continuous) does not change sign." As has been said monotonic increasing is where the gradient is always positive, and simarly I assume monotic decreasing is where the gradient is always negative.

Here's an example of where this can become useful. You could extend the logic of it to show that the coefficient of 1^{n- k}x^k = n!/k!(n-k)! = ⁿC_k. Alternatively consider (1 + x)ⁿ = (1 + x)(1 + x)... (1 + x) --> n times. The number of ways...

You're allowed to just assume it. However, you have to first recognise that the polynomial has real coefficients. Basically you say "P(x) has real coefficients hence if it has a complex root then the conjugate must also be a root. 1 - 2i is a root ∴ 1 + 2i is also a root." If you're...

Because you have doubles matches I think you have to split them into groups of 4 first so the way I'm looking at it it's like: ⁸C₄/2 = the number of ways to make two unique groups of 4 from 8. For group one there are ⁴C₂/2 ways to make two unique...

Here's the way it makes sense to me. First off show that p divides b and q divides a so sub x = p/q into the equation: ap³/q³ - 3p/q + b = 0 ap³ - 3pq² + bq³ = 0 bq³ = p(3q² - ap²) = pR₁...

I felt that the up and coming 2006 young'ns had to be warned. I attached an image this time so that they can recognise satan when he starts to rise out of the page. (P.S. - you have the world's best 4U folder)

LHS = 2tanx/(1-tan²x).cotx = 2/(1 - tan²x) = 2cos²x/(cos²x - sin²x) (multiplying through by cos²x) = (cos²x + cox²x)/(cos2x) = (cos²x - sin²x + 1)/cos2x .... (since...

Ussually it's a given that conics = le bash algebraique but I don't see why you shouldn't be able to use conic definitions in your proof. I'd probably go with the bash (which isn't too bad, relatively speaking) in order to make sure I got the marks. Btw:

Another way you could do it is using the property (a)ⁿ = e^n.ln(a), if you do this then: y = 1.1ⁿ = e^n.ln(1.1) dy/dn = ln(1.1)e^n.ln(1.1) = ln(1.1)(1.1ⁿ) or = ln(1.1)y

Well, if they gave an "or otherwise" option then: http://www.braungardt.com/Theology/Godel-Proof%20of%20God.htm

I think I got something like the 24th. It was very lucky because the day after that I'm heading up to brisbane to catch Oasis and then going back down to Byron for schoolies. Another date could have been very messy.

ohoh... there are formulas?

Nice method, it's very simple. I geuss you can safely assume that u_n --> ∞ as n--> ∞ but first would you show that there is a term u_k where u_k > 1 or just not bother?

But the way the question is phrased suggests that that situation is not a possibility. Alternatively I geuss you could say that the people picking the comitee members are unaware of Mr X's issues so they might inadvertently create that conflicting situation but then doesn't that just disregard...