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i think thats pretty good advice there. Oh well, off to do it tomorrow. Perhaps being online isn't the best way to 'deal' with it, but I stand by my choice. In any case, good luck everyone!

they have to firstly know what transcendental means. Be interesting if they have like a whole paragraph telling you just exactly what transcendental means. Hmm if they make us prove irrationality of a number, it's not too bad because pi and e are done, and thats all the 'special' numbers we have...

Mechanics, only the circular motion stuff though, that is just cruel, I hate that stuff, it's annoying. Hmm, part from that the 'harder' 3U topics can be nasty too. Of course random stuff like proving the irrationality of e, etc. isn't nice either.

yeh but it was a lead on question. It's not too hard if you followed all the steps. Oh and knew what, 'proof by contradiction' meant. or whatever the other ways of sayign it is.

there is nothing in the syllabus which says it *has* be uniform speed, (from my rather poor memory of course). Thus a question with non-uniform speed is perfectly legit, albiet much harder, but completely examinable. Its the same as, there is no rule for saying there is no resisted...

hmm this is a textbook reduction formula question: I_n = ∫cotⁿ.dx (from pi/4 - pi/2) =∫cot²xcot^n-2x.dx =∫(cosec²x - 1)(cot^n-2x)dx =∫cosec²xcot^n-2xdx - I_n-2 (by expansion)...

60 doing it in the grade (this is what you get for going to a nerdy school), and in my class about 20 or so, there are 3 classes.

whoops Final Fantasy beat me to it again. blargh.

on 2nd thought, if we let u = 3x-2: du = 3dx and also: x = (u+2)/3 so int = ∫(u+2)u³/9du = ∫u⁴/9 + 2u³/9 du =u⁵/45 +u⁴/18 +c =(3x-5)⁵/45 + (3x-5)⁴/18 + c though the constants may be wrong, the method holds.

when you start mixing exponents and algberaic expressions, it gets close to impossible to simply use algebraic manilpulations to change subject. y = x + e^x or any variant of that is one of those I think. Did you just make up the question? Or was it actually a question in a textbook? Because it...

wow that is really really neat, beats what I did, by a mile. Hmm that identity, i should get proving it. thanks.

that e^ix method is beyond the course, but it's nice. the way I got it was slighty different, and the answers are also different to what you all have, but I have a feeling it'll boil down to the same thing. The textbook says: +/- isqrt of (7+ sqrt of 48) ,+/- i, +/- isqrt (7-sqrt 48) and I got...

I do have a solution to this, it's just I want to see if there is some other way of doing this. Anyways here's the question: solve: (x+1)⁶ + (x-1)⁶ = 0 over C (this *is* the Ext-2 forum)

but wolfram doesn't accept 'ln', it only accepts log, so therefore that integral is wrong. The one that ngai posted is prolly correct, I don't think this is a 4U integration anymore.

∫dx/(e^x-e^-x) = ∫dx/ (e^x - (1/e^x)) = ∫dx / (e^2x - 1)/e^x = ∫ e^x dx / (e^2x - 1) put u = e^x, du = e^x dx thus Integration is: ∫du / (u^2 -1 ) = 1/2 ln [(u-1)/(u+1)] + C (this step can be either treated as a standard integral, or it is done by partial fractions, either...

thats undefined more than no solution, integrations can't be 'undefined' as such.

i severly doubt there is no solution per se, there could be one, just way beyond the scope of 4U, it doesn't mean there is no solution to it.

i think zero just refers to the number, where as roots is actually like (x-2) or something, i am not entirely sure.

No I didnt' think it was a 4U integration, oh well, i just saw an easier one where the there was an extra 'x' in the denominator, so i thought what would happen if i took that out, obviously made the integration that much more difficult. Oh well, still a solution would be appreciated, even...

it doesn't work does it Slide Rule? and for the (ln^2 x^2)/2 answer, i don't think that works.