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wishful thinking! :rolleyes:

*sigh* post a thread about ruse anyday, and the post count is guaranteed to go thru the roof

easiest way is to recognise that sin(5x)cos(3x) = 1/2(sin8x + sin2x)

Took a long time, but here it is: I_n = {I: 0->a} (a^2 - x^2)^n dx = a^2 * {I: 0->a}(a^2 - x^2)^(n-1) dx - {I: 0->a}x^2 * (a^2 - x^2)^(n-1) dx (*) Now, integrating by parts: {I: 0->a}x^2 * (a^2 - x^2)^(n-1) dx = (-x/2n)(a^2 - x^2)^n |(0->a) + {I: 0->a}(1/2n)(a^2 - x^2)^n = 0 + (1/2n)I_n...

P'(x) = -1 + x - x^2/2! + x^3/3! - ... + (-1)^n-1 x^(n-1)/(n-1)! = -P(x) - (-1)^n x^n/n! now when P'(x) = P(x), - (-1)^n x^n/n! = 0 => x = 0 but when this happens, P(x) =/= 0 thus the condition P'(x) = P(x) = 0 is never satisfied thus no multiple roots.

MATH1141....NOOOO....

i liked your solution better than my own...

we at med have had about 2 - 3 bio lectures where the lecturer forgot to turn up...

hehe...try not to overreact; most ppl r just tryin to help

Umm...for n shooters tryin their luck on n ducks as n -> infinity you have survival chance of lim{n -> infinity}(1 - 1/n)^n = 1/e i think.....

i dun think so acetic acid would be round 0.1%

You'd find that in the real world, acids either dissociate v close to 100%, or they dissociate below 10%. That's the world as it is... there are like one or two exceptions: H3PO4 is like a moderate acid, etc.

i dun think it's an acceptable degree, combining science with med. If it were possible, it would've been what I would've done. Yes I think I know the person kini mini is talking about, but I have doubts about him actually getting a recognised degree for what he's doing now. Med itself is...

My former english tutor reckons that the material in standard english and in advanced english is essentially the same thing, so it's actually unfair how the marks are skewed that way.

posting the actual question would be good, seeing as I (an ex-student) have returned my fitz to the school

well if P (the locus pt) had the co-ords (x,y) then M would have the co-ords (a/e, y) because PM is a horizontal line, and M lies on the directrix x = a/e and M' lies on the other directrix x = -a/e so its co-ords are (-a/e, y) so the distance MM' is obviously = 2a/e

btw, it's an ellipse u have there. the hyperbola should be x^2/a^2 - y^2/b^2 =1 but, yes. hyperbola: alternate definition: the absolute value of the difference of lengths to two set points is a constant. i.e. ||SP| - |S'P|| = k and |SP| = e|PM| where e is eccentricity, M is the base...

use the fact that (cos@)^2 + (sin@)^2 = 1

Normally in covalent bonds, atom A gives one electron, and atom B gives one electron, to form a bonding electron pair (a covalent bond). We say both atoms share one electron to form the covalent bond. In a co-ordinate covalent bond, atom A gives two electrons, while atom B bludges. It's...

the reciprocal of any complex number with mudulus 1, is the conjugate of that number. so1/i = -i think about it in mod-arg form 1 = cis0 i = cis(pi/2) 1/i = cis(0 - pi/2) = cis(-pi/2) = -i