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last one pi > 1 so LHS >= 1 but RHS <= 1 so only solutions are RHS = LHS = 1 sin(sqrt(x)) = 0, /cos(x)/ = 1 sqrt(x) = npi, x=mpi n^2 pi^2 = mpi n^2 pi = m pi is transcedental so only solution will be n=m = 0 so x=0 is only solution

the quartic should be 3x^4 -6x^2 -1 .. you mucked up the trig somewhere 3arctan(x) = pi/2 + arctan(3x) tan(LHS) = tan(RHS) (3x - x^3)/1-3x^2 = -1/3x etc

2.) sqrt(1 + sqrt(4/3))

1.) n=0,2 all x are solutions n=1 only x=pi/4 Pi/4 + (m/2)Pi for even n Pi/4 + 2mPi for odd n and there's another set of solutions for odd n

james? thought argand was french

I dare bet it wouldn't be irrationality of e.. some of the stock questions: Geometry: ptolemy's theorem Butterfly theorem Simpsons theorem(this was in last years) Inequalities: QM-AM-GM-HM Cauchy schwarz Other Harder 3U: fibonnaci sequence/other reccurence sequences the...

worded answers? for maths as long as it's not fudging it's usually given full marks

wrong working = no mark no working... hmm depends on what it is

120/120 is possible (as in practically possible)

well.. or do we consider it as a rectangular slab like fitzpatrick

13 11 12

there you go.. that's a valid complaint.. teaching is not about being smart.. it's about getting the student to understand :p

it's just one of the stock questions.

that's for shells too.. if you are using the strict method. the shell is really a annular cylinder

if it wasn't for the word INDUCTION n^5 + n^3 +2n =n^5 + n^3 -2n +4n = n(n^4 +n^2 -2) + 4n =n(n+1)(n-1)(n^2 + 2) +4n now if n is even, then n^2, n^2 +2 will be even the product n(n^2 + 2) will be the product of 2 even numbers, hence a multiple of four if n is odd, then (n-1)...

those 9.5 are in band turtle

what he meant was.. erh.. get fitzpatrick and arnold and compare them

sort of messy: 1^5 + 1^3 + 2 = 4 is divisible by 4 so the proposition is true for n = 1 now to prove that if the proposition is true for n=k then it is true for n = k+1 the induction hypothesis is therefore k^5 +k^3 + 2k =4a for some integer a. (k+1)^5 + (k+1)^3 + 2(k+1) = k^5...

wait till you see the stew... Turtle, do you know where is stew now? I didn't check the club messages for a while

damn you all.. I have ancient history today! that's one day less for revision