P3 - please help?!

let f(x) = 1 + x 1 - x
2 + x 2 - x

a) show that f(x) can be expressed as 2x
4 - x^
i've managed that bit.......but,

b) hence or otherwise show that, for small x,
f(x) = 1/2x + 1/8xcubed + 1/32xfifth + ...

can anyone please show me how to do this part b??

Erm, could you rewrite the equation, as I don't understand your notation. Is it multiplied or is it a fraction?

I think it's [(1+x)/(2+x)][(1-x)/(2-x)].

eh? the maclarin's what?! this is a question in an OCR paper.....?

Bollocks, can't do it, I'm on the OCR board and therefore didn't learn the Maclaurin's Series thing'a'ma'jig.

Well I'd rather believe the answer to part a) is the sum to infinity of a geometric progression.

how about some help with this other Q?

the parametric eqns of a curve C are: (x=a sin theta) and (y=2a cos theta), where "a" is a positive constant and -pie<theta<=pie

a) show that the eqn of the tangent to C at the point with parameter theta is: "2x sin theta + y cos theta = 2a"

b) this tangent passes thru the point (2a, 3a)
i) show that theta satisfies an equation of the form "5 sin (theta + pie)=2" and state the value of "tan alpha"

ii) hence find the two possible values of theta.


thanku

ok, very sorry bout confusing u all...

2x / (4-Xsquared)

to get to this i just simply made a common denominator from the 1st equation and cancelled throughout

any clearer?

i have to show from that, that for small x.... f(x)=1/2x + .... etc

??

I am presuming that you mean (2X)/(4-X^2) and not (2X)/(4-X)^2?

yeah i meant the first of what u said.

its 15th jan 2003 Q7

that would be great if u do??!

dont u think it sux that u can get answers for aqa and edexcell but not ocr?!