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1. let f(x) = (1 + x / 2 + x) - (1 - 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??
2. It's either a Maclaurin's Series or the sum of a geometric progression. Probably the latter.
3. (Original post by angellotte)
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?
4. (Original post by Bhaal85)
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)].
5. sorry, have edited it........?
6. (Original post by XTinaA)
I think it's [(1+x)/(2+x)][(1-x)/(2-x)].
*******s, can't do it, I'm on the OCR board and therefore didn't learn the Maclaurin's Series thing'a'ma'jig.
7. eh? the maclarin's what?! this is a question in an OCR paper.....?
8. pleasssssse rewrite the question!
9. (Original post by angellotte)
eh? the maclarin's what?! this is a question in an OCR paper.....?
What power is '2x / 4-x^' raised to?
10. (Original post by Bhaal85)
*******s, 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.
11. 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
12. (Original post by XTinaA)
Well I'd rather believe the answer to part a) is the sum to infinity of a geometric progression.
Yeah, a binomial expansion.
13. 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
14. (Original post by angellotte)
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
You have to differentiate both 'X' and 'Y' with respect to theta, I don't know how good you are in maths, but you may need to do the product rule on both just so you don't get confused with the working out. you would then have dx/[email protected] and dy/[email protected] where @=theta, you then multiply dy/[email protected] by (dx/[email protected])^-1. This will give you the derivative, dy/dx. Then you follow on from there.
15. thanku
16. 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

??
17. (Original post by angellotte)
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?
18. (Original post by Bhaal85)
I am presuming that you mean (2X)/(4-X^2) and not (2X)/(4-X)^2?
Which paper is it? I might have a copy if it is OCR board, as P3 is the one I am concentrating on the most.
19. 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?!
20. (Original post by angellotte)
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?!
Gimme a second, let me do the math, I have the paper in front of me, just be a minute.

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