Many many problems i'm facing with this paper, I'd be glad and really appreciate it if you could help me see the light:

_

I'm fine with all of the first part up to the point where you mention symmetry - why?

-2 < x < -1

is not even on the graph:

We have (|x|-1)(|x|-2) < 0. Because of the modulus, anything that is true for x is also true for -x (alternatively, plot the quadratic that you have posted with |x| along the horizontal axis. This gives 1 < |x| < 2, which gives the same result)

--------------------------------------------------

Everything is clear here, except one tiny point -

Unparseable latex formula:

\implies \mbox{minimum at } (2,0)

Why did you say it was a minimum when

\frac{d^2y}{dx^2} = 0

We had a maximum at x = 1/2, so the curve is decreasing between x = 1/2 and x = 2. As x approaches infinity, so does y, so the curve must turn back round again, and we know x = 2 is a stationary point.

-------------------------------------------------

Once again, its a tiny (but key) point which alludes me -

Why did you substitute x for t, and t for x? Or is there another way you produced the result

f(x) = x + A\sin{x} + B\cos{x}

?

The question says "Use the expression (**) to find A and B by substituting for f(t) and f(x) in (*)". (**) gives f(t) = t + Asint + Bcost, and f(x) = x + Asinx + Bcosx.

(really sorry for the long post but these little things just keep knawing away at me, they're preventing me from completing the questions) : )

Absolutely no problem :smile:

Reply 26

TheLoneRanger

7

Daniel Freedman

We have (|x|-1)(|x|-2) < 0. Because of the modulus, anything that is true for x is also true for -x (alternatively, plot the quadratic that you have posted with |x| along the horizontal axis. This gives 1 < |x| < 2, which gives the same result)

So frustrasted with myself now, i overlooked the modulus symbol as something unimportant (like a bracket!), will adress this lack of attention to detail in future i hope.

Daniel Freedman

We had a maximum at x = 1/2, so the curve is decreasing between x = 1/2 and x = 2. As x approaches infinity, so does y, so the curve must turn back round again, and we know x = 2 is a stationary point.

Should have been more aware, again. I just took the standard method and found the second derative, determined it equaled 0 and stuck to my idea that it was a point of inflexsion - even though simple inspection of the equation would have revealed otherwise. So frustated, I'm finished if I dont become thourogh and systematic.

Daniel Freedman

The question says "Use the expression (**) to find A and B by substituting for f(t) and f(x) in (*)". (**) gives f(t) = t + Asint + Bcost, and f(x) = x + Asinx + Bcosx.

Absolutely no problem :smile:

Once again, I should have realised the importance of the last line - they wouldnt be giving hints for no reason... :redface:

Thanks for your kind guidance Daniel, I really appreciate it : )

Will have to work on becoming more aware and thourough in future

Thanks again :smile:

Reply 27

Daniel Freedman

7

TheLoneRanger

Thanks for your kind guidance Daniel, I really appreciate it : )

Will have to work on becoming more aware and thourough in future

Thanks again :smile:

Reply 28

Daniel Freedman

7

STEP III, 2004, Question 2

Spoiler

STEP III, 2004, Question 3

Spoiler

STEPIII.GIF5.8KB

Reply 30

Oh I Really Don't Care

17

TEP III, Question 5

Spoiler

Reply 31

SimonM

OP

18

Dean, do you think you could update the first post to be a similar format to the other STEP threads. I'll then it to the list of links.

Reply 32

Oh I Really Don't Care

17

SimonM

Dean, do you think you could update the first post to be a similar format to the other STEP threads. I'll then it to the list of links.

I know what you mean. I did infact try adding links when I edited the last time. Unfortunately it did not go well.

I could paste all the questions to one page though? Would that help ?

Reply 33

Oh I Really Don't Care

17

STEP III, Question 7

Spoiler

Reply 34

Oh I Really Don't Care

17

STEP III, Question 11

Spoiler

Reply 35

SimonM

OP

18

DeanK22

I know what you mean. I did infact try adding links when I edited the last time. Unfortunately it did not go well.

I could paste all the questions to one page though? Would that help ?