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Iteration method in C3

http://www.examsolutions.net/exampapers/edexcel-c3-january-2007/

For question 6e of this paper, can anyone pls explain why iteration method is used to find k? It is only 2 marks so surely it should be quite straight forward. Why would you not solve for x by equating x+2 and 2-e^x/2 ?? How do you know that you need to use the iteration method instead??

Cheers
Reply 1
Because it tells you above part (d) that an iterative formula is used to find k. THerefore, that is what you are expected to do.

There are sometimes alternative ways to do the questions you are set, and sometimes they are easier. But you are being tested on your understanding and application of iterative methods in this question, so that's what you have to do.
Reply 2
Original post by coconut64
http://www.examsolutions.net/exampapers/edexcel-c3-january-2007/

For question 6e of this paper, can anyone pls explain why iteration method is used to find k? It is only 2 marks so surely it should be quite straight forward. Why would you not solve for x by equating x+2 and 2-e^x/2 ?? How do you know that you need to use the iteration method instead??

Cheers


I challenge you to try and solve it yourself and give an exact solution.
You will find that it cannot be done so we use numerical methods to approximate the root.
Reply 3
Original post by Pangol
Because it tells you above part (d) that an iterative formula is used to find k. THerefore, that is what you are expected to do.

There are sometimes alternative ways to do the questions you are set, and sometimes they are easier. But you are being tested on your understanding and application of iterative methods in this question, so that's what you have to do.


I thought that only applies to d though at the start.
Reply 4
Original post by B_9710
I challenge you to try and solve it yourself and give an exact solution.
You will find that it cannot be done so we use numerical methods to approximate the root.


In fact I did that at first and as you correctly stated that it cannot be worked out. However I am wondering in other occasions when you can solve for x, would that an alternative way to work out the answer?

Thanks
Reply 5
Original post by coconut64
I thought that only applies to d though at the start.


I would say that it applies for the rest of the question. But I also agree with the above poster that you can't easily do this any other way.

It is slightly ambiguous in this case, but in general, if there is a line that does not form part of the question, it applies from that point on. So the statement above (d) applies to (d) and (e).
Reply 6
Thanks for the help!
Reply 7
Original post by coconut64
In fact I did that at first and as you correctly stated that it cannot be worked out. However I am wondering in other occasions when you can solve for x, would that an alternative way to work out the answer?

Thanks


If the question says to use the iterative formula then use it. I'm pretty sure that when they ask you to use numerical methods that the root is impossible or very difficult to find so in fact you probably can never solve it analytically. That's what this section is teaching you, how to find approximate solutions without finding them exactly.
They will generally be ask you to solve things like x=cosx x=\cos x .

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