Graph Sketch
(i) Show by sketching two curves on the same axes that the equation
x^2=cosx ,
where x is in radians, has exactly one positive root. Give a rough initial estimate of the root
0.5, 1
(ii) By re-arranging the equation, find an iterative formula for xr+1 in terms of xr. Use this iterative formula
to find the root correct to 2 decimal places. [5]
How do you rearragne for part 2
x^2=cosx ,
where x is in radians, has exactly one positive root. Give a rough initial estimate of the root
0.5, 1
(ii) By re-arranging the equation, find an iterative formula for xr+1 in terms of xr. Use this iterative formula
to find the root correct to 2 decimal places. [5]
How do you rearragne for part 2
(edited 9 years ago)
There is only one positive root.
You rearrange to get x on one side.
You rearrange to get x on one side.
for 1). Try using a domain of (0,pi/2) for the sketch.
for 2) it is asking you to re-arrange to work out what the next x is from the previous one. - The previous one can be workrd out form any function that fits the equation.
i would suggest:
with your root estimate from the plot.
for 2) it is asking you to re-arrange to work out what the next x is from the previous one. - The previous one can be workrd out form any function that fits the equation.
i would suggest:
with your root estimate from the plot.
(edited 9 years ago)
It doesn't matter what domain you use as long as it includes the root, there is only one positive root.
Original post by morgan8002
It doesn't matter what domain you use as long as it includes the root , there is only one positive root.
...merely indicating the most convenient domain for the sketch...
(edited 9 years ago)
Original post by Hasufel
...merely indicating the most convenient domain for the sketch...
Yes, that is the best domain to use, but I was just saying that they shouldn't have gotten two positive roots from using a different domain.
Original post by morgan8002
Yes, that is the best domain to use, but I was just saying that they shouldn't have gotten two positive roots from using a different domain.
no, no - just the one
(myself, i don`t know what the "0.5,1 is meant to be!)
(edited 9 years ago)
Original post by Hasufel
no, no - just the one
(myself, i don`t know what the "0.5,1 is meant to be!)
(myself, i don`t know what the "0.5,1 is meant to be!)
I think they're the root estimates-the OP thinks there are two roots.
Original post by morgan8002
I think they're the root estimates-the OP thinks there are two roots.
Estimate in root [0.5,1]
Original post by Acrux
Estimate in root [0.5,1]
You mean that's the interval the root is in?
Original post by morgan8002
You mean that's the interval the root is in?
its the estimate of the root
question is asking to give a rough initial estimate of the root
Original post by Acrux
its the estimate of the root
question is asking to give a rough initial estimate of the root
question is asking to give a rough initial estimate of the root
I'd say an estimate is one number. You've given two, so I assume that's the interval you think the root is in, which is correct.
Now rearrange the equation to get x on one side and do iteration.
Original post by morgan8002
I'd say an estimate is one number. You've given two, so I assume that's the interval you think the root is in, which is correct.
Now rearrange the equation to get x on one side and do iteration.
Now rearrange the equation to get x on one side and do iteration.
http://www.mei.org.uk/files/papers/June13/NM_2013_June.pdf
And done it.
However i am struggling on question 6 not sure how to work it out.
Treapezium part
(edited 9 years ago)
Original post by Acrux
No need to assume. http://www.mei.org.uk/files/papers/June13/NM_2013_June.pdf
And done it.
However i am struggling on question 6 not sure how to work it out
And done it.
However i am struggling on question 6 not sure how to work it out
Even though the mark scheme accepts that, they will expect a single value as an estimate.
For question 6ii, decrease h each time to get more accurate estimates.
Original post by morgan8002
Even though the mark scheme accepts that, they will expect a single value as an estimate.
For question 6ii, decrease h each time to get more accurate estimates.
For question 6ii, decrease h each time to get more accurate estimates.
How are they calculating the intervals for part two of question 6 look at the mark scheme
and how do i rembeber which value of x to take when doing trapezium
Original post by Acrux
How are they calculating the intervals for part two of question 6 look at the mark scheme
and how do i rembeber which value of x to take when doing trapezium
and how do i rembeber which value of x to take when doing trapezium
For 6ii they don't find intervals, they find two estimates(single numbers) for the integral using each of the three numerical integration techniques.
Use the trapezium rule in your formula booklet. It will tell you the values of x to use.
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