Using Excel for Iteration Formula
2
Using Excel for Iteration Formula Suppose we want to solve 0 1 3 2 = + − x x , we know there is a root between 0 and 1 because if we write ( ) 1 3 2 + − = x x x f then ( ) 0 1 0 > = f and ( ) 0 1 1 1 3 1 1 2 < − = + × − = f we can rearrange the given equation into the iteration formula 3 1 2 1 + = + n n x x with a start value of 5 . 0 0 = x his can be entered into !"cel as shown below# a$ enter the start value in a cell b$ enter the iteration formula in another cell. his %&S be entered e"actl' shown ()cell number of start value*2+1$ 3 c$ cop' this formula into cell below d$ repeat this until 'ou are satisfied with 'our answer -our spreadsheet formula will look this 1 Solve x^2-3x+1 = 0 n x 0 0.5 1 =(B2^2+1)/3 2 =(B3^2+1)/3 3 =(B4^2+1)/3 4 =(B5^2+1)/3 5 =(B6^2+1)/3 6 =(B7^2+1)/3 7 =(B8^2+1)/3 8 =(B9^2+1)/3 9 =(B10^2+1)/3 10 =(B11^2+1)/3 11 =(B12^2+1)/3 -our answers will look like this 1 Solve x^2-3x+1 = 0 n X 0 0.5 1 0.416666667 2 0.391203704 3 0.384346779 4 0.382574149 5 0.382120993 6 0.382005484 7 0.381976063 8 0.381968571 9 0.381966663 10 0.381966177 11 0.381966054
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Transcript of Using Excel for Iteration Formula
Using Excel for Iteration Formula
Using Excel for Iteration Formula
Suppose we want to solve , we know there is a root between 0 and 1 because if we write
then
and
we can rearrange the given equation into the iteration formula
with a start value of
This can be entered into Excel as shown below:
a) enter the start value in a cell
b) enter the iteration formula in another cell. This MUST be entered exactly as shown
=(cell number of start value^2+1)/3
c) copy this formula into cell below
d) repeat this until you are satisfied with your answer
Your spreadsheet formula will look this
1 Solve x^2-3x+1 = 0
nx
00.5
1=(B2^2+1)/3
2=(B3^2+1)/3
3=(B4^2+1)/3
4=(B5^2+1)/3
5=(B6^2+1)/3
6=(B7^2+1)/3
7=(B8^2+1)/3
8=(B9^2+1)/3
9=(B10^2+1)/3
10=(B11^2+1)/3
11=(B12^2+1)/3
Your answers will look like this
1 Solve x^2-3x+1 = 0
nX
00.5
10.416666667
20.391203704
30.384346779
40.382574149
50.382120993
60.382005484
70.381976063
80.381968571
90.381966663
100.381966177
110.381966054
2a) Find the other solution to , by making another iteration formula
using a start value of
This has to be entered into Excel as
=SQRT(3* cell number-1)
Find a root to 3dp.
b) Change your start value to see what happens.
c) Format your results to 3 decimal places by using the icon
3. Show that has a root near x = 1.2.
Solve the equation using the iteration formula
4. Given that show that the equation has a root in the interval . Find the root using the iteration formula . This has to be entered into Excel as =EXP(cell number)/4
5a) Sketch the graphs of and on the same diagram.
b) How many roots are there to the equation
c) Show that the equation has a root in the interval 0.5 < x < 0.6 Find the root to 2dp. Use the iteration formula
6. Show that the equation has a root lying between 0 and 0.5. Use the iteration formula with to find this root to 3dp.
7. Using the iteration formula and find a root to the equation to 4sf. Check that your answer is correct to 4sf.
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