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Write down the Newton-Raphson formula for finding a numerical solution to the equation emx+bx−a=0. If x0=1 find x1.
Included in the Advice of this question are:
6 iterations of the method.
Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.
Metadata
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England schools
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England university
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Scotland schools
Taxonomy: mathcentre
Taxonomy: Kind of activity
Taxonomy: Context
Contributors
History
J. Richard Snape was given access to the Min_max_v2 5 years, 7 months ago
Anna Strzelecka 5 years, 9 months ago
Created this as a copy of Min_max_v1.| Name | Status | Author | Last Modified | |
|---|---|---|---|---|
| Interactive Newton-Raphson method | Ready to use | Bill Foster | 19/04/2017 11:03 | |
| Interactive Newton-Raphson method | Should not be used | Christian Lawson-Perfect | 14/02/2020 12:57 | |
| Senida's copy of Interactive Newton-Raphson method | draft | Senida Krcic | 15/11/2018 03:27 | |
| Mario's copy of Interactive Newton-Raphson method | draft | Mario Stevanovski | 15/11/2018 03:44 | |
| Maria's copy of Mario's copy of Interactive Newton-Raphson method | draft | Maria Aneiros | 27/05/2019 05:57 | |
| Keith's copy of Maria's copy of Mario's copy of Interactive Newton-Raphson method | draft | Keith Tarnowski | 03/06/2019 14:24 | |
| Anna's copy of Maria's copy of Mario's copy of Interactive Newton-Raphson method | Doesn't work | Anna Strzelecka | 16/08/2019 15:12 | |
| Min_max_v1 | draft | Anna Strzelecka | 10/01/2020 14:29 | |
| Min_max_v2 | draft | Anna Strzelecka | 16/08/2019 14:51 | |
| Maths_and_Stats's copy of Interactive Newton-Raphson method | draft | Maths_and_Stats Advice | 19/09/2019 13:49 |
There are 8 other versions that do you not have access to.
| Name | Type | Generated Value |
|---|
| b1 | number |
0.8
|
||||
| b2 | integer |
5
|
||||
| p1 | number |
0.8
|
||||
| p2 | number |
4
|
||||
| exp1 | integer |
7
|
||||
| p13 | number |
2.4
|
||||
| p1_positive | number |
-0.8
|
||||
| p2_positive | number |
-4
|
||||
| s1 | number |
20.8
|
||||
| s2 | number |
56
|
||||
| p22 | number |
8
|
||||
| x1 | number |
3.0501256289
|
||||
| x2 | number |
22.9498743711
|
||||
| f_x1 | number |
-9.3863332388
|
||||
| f_x2 | number |
285.0062210045
|
||||
| fake_1 | number |
5.4875078027
|
||||
| fake_2 | number |
25.5124921973
|
||||
| fake_3 | number |
1.5980297479
|
||||
| fake_4 | number |
21.9019702521
|
||||
| fake_5 | number |
1.5980297479
|
||||
| fake_6 | number |
21.9019702521
|
| Name | Type | Generated Value |
|---|
| a | integer |
15
|
||||
| maxy | integer |
63
|
||||
| ans1 | number |
0.7655
|
||||
| m | number |
1.9
|
||||
| results | list |
List of 7 items
|
||||
| b | integer |
14
|
||||
| tol | integer |
0
|
||||
| ans | number |
1.4168
|
||||
| tans | number |
1.4167606197
|
||||
| a1 | number |
7.7
|
||||
| a2 | integer |
15
|
||||
| a3 | integer |
11
|
||||
| a4 | number |
0.9
|
||||
| maxy_poly | integer |
462
|
||||
| maxysincos | integer |
9
|
||||
| as1 | integer |
3
|
||||
| as2 | integer |
3
|
||||
| as3 | integer |
7
|
||||
| minysincos | integer |
-8
|
||||
| ANSas2 | integer |
2
|
||||
| ANSas3 | integer |
24
|
||||
| inv_tan_sol1 | decimal |
dec("-8.314123188844122991066831465078129753113e-2")
|
||||
| inv_tan_sol2 | decimal |
dec("3.056858768111558770089331685349218702469")
|
||||
| inv_tan_sol3 | decimal |
dec("1.165904540509813195919248762630308825547")
|
||||
| inv_tan_sol4 | decimal |
dec("-1.974095459490186804080751237369691174453")
|
||||
| f_min | number |
-7.027475261
|
||||
| f_max | number |
20.0258441322
|
Generated value: number
- p1
- p2
- Statement
- "Part a)" - prompt
Parts
Choose one from a list
Ask the student a question, and give any hints about how they should answer this part.
Which of the following graphs represents the function
${f(x)=e^{-x/{\var{exp1}}}({\var{p1}}x^3 -{\var{p2}}x^2)}$
Roots (they are defined as the main variables. The ones above are calucated based on them. Find it easier to control the polynomial):
${\var{b1}},{\var{b2}}$
Notes:
- Make sure min/max is ok with current definitions
- Add some hints
-
Choice 1
{poly1(p1,p2,exp1,f_x2,x2,f_x1)} -
Choice 2
{poly1(p1/2,p2,exp1,f_x2/2,x2*2,f_x1*2.5)} -
Choice 3
{poly1(2*p1,p2,exp1,3*f_x2,x2,f_x1-5)} -
Choice 4
{poly1(p1,p2/2,exp1,2*f_x2,1.5*x2,f_x1-5)}
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This question is used in the following exam: