Maria's copy of Newton-Raphson method

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From users who are members of MY QUESTIONS :

Maria Aneiros

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Ready to use

3 years, 4 months ago

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Maria Aneiros 3 years, 4 months ago

Gave some feedback: Ready to use

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Maria Aneiros 5 years, 11 months ago

Created this as a copy of Newton-Raphson method.

Name	Status	Author	Last Modified
Newton-Raphson method	Ready to use	Frank Doheny	14/03/2018 21:21
Maria's copy of Newton-Raphson method	Ready to use	Maria Aneiros	29/11/2021 01:13

Question statement

Perform four iterations of the Newton-Raphson method, taking $x_0=\var{x0}$ as your initial estimate to find a root of the function:

$f(x)=\var{a}x^3-\var{b}x^2+\var{c}x+\var{d}$

Give your answers correct to three decimal places.

Give any introductory information the student needs.

			Name	Type	Generated Value

k	integer	3
a	integer	4
b	integer	24
c	integer	2
x1	decimal	dec("1.529411764705882")
d	integer	36
x2	decimal	dec("1.465507039475538")
x3	decimal	dec("1.464940809406718")
x4	decimal	dec("1.464940761076976")
x5	decimal	dec("1.464940761076975")
x0	decimal	dec("1")

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$x_0=\var{x0}$

$x_1=$ Gap 0.

$x_2=$ Gap 1.

$x_3=$ Gap 2.

$x_4=$ Gap 3.

Advice

$x_{n+1}=x_n-\frac{\var{a}x_n^3-\var{b}x_n^2+\var{c}x+\var{d}}{3(\var{a})x_n^2-2(\var{b})x+\var{c}}$

$x_0=\var{x0}$

$x_1=\var{x0}-\frac{(\var{a})*(\var{x0})^3-\var{b}*(\var{x0})^2+\var{c}*(\var{x0})+\var{d}}{3(\var{a})(\var{x0})^2-2(\var{b})(\var{x0})+\var{c}}=\var{x1}$

$x_2=\var{x1}-\frac{(\var{a})*(\var{x1})^3-\var{b}*(\var{x1})^2+\var{c}*(\var{x1})+\var{d}}{3(\var{a})(\var{x1})^2-2(\var{b})(\var{x1})+\var{c}}=\var{x2}$

$x_3=\var{x2}-\frac{(\var{a})*(\var{x2})^3-\var{b}*(\var{x2})^2+\var{c}*(\var{x2})+\var{d}}{3(\var{a})(\var{x2})^2-2(\var{b})(\var{x2})+\var{c}}=\var{x3}$

$x_4=\var{x3}-\frac{(\var{a})*(\var{x3})^3-\var{b}*(\var{x3})^2+\var{c}*(\var{x3})+\var{d}}{3(\var{a})(\var{x3})^2-2(\var{b})(\var{x3})+\var{c}}=\var{x4}$

$x_5=\var{x4}-\frac{(\var{a})*(\var{x4})^3-\var{b}*(\var{x4})^2+\var{c}*(\var{x4})+\var{d}}{3(\var{a})(\var{x4})^2-2(\var{b})(\var{x4})+\var{c}}=\var{x5}$

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Maria Aneiros 3 years, 4 months ago

Maria Aneiros 5 years, 11 months ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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Maria's copy of Newton-Raphson method

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Maria Aneiros 3 years, 4 months ago

Maria Aneiros 5 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`