Oracle function root estimation

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Philip Walker

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8 years, 5 months ago

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Philip Walker 8 years, 5 months ago

Gave some feedback: Ready to use

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Philip Walker 8 years, 5 months ago

Gave some feedback: Needs to be tested

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Philip Walker 8 years, 5 months ago

Created this as a copy of Oracle function estimation.

Name	Status	Author	Last Modified
Create an equilateral triangle in GeoGebra	Doesn't work	Christian Lawson-Perfect	21/05/2020 14:39
Create an equilateral triangle in GeoGebra	draft	Marlon Arcila	02/08/2016 13:36
Oracle function estimation	Needs to be tested	Philip Walker	25/01/2017 14:26
Mystery derivatives	Ready to use	Philip Walker	20/03/2017 14:14
Oracle function root estimation	Ready to use	Philip Walker	25/01/2017 14:24
Numbas demo: Create an equilateral triangle in GeoGebra	Needs to be tested	Christian Lawson-Perfect	25/08/2020 14:57
Nuala's copy of Numbas demo: Create an equilateral triangle in GeoGebra	draft	Nuala Curley	15/12/2016 14:30
Christian's copy of Mystery derivatives	draft	Christian Lawson-Perfect	14/02/2017 15:02
Sid's copy of Oracle function estimation	draft	Sid Fox	12/03/2017 14:19
Hollie's copy of Create an equilateral triangle in GeoGebra	draft	Hollie Tarr	27/04/2017 17:35
Kelsie's copy of Hollie's copy of Create an equilateral triangle in GeoGebra	draft	Kelsie Nguyen	23/06/2017 19:38
Paul's copy of Mystery derivatives	draft	Paul Hancock	01/07/2018 22:50
Use information from a GeoGebra applet in marking	draft	Christian Lawson-Perfect	10/07/2018 08:57
Arnd's copy of: Create an equilateral triangle in GeoGebra	draft	Arnd Ludwig	31/07/2018 13:15
Arnd's copy of: Create an equilateral triangle in GeoGebra	draft	Arnd Ludwig	31/07/2018 15:24
Luis's copy of Oracle function estimation	draft	Luis Hernandez	27/12/2018 14:27
Oracle function estimation	draft	Luis Hernandez	27/12/2018 17:51
Oracle function estimation	draft	Luis Hernandez	27/12/2018 18:00
Numbas demo: Create an equilateral triangle in GeoGebra	draft	Xiaodan Leng	10/07/2019 23:59
Mystery derivatives	draft	Xiaodan Leng	11/07/2019 05:15
Ann's copy of Create an equilateral triangle in GeoGebra	draft	Ann Smith	22/08/2019 12:23
Leonardo's copy of Ann's copy of Create an equilateral triangle in GeoGebra	draft	Leonardo Juliano	03/09/2019 16:25

There are 18 other versions that do you not have access to.

Question statement

I am thinking of a function, but I will not tell you what it is! However:

I will tell you that it is continuous everywhere.
I will tell you the value of the function anywhere you ask, to three decimal places. You can use the box below to inquire of me. (You may need to wait a little for it to load.)

{geogebra_applet('ufgKrAzb',defs)}

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	1
b	number	-4.0026
c	number	-4.91463136
d	number	0.4829957127

			Name	Type	Generated Value

rootsInteger	list	[ -2, 0, 4 ]
rootsDecimal	list	List of 3 items
roots	list	[ -1.0606, 0.0916, 4.9716 ]

			Name	Type	Generated Value

k	integer	1
testRoots	number	0.0916
testRootsExplicit	decimal	dec("0.0916")
testRootsInteger	number	0
testRootsDecimal	rational	229/2500

			Name	Type	Generated Value

pos	integer	1
extend	list	[ 1.02, 0.89 ]
minExtent	number	1.15

			Name	Type	Generated Value

defs

list

Nested 4×2 list

			Name	Type	Generated Value

intervalBisected	list	[ -0.93, 0.03, 0.98 ]
functionValues	list	[ 0.787, 0.332, -7.236 ]
intervalChoice	list	[ 0.03, 0.98 ]

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-3..3 except 0)

JME function reference

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:

b
d
defs
functionValues

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Number entry
  Add

Gap-fill

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

I will also tell you that there is a root in the open interval $(\var{intervalBisected[0]},\var{intervalBisected[2]})$ . Using interval bisection and the intermediate value theorem, identify the location of this root to two decimal places.

The root is located at $x=\;$ Unnamed gap

Advice

Interval bisection means, simply, taking an interval and cutting it in half.

Let us define $I_0 = (\var{intervalBisected[0]},\var{intervalBisected[2]})$.

In this instance, the idea is that we generate two subintervals of our initial interval, $I_0$, and by the intermediate value theorem, we can guarantee that one of them will contain our root. Here are the first steps.

Firstly, we check the values of the function at the endpoints of $I_0$: $f(\var{intervalBisected[0]}) = \var{functionValues[0]}$ and $f(\var{intervalBisected[2]}) = \var{functionValues[2]}$. Hence, by the intermediate value theorem, there is at least one $c \in I_0$ such that $f(c) = 0$.

Now, we cut the interval $I_0$ in half, producing the subintervals $(\var{intervalBisected[0]},\var{intervalBisected[1]})$ and $(\var{intervalBisected[1]},\var{intervalBisected[2]})$. Now, $f(\var{intervalBisected[1]}) = \var{functionValues[1]}$, and so we choose the subinterval where the sign of $f$ differs at the endpoints, which is to say, we take $I_1 = (\var{intervalChoice[0]},\var{intervalChoice[1]})$. By the intermediate value theorem, we guarantee that there is a $c \in I_1$ such that $f(c) = 0$.

We repeat this procedure on our new, smaller interval, $I_1$, choosing a smaller interval still, until eventually we have an interval so small that we can guarantee the answer to two decimal places, which is $c = \var{dpformat(roots[pos],2)}$.

Give a worked solution to the whole question.

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exam:

Intermediate value theorem exercise by Philip Walker in MATH1010 Mathematics I.

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Philip Walker 8 years, 5 months ago

Philip Walker 8 years, 5 months ago

Philip Walker 8 years, 5 months ago

Error in variable testing condition

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Warning

Generated value: `integer`

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Oracle function root estimation

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Philip Walker 8 years, 5 months ago

Philip Walker 8 years, 5 months ago

Philip Walker 8 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`