Limits: L'Hospital's rule: Indeterminate forms involving powers

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7 years, 5 months ago

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Ben Brawn 7 years, 5 months ago

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Ben Brawn 7 years, 6 months ago

Created this as a copy of Limits: L'Hospital's rule: Indeterminate form 0/0.

Name	Status	Author	Last Modified
Limits: L'Hospital's rule: Indeterminate form infinity/infinity	Ready to use	Ben Brawn	16/10/2017 06:29
Limits: L'Hospital's rule: Indeterminate form 0/0	Ready to use	Ben Brawn	16/10/2017 06:29
Stanley's copy of Limits: L'Hospital's rule: Indeterminate form infinity/infinity	draft	Stanley Smith	11/10/2017 18:47
Limits: L'Hospital's rule: Indeterminate form 0*infinity	Ready to use	Ben Brawn	16/10/2017 06:29
Limits: L'Hospital's rule: Indeterminate forms involving powers	Ready to use	Ben Brawn	22/11/2017 04:48
JPO's copy of Limits: L'Hospital's rule: Indeterminate forms involving powers	draft	JPO AddMath	15/04/2019 14:17
In Progress	draft	JPO AddMath	15/04/2019 14:38
Maria's copy of Limits: L'Hospital's rule: Indeterminate form 0*infinity	Ready to use	Maria Aneiros	29/11/2021 01:13
Maria's copy of Limits: L'Hospital's rule: Indeterminate forms involving powers	Ready to use	Maria Aneiros	29/11/2021 01:12
Maria's copy of Limits: L'Hospital's rule: Indeterminate form infinity/infinity	Ready to use	Maria Aneiros	29/11/2021 01:12
Maria's copy of Limits: L'Hospital's rule: Indeterminate form 0/0	Ready to use	Maria Aneiros	29/11/2021 01:12
Sid's copy of Limits: L'Hospital's rule: Indeterminate form infinity/infinity	draft	Sid Grover	05/06/2019 02:08

There are 14 other versions that do you not have access to.

Question statement

This question is about limits of indeterminate forms.

Give any introductory information the student needs.

			Name	Type	Generated Value

pL	list	[ 6, 12, 9, 7, 2 ]
pa	number	6
pb	number	12
pc	number	9
pd	number	7
pe	number	2
nL	list	[ 1, 8, 3, -7, -9 ]
na	integer	1
nb	integer	8
nc	integer	3
nd	integer	-7
ne	integer	-9
alt1	integer	-1
zero_zero	list	Nested 14×10 list
inf_zero	list	List of 12 items
one_inf	list	Nested 6×10 list
choice1	list	Nested 14×10 list
choice2	list	List of 10 items

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
shuffle(2..12)[0..5]

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: `list`

[ 6, 12, 9, 7, 2 ]

→ Used by:

Parts

Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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As {choice2[0]}, {choice2[2]} approaches Unnamed gap

Note: infinity is simply entered by typing infinity

Advice

As {choice2[0]}, it appears {choice2[2]} approaches {choice2[1]}, but it isn't clear what this means. This is known as an indeterminate form of type {choice2[1]}. We can use a standard trick to write this expression to involve an indeterminate form of type {choice2[3]} in the exponent

{choice2[4]}

As usual, to deal with an indeterminate form of type {choice2[3]} we rewrite the product as a quotient, in this case, to involve an indeterminate form of type {choice2[5]} as such

{choice2[6]}

Now we apply L'Hospital's rule to the exponent, which means we now need to determine what {choice2[7]} approaches as {choice2[0]}. But this is again an indeterminate form so we repeatedly apply L'Hospital's rule until it is not an indeterminate form and we arrive at needing to determine what {choice2[4]} approaches as {choice2[0]}. Now that this is no longer an indeterminate form, it should be clear that the limit is {choice2[-1]}.

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet

This question is used in the following exam:

Limits: L'Hospital's rule: Indeterminate forms involving powers by Ben Brawn in Limits.

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Limits: L'Hospital's rule: Indeterminate forms involving powers

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Taxonomy: mathcentre

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Taxonomy: Context

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Checkpoint description

Ben Brawn 7 years, 5 months ago

Ben Brawn 7 years, 5 months ago

Ben Brawn 7 years, 6 months ago

Error in variable testing condition

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Warning

Generated value: `list`

Parts

Gap-fill

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Limits: L'Hospital's rule: Indeterminate forms involving powers

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben Brawn 7 years, 5 months ago

Ben Brawn 7 years, 5 months ago

Ben Brawn 7 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`