Tangent line approximation

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Paul Verheyen

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Paul Verheyen

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Ready to use

5 years, 5 months ago

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Paul Verheyen 5 years, 5 months ago

Published this.

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Paul Verheyen 5 years, 5 months ago

Gave some feedback: Ready to use

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Paul Verheyen 5 years, 5 months ago

Created this as a copy of Raaklijnbenadering.

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

m	integer	2
n	integer	4
a	number	16
p	integer	4
eps	number	0.0001
ricoN	number	32
rklcT	integer	6
rklcN	integer	4
rklbenadering	number	2.000003125
rklben	string	2.000003125000

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..10)

JME function reference

Description

grondtal in a = m^n

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`

This variable doesn't seem to be used anywhere.

Parts

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Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add

Information only

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

Consider the function $f: \mathbb{R}^+ \to \mathbb{R} : x \mapsto \sqrt[\var{n}]{x} \, \, .$

Advice

a) The derivative of

$f(x) = \sqrt[\var{n}]{x} = x^{\frac{1} {\var{n}}}$ is given by

$f'(x) = \frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{1} {\var{n}}}) = {\frac{1} {\var{n}}} \cdot x^{\frac{\var{1-n}} {\var{n}}} .$

The equation of the tangent to the graph of $f$ at $( a, f(a))$ is obtained by

$y - f(a) = f'(a) \cdot (x-a)$

For $a = \var{a}$ , this means

$y - \var{m} = \frac{1} {\var{ricoN}} \cdot \left( x-\var{a} \right)$
or equivalently

$y = \var{m} + \frac{1} {\var{ricoN}} \cdot \left( x-\var{a} \right) = \frac{1} {\var{ricoN}} \cdot x + \frac {\var{m*(n-1)}} {\var{n}}$

b) The linear approximation of $f(a+\var{eps})$ is given by

$f(a) + f'(a) \cdot \var{eps}$
When

$a = \var{a}$ this leads to

$\var{rklben}$
which needs to be rounded up to

$\var{p+3}$ decimals.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Paul Verheyen 5 years, 5 months ago

Paul Verheyen 5 years, 5 months ago

Paul Verheyen 5 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Information only

Consider the function $f: \mathbb{R}^+ \to \mathbb{R} : x \mapsto \sqrt[\var{n}]{x} \, \, .$

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Tangent line approximation

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Paul Verheyen 5 years, 5 months ago

Paul Verheyen 5 years, 5 months ago

Paul Verheyen 5 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Information only

Consider the function f:R+→R:x↦{n}√x. f: \mathbb{R}^+ \to \mathbb{R} : x \mapsto \sqrt[\var{n}]{x} \, \, .

Generated value: `integer`

Consider the function $f: \mathbb{R}^+ \to \mathbb{R} : x \mapsto \sqrt[\var{n}]{x} \, \, .$