isc_teaching_templates/samples/sample_lab_html/html/lab-fp.html at master · ISC-HEI/isc_teaching_templates · GitHub

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<!DOCTYPE html>
<!--
==============================================================================
           "GitHub HTML5 Pandoc Template" v2.2 — by Tristano Ajmone
==============================================================================
Copyright © Tristano Ajmone, 2017-2020, MIT License (MIT). Project's home:

- https://github.com/tajmone/pandoc-goodies

The CSS in this template reuses source code taken from the following projects:

- GitHub Markdown CSS: Copyright © Sindre Sorhus, MIT License (MIT):
  https://github.com/sindresorhus/github-markdown-css

- Primer CSS: Copyright © 2016-2017 GitHub Inc., MIT License (MIT):
  http://primercss.io/

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The MIT License

Copyright (c) Tristano Ajmone, 2017-2020 (github.com/tajmone/pandoc-goodies)
Copyright (c) Sindre Sorhus <sindresorhus@gmail.com> (sindresorhus.com)
Copyright (c) 2017 GitHub Inc.

"GitHub Pandoc HTML5 Template" is Copyright (c) Tristano Ajmone, 2017-2020,
released under the MIT License (MIT); it contains readaptations of substantial
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  <meta name="author" content="Dr P.-A. Mudry" />
  <title>Assignment 1 – Introduction</title>

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<header>
<div class="headCls">
<h1 class="title" id="title1" style="font-size:3em;border-bottom:none; margin-bottom:0;">Assignment
1 – Introduction</h1>
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" class="header-logo" style="width:300px;" />
</div>
<h4><p class="subtitle">205.1 Functional Programming — Dr P.-A.
Mudry, v1.0.1</p></h4>
</header>

<style> r { color: Red } y { color: Yellow } FIXME { color: Yellow }
TODO {color: Black; background-color: Yellow}
</style>
<h1 id="exercise-1-starting-slowly-and-installing-tools-difficulty">Exercise
1 – Starting slowly and installing tools (difficulty <span class="emoji" data-emoji="star">⭐</span>)</h1>
<p>In this first assignment, you will start by exploring the various
tools at your disposal for developing functional programs. You will also
be able to check that your tools have been installed correctly. In the
second part of the assignment, you will apply some of the knowledge you
got during the first lesson in a practical exercise.</p>
<div class="Success">
<p><strong>Installation</strong> — Verify that you have a working
version of <em>IntelliJ</em> with a proper <code>Scala 2.13</code>
installed. For this first assignment, we will focus on the usage of
<em>worksheets</em>. Reminder : worksheets are similar to the REPL,
except that you have access to multiple commands at the same time.</p>
</div>
<p>With the tools installed, you can configure your IDE so that
evaluation takes place every time you modify the file or that you press
a key combination. The result of the evaluation is then displayed on the
right-hand side of the screen (as depicted below):</p>
<div style="text-align:center" width="80%">
<img role="img" width="80%" 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/>
</div>
<p>Note that the evaluation window directly displays the return type and
value of the expression on the left. If required, you can force the
evaluation of the worksheet by pressing the keys <kbd>Ctrl</kbd> +
<kbd>Alt</kbd> + <kbd>W</kbd> together.</p>
<ol type="1">
<li><p>Add a new worksheet called <code>FirstSteps.sc</code> to the
project.</p></li>
<li><p>In the worksheet, define a function that returns the square of a
value. Check that your function works correctly by applying various
values to it.</p></li>
<li><p>Define another function that returns the
4<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi></mi><mrow><mi>t</mi><mi>h</mi></mrow></msup><annotation encoding="application/x-tex">^{th}</annotation></semantics></math>
power of a value, using the <code>square</code> function you just
defined.</p></li>
<li><p>As you can see, the worksheet always returns the type that has
been inferred for the expression you type or from the evaluation. What
do you expect the worksheet to return for the following definition?</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode scala"><code class="sourceCode scala"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> <span class="fu">bar</span><span class="op">(</span>x<span class="op">:</span> <span class="bu">Int</span><span class="op">,</span> y<span class="op">:</span> <span class="ex">Boolean</span><span class="op">)</span> <span class="op">=</span> <span class="st">&quot;Hello&quot;</span></span></code></pre></div></li>
</ol>
<p>What is the most difficult :</p>
<ul>
<li>Finding nice things to</li>
<li>Have fun</li>
</ul>
<h1 id="exercise-2-getting-our-hands-dirty-difficulty">Exercise 2 –
Getting our hands dirty (difficulty <span class="emoji" data-emoji="star">⭐</span>)</h1>
<div class="Warning">
<p><strong>How to be efficient in the series</strong> — There is always
a method to find a solution on the Internet, using ChatGPT or looking at
the solution. However, you <strong>NEED</strong> to work by yourself and
find your own path to the knowledge. This is the way.</p>
</div>
<p>You are now asked to write a function to compute the square root of a
number. Its prototype should be as follows:</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode scala"><code class="sourceCode scala"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> <span class="fu">sqrt</span><span class="op">(</span>x<span class="op">:</span> <span class="ex">Double</span><span class="op">)</span> <span class="op">:</span> <span class="ex">Double</span></span></code></pre></div>
<h2 id="task-1-newtons-method">Task 1 – Newton’s method</h2>
<p>A typical numerical method to compute the zeroes (or roots) of a
function is the Newton’s method. Given a function
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>f</mi><annotation encoding="application/x-tex">f</annotation></semantics></math>
and its derivative
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>f</mi><mo>′</mo></msup><annotation encoding="application/x-tex">f&#39;</annotation></semantics></math>,
we begin with a guess
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>x</mi><mn>0</mn></msub><annotation encoding="application/x-tex">x_0</annotation></semantics></math>
for the root. A better approximation
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>x</mi><mn>1</mn></msub><annotation encoding="application/x-tex">x_1</annotation></semantics></math>
of the root is then given by :</p>
<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><msub><mi>x</mi><mn>0</mn></msub><mo>−</mo><mfrac><mrow><mi>f</mi><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo stretchy="false" form="postfix">)</mo></mrow><mrow><msup><mi>f</mi><mo>′</mo></msup><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo stretchy="false" form="postfix">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">x_1 = x_0 - \frac{f(x_0)}{f&#39;(x_0)}</annotation></semantics></math></p>
<p>The process is then repeated with the recursion equation:</p>
<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>x</mi><mi>n</mi></msub><mo>−</mo><mfrac><mrow><mi>f</mi><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mi>n</mi></msub><mo stretchy="false" form="postfix">)</mo></mrow><mrow><msup><mi>f</mi><mo>′</mo></msup><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mi>n</mi></msub><mo stretchy="false" form="postfix">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">x_{n+1} = x_n - \frac{f(x_n)}{f&#39;(x_n)}</annotation></semantics></math></p>
<p>and stopped when the residual
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ϵ</mi><annotation encoding="application/x-tex">\epsilon</annotation></semantics></math>
is small enough.</p>
<h2 id="task-2-application-to-the-square-root-function">Task 2 –
Application to the square root function</h2>
<p>Let’s say one wishes to compute<a href="#fn1" class="footnote-ref" id="fnref1" role="doc-noteref"><sup>1</sup></a>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msqrt><mn>612</mn></msqrt><annotation encoding="application/x-tex">\sqrt{612}</annotation></semantics></math>.
This is equivalent to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>612</mn></mrow><annotation encoding="application/x-tex">x^2 = 612</annotation></semantics></math>.
The function to use in Newton’s method is then
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>612</mn></mrow><annotation encoding="application/x-tex">f(x) = x^2 - 612</annotation></semantics></math>.
Its derivative is
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>f</mi><mo>′</mo></msup><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo><mo>=</mo><mn>2</mn><mi>x</mi></mrow><annotation encoding="application/x-tex">f&#39;(x) = 2x</annotation></semantics></math>.
With an initial approximation of 10 (you can choose what you want here),
the steps are then :</p>
<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable><mtr><mtd columnalign="right" style="text-align: right; padding-right: 0"><msub><mi>x</mi><mn>1</mn></msub></mtd><mtd columnalign="left" style="text-align: left; padding-left: 0"><mo>=</mo><msub><mi>x</mi><mn>0</mn></msub><mo>−</mo><mfrac><mrow><mi>f</mi><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo stretchy="false" form="postfix">)</mo></mrow><mrow><msup><mi>f</mi><mo>′</mo></msup><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo stretchy="false" form="postfix">)</mo></mrow></mfrac><mo>=</mo><mn>10</mn><mo>−</mo><mfrac><mrow><msup><mn>10</mn><mn>2</mn></msup><mo>−</mo><mn>612</mn></mrow><mrow><mn>2</mn><mo>⋅</mo><mn>10</mn></mrow></mfrac><mo>=</mo><mn>35.6</mn></mtd></mtr><mtr><mtd columnalign="right" style="text-align: right; padding-right: 0"><msub><mi>x</mi><mn>2</mn></msub></mtd><mtd columnalign="left" style="text-align: left; padding-left: 0"><mo>=</mo><msub><mi>x</mi><mn>1</mn></msub><mo>−</mo><mfrac><mrow><mi>f</mi><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false" form="postfix">)</mo></mrow><mrow><msup><mi>f</mi><mo>′</mo></msup><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false" form="postfix">)</mo></mrow></mfrac><mo>=</mo><mn>35.6</mn><mo>−</mo><mfrac><mrow><msup><mn>35.6</mn><mn>2</mn></msup><mo>−</mo><mn>612</mn></mrow><mrow><mn>2</mn><mo>⋅</mo><mn>35.6</mn></mrow></mfrac><mo>=</mo><mn>26.3955</mn><mi>…</mi></mtd></mtr><mtr><mtd columnalign="right" style="text-align: right; padding-right: 0"><mi>⋮</mi></mtd></mtr><mtr><mtd columnalign="right" style="text-align: right; padding-right: 0"><msub><mi>x</mi><mn>5</mn></msub></mtd><mtd columnalign="left" style="text-align: left; padding-left: 0"><mo>=</mo><mn>24.73863375</mn><mi>…</mi></mtd></mtr></mtable><annotation encoding="application/x-tex">
\begin{aligned}
x_1 &amp;= x_0 - \frac{f(x_0)}{f&#39;(x_0)} = 10 - \frac{10^2 - 612}{2\cdot10} = 35.6\\
x_2 &amp;= x_1 - \frac{f(x_1)}{f&#39;(x_1)} = 35.6 - \frac{35.6^2 - 612}{2 \cdot 35.6} = 26.3955\ldots\\
\vdots\\
x_5 &amp;= 24.73863375\ldots
\end{aligned}
</annotation></semantics></math></p>
<h2 id="task-3-implementation">Task 3 – Implementation</h2>
<p>As you can see, with only five steps the solution is already accurate
to more than five decimal places (all the decimals written are correct).
With the help of recursion, you now have to implement this method for
computing square roots.</p>
<ol type="1">
<li><p>Create a new worksheet in <em>IntelliJ</em> to write your code
for this assignment.</p></li>
<li><p>Define a function <code>isGoodEnough</code> that determines if
your solution is good enough. You solution can be considered good enough
for example when
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϵ</mi><mo>&lt;</mo><mn>0.0001</mn></mrow><annotation encoding="application/x-tex">\epsilon &lt; 0.0001</annotation></semantics></math>.
To compute the value of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ϵ</mi><annotation encoding="application/x-tex">\epsilon</annotation></semantics></math>
you can simply consider the error made by your function in the
approximation. For this part, you need to compute an absolute value
function.</p></li>
<li><p>Define another function, called <code>improve</code>, to compute
the value of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><annotation encoding="application/x-tex">x_{n+1}</annotation></semantics></math>,
given the current approximated value and the value of x.</p></li>
<li><p>Using the previously defined functions, define the
<code>sqrt</code> method. Please note that you can add other functions
if you need to!</p></li>
<li><p>Test your method and check your results.</p></li>
<li><p>[<em>Optional</em>] Implement the cubic root using the same
approach and check your results.</p></li>
</ol>
<h1 id="exercise-3-getting-our-hands-dirty-difficulty">Exercise 3 –
Getting our hands dirty (difficulty <span class="emoji" data-emoji="star">⭐</span>)</h1>
<div class="Warning">
<p><strong>How to be efficient in the series</strong> — There is always
a method to find a solution on the Internet, using ChatGPT or looking at
the solution. However, you <strong>NEED</strong> to work by yourself and
find your own path to the knowledge. This is the way.</p>
</div>
<p>You are now asked to write a function to compute the square root of a
number. Its prototype should be as follows:</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode scala"><code class="sourceCode scala"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> <span class="fu">sqrt</span><span class="op">(</span>x<span class="op">:</span> <span class="ex">Double</span><span class="op">)</span> <span class="op">:</span> <span class="ex">Double</span></span></code></pre></div>
<h2 id="task-1-newtons-method-1">Task 1 – Newton’s method</h2>
<p>A typical numerical method to compute the zeroes (or roots) of a
function is the Newton’s method. Given a function
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>f</mi><annotation encoding="application/x-tex">f</annotation></semantics></math>
and its derivative
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>f</mi><mo>′</mo></msup><annotation encoding="application/x-tex">f&#39;</annotation></semantics></math>,
we begin with a guess
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>x</mi><mn>0</mn></msub><annotation encoding="application/x-tex">x_0</annotation></semantics></math>
for the root. A better approximation
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>x</mi><mn>1</mn></msub><annotation encoding="application/x-tex">x_1</annotation></semantics></math>
of the root is then given by :</p>
<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><msub><mi>x</mi><mn>0</mn></msub><mo>−</mo><mfrac><mrow><mi>f</mi><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo stretchy="false" form="postfix">)</mo></mrow><mrow><msup><mi>f</mi><mo>′</mo></msup><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo stretchy="false" form="postfix">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">x_1 = x_0 - \frac{f(x_0)}{f&#39;(x_0)}</annotation></semantics></math></p>
<p>The process is then repeated with the recursion equation:</p>
<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>x</mi><mi>n</mi></msub><mo>−</mo><mfrac><mrow><mi>f</mi><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mi>n</mi></msub><mo stretchy="false" form="postfix">)</mo></mrow><mrow><msup><mi>f</mi><mo>′</mo></msup><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mi>n</mi></msub><mo stretchy="false" form="postfix">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">x_{n+1} = x_n - \frac{f(x_n)}{f&#39;(x_n)}</annotation></semantics></math></p>
<p>and stopped when the residual
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ϵ</mi><annotation encoding="application/x-tex">\epsilon</annotation></semantics></math>
is small enough.</p>
<h2 id="task-2-application-to-the-square-root-function-1">Task 2 –
Application to the square root function</h2>
<p>Let’s say one wishes to compute<a href="#fn2" class="footnote-ref" id="fnref2" role="doc-noteref"><sup>2</sup></a>
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msqrt><mn>612</mn></msqrt><annotation encoding="application/x-tex">\sqrt{612}</annotation></semantics></math>.
This is equivalent to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>612</mn></mrow><annotation encoding="application/x-tex">x^2 = 612</annotation></semantics></math>.
The function to use in Newton’s method is then
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>612</mn></mrow><annotation encoding="application/x-tex">f(x) = x^2 - 612</annotation></semantics></math>.
Its derivative is
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>f</mi><mo>′</mo></msup><mo stretchy="false" form="prefix">(</mo><mi>x</mi><mo stretchy="false" form="postfix">)</mo><mo>=</mo><mn>2</mn><mi>x</mi></mrow><annotation encoding="application/x-tex">f&#39;(x) = 2x</annotation></semantics></math>.
With an initial approximation of 10 (you can choose what you want here),
the steps are then :</p>
<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable><mtr><mtd columnalign="right" style="text-align: right; padding-right: 0"><msub><mi>x</mi><mn>1</mn></msub></mtd><mtd columnalign="left" style="text-align: left; padding-left: 0"><mo>=</mo><msub><mi>x</mi><mn>0</mn></msub><mo>−</mo><mfrac><mrow><mi>f</mi><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo stretchy="false" form="postfix">)</mo></mrow><mrow><msup><mi>f</mi><mo>′</mo></msup><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo stretchy="false" form="postfix">)</mo></mrow></mfrac><mo>=</mo><mn>10</mn><mo>−</mo><mfrac><mrow><msup><mn>10</mn><mn>2</mn></msup><mo>−</mo><mn>612</mn></mrow><mrow><mn>2</mn><mo>⋅</mo><mn>10</mn></mrow></mfrac><mo>=</mo><mn>35.6</mn></mtd></mtr><mtr><mtd columnalign="right" style="text-align: right; padding-right: 0"><msub><mi>x</mi><mn>2</mn></msub></mtd><mtd columnalign="left" style="text-align: left; padding-left: 0"><mo>=</mo><msub><mi>x</mi><mn>1</mn></msub><mo>−</mo><mfrac><mrow><mi>f</mi><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false" form="postfix">)</mo></mrow><mrow><msup><mi>f</mi><mo>′</mo></msup><mo stretchy="false" form="prefix">(</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false" form="postfix">)</mo></mrow></mfrac><mo>=</mo><mn>35.6</mn><mo>−</mo><mfrac><mrow><msup><mn>35.6</mn><mn>2</mn></msup><mo>−</mo><mn>612</mn></mrow><mrow><mn>2</mn><mo>⋅</mo><mn>35.6</mn></mrow></mfrac><mo>=</mo><mn>26.3955</mn><mi>…</mi></mtd></mtr><mtr><mtd columnalign="right" style="text-align: right; padding-right: 0"><mi>⋮</mi></mtd></mtr><mtr><mtd columnalign="right" style="text-align: right; padding-right: 0"><msub><mi>x</mi><mn>5</mn></msub></mtd><mtd columnalign="left" style="text-align: left; padding-left: 0"><mo>=</mo><mn>24.73863375</mn><mi>…</mi></mtd></mtr></mtable><annotation encoding="application/x-tex">
\begin{aligned}
x_1 &amp;= x_0 - \frac{f(x_0)}{f&#39;(x_0)} = 10 - \frac{10^2 - 612}{2\cdot10} = 35.6\\
x_2 &amp;= x_1 - \frac{f(x_1)}{f&#39;(x_1)} = 35.6 - \frac{35.6^2 - 612}{2 \cdot 35.6} = 26.3955\ldots\\
\vdots\\
x_5 &amp;= 24.73863375\ldots
\end{aligned}
</annotation></semantics></math></p>
<h2 id="task-3-implementation-1">Task 3 – Implementation</h2>
<p>As you can see, with only five steps the solution is already accurate
to more than five decimal places (all the decimals written are correct).
With the help of recursion, you now have to implement this method for
computing square roots.</p>
<ol type="1">
<li><p>Create a new worksheet in <em>IntelliJ</em> to write your code
for this assignment.</p></li>
<li><p>Define a function <code>isGoodEnough</code> that determines if
your solution is good enough. You solution can be considered good enough
for example when
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϵ</mi><mo>&lt;</mo><mn>0.0001</mn></mrow><annotation encoding="application/x-tex">\epsilon &lt; 0.0001</annotation></semantics></math>.
To compute the value of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ϵ</mi><annotation encoding="application/x-tex">\epsilon</annotation></semantics></math>
you can simply consider the error made by your function in the
approximation. For this part, you need to compute an absolute value
function.</p></li>
<li><p>Define another function, called <code>improve</code>, to compute
the value of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><annotation encoding="application/x-tex">x_{n+1}</annotation></semantics></math>,
given the current approximated value and the value of x.</p></li>
<li><p>Using the previously defined functions, define the
<code>sqrt</code> method. Please note that you can add other functions
if you need to!</p></li>
<li><p>Test your method and check your results.</p></li>
<li><p>[<em>Optional</em>] Implement the cubic root using the same
approach and check your results.</p></li>
</ol>
<section id="footnotes" class="footnotes footnotes-end-of-document" role="doc-endnotes">
<hr />
<ol>
<li id="fn1"><p>Example from <a href="http://en.wikipedia.org/wiki/Newton&#39;s_method" class="uri">http://en.wikipedia.org/wiki/Newton&#39;s_method</a><a href="#fnref1" class="footnote-back" role="doc-backlink">↩︎</a></p></li>
<li id="fn2"><p>Example from <a href="http://en.wikipedia.org/wiki/Newton&#39;s_method" class="uri">http://en.wikipedia.org/wiki/Newton&#39;s_method</a><a href="#fnref2" class="footnote-back" role="doc-backlink">↩︎</a></p></li>
</ol>
</section>
</article>

<div class="cstTOC" style="position: fixed;top: 20px;right: 0;width:15%;border:none;display:flex;flex-direction:column;max-width:250px;">
  <nav id="TOC" style="font-size:15px;margin-right:20px;">
  <h1 class="toc-title" style="font-size:20px;margin-bottom:5px;">Assignment
1 – Introduction</h1>
    <ul>
    <li><a href="#exercise-1-starting-slowly-and-installing-tools-difficulty" id="toc-exercise-1-starting-slowly-and-installing-tools-difficulty">Exercise
    1 – Starting slowly and installing tools (difficulty <span class="emoji" data-emoji="star">⭐</span>)</a></li>
    <li><a href="#exercise-2-getting-our-hands-dirty-difficulty" id="toc-exercise-2-getting-our-hands-dirty-difficulty">Exercise 2 –
    Getting our hands dirty (difficulty <span class="emoji" data-emoji="star">⭐</span>)</a>
    <ul>
    <li><a href="#task-1-newtons-method" id="toc-task-1-newtons-method">Task 1 – Newton’s method</a></li>
    <li><a href="#task-2-application-to-the-square-root-function" id="toc-task-2-application-to-the-square-root-function">Task 2 –
    Application to the square root function</a></li>
    <li><a href="#task-3-implementation" id="toc-task-3-implementation">Task 3 – Implementation</a></li>
    </ul></li>
    <li><a href="#exercise-3-getting-our-hands-dirty-difficulty" id="toc-exercise-3-getting-our-hands-dirty-difficulty">Exercise 3 –
    Getting our hands dirty (difficulty <span class="emoji" data-emoji="star">⭐</span>)</a>
    <ul>
    <li><a href="#task-1-newtons-method-1" id="toc-task-1-newtons-method-1">Task 1 – Newton’s method</a></li>
    <li><a href="#task-2-application-to-the-square-root-function-1" id="toc-task-2-application-to-the-square-root-function-1">Task 2 –
    Application to the square root function</a></li>
    <li><a href="#task-3-implementation-1" id="toc-task-3-implementation-1">Task 3 – Implementation</a></li>
    </ul></li>
    </ul>
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