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Adding omniauth-coursera strategy
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@kisonecat
kisonecat committed Dec 23, 2012
2 parents 8231c82 + cf4d155 commit a889995
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293 changes: 293 additions & 0 deletions curriculum/khanExercise/exercises/limitsAtInfinityGraphical.html
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<!DOCTYPE html>
<html data-require="math polynomials graphie word-problems steveMath8">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Approximating Limits at Infinity Graphically</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">


<var id = "p">new Polynomial(0,4)</var>
<var id = "A">randRange(0,2)</var>
<var id = "B">randRange(1,9)</var>
<var id = "C">randRangeExclude(-4,4,[p.coefs[4]])</var>
<var id = "D">randRangeNonZero(-1,1)</var>
<var id = "E">randRangeNonZero(-1,1)</var>
<var id = "f">(function(x){
if (x &gt;0){
return p.evalOf(x)/(x*x*x*x+A*x*x+B);
}
else {
return p.evalOf(x)/(x*x*x*x+A*x*x+B)+(C-p.coefs[4])*x*x/(x*x+1)
}
}
)
</var>
<var id = "Xs">makeXList()</var>
<var id = "Ys">makeYList(-8,8,Xs.length)</var>
<var id = "points">makeCoordinates(Xs,Ys)</var>
<var id = "g">(function(x){
if (x &gt;0){
return p.evalOf(x)/(x*x*x*x+A*x*x+B)+D*x*x/10;
}
else {
return p.evalOf(x)/(x*x*x*x+A*x*x+B)+E*x*x/10
}
}
)
</var>
<var id = "h">(function(x){
if (x &gt;0){
return p.evalOf(x)/(x*x*x*x+A*x*x+B);
}
else {
return p.evalOf(x)/(x*x*x*x+A*x*x+B)+E*x*x/10
}
}
)
</var>
<var id = "k">(function(x){
if (x &lt;0){
return p.evalOf(x)/(x*x*x*x+A*x*x+B);
}
else {
return p.evalOf(x)/(x*x*x*x+A*x*x+B)+D*x*x/10
}
}
)
</var>
<var id = "sol">(function(A){
if (A &gt; 0){
return "infinity"
}
else {
return "-infinity"
}
})
</var>

<var id = "negSol">sol(E)</var>
<var id = "posSol">sol(D)</var>


</div>

<div class="problems">
<div id="bothFinite" >

<div class="question">

<p>
Consider the function <code>f(x)</code> graphed below. Find
the value of each of the indicated limits with an error of at most <code>\frac{1}{2}</code>.
If one of the limits appears to be <code>\infty</code> or <code>-\infty</code>, just type "infinity"
or "-infinity".
</p>


<div class = graphie id="grid">
graphInit({
range: [20,10],
scale: [12,20],
labelStep: [2,1],
gridOpacity: 0,
axisArrows: "<->"
});

plot(function( x ) {
return ( f(x));
}, [-20, 20], {
stroke: RED,
strokeWidth: 1
});
</div>

</div>

<div class="solution" data-type="multiple">

<p>
<code>\displaystyle\lim_{x \to +\infty}f(x)</code>:
<span class="sol" data-inexact data-max-error="0.5" data-type="decimal"><var>p.coefs[4]</var></span>
<br>
<code>\displaystyle\lim_{x \to -\infty}f(x)</code>:
<span class="sol" data-inexact data-max-error="0.5" data-type="decimal"><var>C</var></span>
</p>

</div>


<div class="hints">

<p>hint</p>
</div>
</div>

<div id="bothInfinite" >

<div class="question">

<p>
Consider the function <code>f(x)</code> graphed below. Find
the value of each of the indicated limits with an error of at most <code>\frac{1}{2}</code>.
If one of the limits appears to be <code>\infty</code> or <code>-\infty</code>, just type "infinity"
or "-infinity".
</p>


<div class = graphie id="grid">
graphInit({
range: [20,10],
scale: [12,20],
labelStep: [2,1],
gridOpacity: 0,
axisArrows: "<->"
});

plot(function( x ) {
return ( g(x));
}, [-20, 20], {
stroke: RED,
strokeWidth: 1
});
</div>

</div>

<div class="solution" data-type="multiple">

<p>
<code>\displaystyle\lim_{x \to +\infty}f(x)</code>:
<span class="sol" data-type="text"><var>posSol</var></span>
<br>
<code>\displaystyle\lim_{x \to -\infty}f(x)</code>:
<span class="sol" data-type="text"><var>negSol</var></span>
</p>

</div>


<div class="hints">

<p>hint</p>
</div>
</div>

<div id="leftInfinite" >

<div class="question">

<p>
Consider the function <code>f(x)</code> graphed below. Find
the value of each of the indicated limits with an error of at most <code>\frac{1}{2}</code>.
If one of the limits appears to be <code>\infty</code> or <code>-\infty</code>, just type "infinity"
or "-infinity".
</p>


<div class = graphie id="grid">
graphInit({
range: [20,10],
scale: [12,20],
labelStep: [2,1],
gridOpacity: 0,
axisArrows: "<->"
});

plot(function( x ) {
return ( h(x));
}, [-20, 20], {
stroke: RED,
strokeWidth: 1
});
</div>

</div>

<div class="solution" data-type="multiple">

<p>
<code>\displaystyle\lim_{x \to +\infty}f(x)</code>:
<span class="sol" data-type="text"><var>p.coefs[4]</var></span>
<br>
<code>\displaystyle\lim_{x \to -\infty}f(x)</code>:
<span class="sol" data-type="text"><var>negSol</var></span>
</p>

</div>


<div class="hints">

<p>hint</p>
</div>
</div>

<div id="rightInfinite" >

<div class="question">

<p>
Consider the function <code>f(x)</code> graphed below. Find
the value of each of the indicated limits with an error of at most <code>\frac{1}{2}</code>.
If one of the limits appears to be <code>\infty</code> or <code>-\infty</code>, just type "infinity"
or "-infinity".
</p>


<div class = graphie id="grid">
graphInit({
range: [20,10],
scale: [12,20],
labelStep: [2,1],
gridOpacity: 0,
axisArrows: "<->"
});

plot(function( x ) {
return ( k(x));
}, [-20, 20], {
stroke: RED,
strokeWidth: 1
});
</div>

</div>

<div class="solution" data-type="multiple">

<p>
<code>\displaystyle\lim_{x \to +\infty}f(x)</code>:
<span class="sol" data-type="text"><var>posSol</var></span>
<br>
<code>\displaystyle\lim_{x \to -\infty}f(x)</code>:
<span class="sol" data-type="text"><var>p.coefs[4]</var></span>
</p>

</div>


<div class="hints">

<p>hint</p>
</div>
</div>







</div>


</div>
</body>
</html>



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