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<p><font size="3">Considereu el polinomi p(x)=#px. Volem demostrar que <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mrow»«mi»lim«/mi»«mo»§nbsp;«/mo»«mo»(«/mo»«/mrow»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mi»a«/mi»«/mrow»«/munder»«mi»p«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»)«/mo»«mo»=«/mo»«mi»p«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«/math»</span></span></span></span>, és a dir que </font><font size="3"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mi»a«/mi»«/mrow»«/munder»«mi»#px«/mi»«mo»=«/mo»«mi»#pa«/mi»«/math»</span></span></span></span></font>.<br /><font size="3">Això és cert si <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8704;«/mo»«mi»§#949;«/mi»«mo»§gt;«/mo»«mn»0«/mn»«mo»§nbsp;«/mo»«mo»§#8707;«/mo»«mi»§#948;«/mi»«mo»§gt;«/mo»«mn»0«/mn»«/math»</span></span></span></span> tal que si agafem un <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mi»a«/mi»«/math»</span></span></span></span> tal que <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8712;«/mo»«mo»(«/mo»«mi»a«/mi»«mo»-«/mo»«mi»§#948;«/mi»«mo»,«/mo»«mi»a«/mi»«mo»+«/mo»«mi»§#948;«/mi»«mo»)«/mo»«/math»</span></span></span></span> llavors <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#8712;«/mo»«mo»(«/mo»«mi»p«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mo»-«/mo»«mi»§#949;«/mi»«mo»,«/mo»«mi»p«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«mo»+«/mo»«mi»§#949;«/mi»«mo»)«/mo»«/math»</span></span></span></span>.</font></p><font size="3"> <p><br />Determineu donat <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#949;«/mi»«mo»§gt;«/mo»«mn»0«/mn»«/math»</span></span></span></span><font size="3"> quin és el mínim valor de δ que verifica la definició de límit. </font></p> <p></p> <p><font size="3"></font></p> <p><font size="3">El valor de δ que heu de trobar sempre dependrà d' ε de la manera <span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#948;«/mi»«mo»=«/mo»«mi»k«/mi»«mo»*«/mo»«mi»§#949;«/mi»«/math»</span></span>. Introduiu com a solució el valor de k (així, si trobeu que</font><font size="3"> </font><font size="3"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#948;«/mi»«mo»=«/mo»«mn»5«/mn»«mo»*«/mo»«mi»§#949;«/mi»«/math»</span></span>, la solució que heu d'introduir és 5).</span></span></font><font size="3"><br /><br /></font></p></font>
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<font size="3">1. Calculeu qui és la imatge dels punts <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»-«/mo»«mi»§#948;«/mi»«/math»</span></span></span></span> i <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»+«/mo»«mi»§#948;«/mi»«/math»</span></span></span></span></font>.<br /><font size="3">2. Calculeu la distància entre <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«/math»</span></span></span></span> i <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»(«/mo»«mi»a«/mi»«mo»+«/mo»«mi»§#948;«/mi»«mo»)«/mo»«/math»</span></span></span></span>, que és la mateixa que entre <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«/math»</span></span></span></span> i <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»(«/mo»«mi»a«/mi»«mo»-«/mo»«mi»§#948;«/mi»«mo»)«/mo»«/math»</span></span></span></span>.</font><br /><br /><font size="3">3. La distància mínima es calcula resolent l'equació <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨|¨ open=¨|¨»«mrow»«mi»p«/mi»«mo»(«/mo»«mi»a«/mi»«mo»+«/mo»«mi»§#948;«/mi»«mo»)«/mo»«mo»-«/mo»«mi»p«/mi»«mo»(«/mo»«mi»a«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»=«/mo»«mi»§#949;«/mi»«/math»</span></span></span></span>.</font><br /><br /><br />
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Answer 1
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83.33333%
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75%
70%
66.66667%
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33.33333%
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16.66667%
14.28571%
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11.11111%
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Answer 2
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None
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90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
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33.33333%
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