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<p><span style="font-weight: bold; color: #003300;" data-mce-mark="1">Estudia la continuïtat de la funció f(x) definida a trossos:</span></p> <div style="text-align: center;"><span style="font-weight: bold; color: #003300;" data-mce-mark="1"><span class="nolink" data-mce-mark="1">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»f«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»g_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»si«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»§lt;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»g_«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»s«/mi»«mi mathvariant=¨bold¨»i«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»§#8805;«/mo»«mi mathvariant=¨bold¨»#a«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«/mstyle»«/math»</span></span><br /> <div style="text-align: justify;"><span style="color: #003300;" data-mce-mark="1"><span style="color: #ff6600;"><strong>Format de la resposta</strong></span> <strong>Els infinits s'escriuen amb la lletra ¨i¨ minúscula, -i, i.</strong></span></div> <div style="text-align: justify;"><span style="color: #003300;" data-mce-mark="1"> </span></div> </div> <p><span style="font-size: large; color: #003300;"><span style="font-weight: bold;">En x = #d:</span></span><br /><span style="font-weight: bold; color: #003300;"><span style="font-weight: bold;">La funció està definida en x = #d? {1:MULTICHOICE: ~SI ~=NO}<br /></span><span style="font-weight: bold;"><span style="font-weight: bold;">El límit de la funció quan x tendeix a #d<sup>-</sup> és </span><span style="font-weight: bold;">{1:SHORTANSWER: ~=#j_5}</span></span></span><br /><span style="font-weight: bold; color: #003300;"><span style="font-weight: bold;">El límit de la funció quan x tendeix a #d<sup>+</sup> és </span><span style="font-weight: bold;">{1:SHORTANSWER: ~=#j_6}</span></span><br /><span style="color: #003300;"><span style="font-weight: bold;"><span style="font-weight: bold;">La discontinuïtat de la funció </span><span style="font-weight: bold;">{1:MULTICHOICE: ~#t_2~#t_3~#t_4 ~=#t_1}<br /><br /><br /><span style="font-size: large;">En x = #a</span><br /></span></span><span style="font-weight: bold;"><span style="font-weight: bold;"><span style="font-weight: bold;">La funció està definida en x = #a? {1:MULTICHOICE: ~NO ~=SI}</span></span></span></span><br /><span style="font-weight: bold; color: #003300;"><span style="font-weight: bold;"><span style="font-weight: bold;"> </span><span style="font-weight: bold;"><span>El límit de la funció quan x tendeix a #a</span><sup>-</sup><span> és</span>{1:SHORTANSWER: ~=#l_1}</span></span></span><br /><span style="font-weight: bold; color: #003300;"><span style="font-weight: bold;"><span style="font-weight: bold;"><span>El límit de la funció quan x tendeix a #a</span><sup>+</sup><span> és</span> </span><span style="font-weight: bold;">{1:SHORTANSWER: ~=#i_1}</span></span></span><br /><span style="font-weight: bold; color: #003300;"><span style="font-weight: bold;"> <span style="font-weight: bold;">La discontinuïtat de la funció </span><span style="font-weight: bold;">{1:MULTICHOICE: ~#r_2~#r_3~#r_4 ~=#r_1}</span></span></span><br /><span style="font-weight: bold; color: #003300;"><br /></span><span style="font-weight: bold; color: #009900;"><br /><br /><br /></span></p>
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<p><span style="color: #000080;"><strong>EN x = #d</strong></span><br /><span style="color: #000080;"><strong>Calculem els límits laterals per saber si són infinits o són del tipus 0/0 simplificable i corresponen a una discontinuïtat asimptòtica o evitable.</strong></span></p> <p><span style="color: #000080;"><strong> </strong></span></p> <p><span style="color: #000080;" data-mce-mark="1"><strong>EN x = #a</strong></span><br /><span style="color: #000080;" data-mce-mark="1"><strong>Calculem el límit de #g_1 quan x tendeix a #a<sup>-</sup> ja que, en #a<sup>+</sup>, f(x) = #g_2 que té imatge en #a.</strong></span><br /><span style="color: #000080;" data-mce-mark="1"><strong>Calculem f(#a) amb la funció #g_2 que és contínua en [#a,+oo) ja que és polinòmica.</strong></span><br /><br /><br /></p>
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