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<p align="justify"><em><span style="font-family: 'times new roman', times, serif; font-size: large;">CRE1</span></em></p> <p align="justify"><em><span style="font-family: 'times new roman', times, serif; font-size: large;">La funciĆ³n <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«miĀ»fĀ«/miĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#fĀ«/miĀ»Ā«/mathĀ»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> es #cr si y sĆ³lo si:</span></em></p>
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<div align="justify"><span style="font-size: large;"><em><span style="font-family: 'times new roman', times, serif;">SoluciĆ³n</span><span style="font-family: 'times new roman', times, serif;">:</span></em></span></div> <div align="justify">Ā </div> <div style="text-align: left;" align="justify"><em><span style="font-size: large;">Recordemos que la funciĆ³n <span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«miĀ»fĀ«/miĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#fĀ«/miĀ»Ā«/mathĀ»</span> serĆ” #cr si:</span></em></div> <div style="text-align: left;" align="justify"><em style="text-align: center;"><span class="nolink"><span class="nolink"><span style="font-size: large;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»fĀ«/miĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«miĀ»#desĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«/mathĀ»</span></span></span></span></span></span></span></em></div> <div style="text-align: left;" align="justify"><em style="text-align: center;"><span style="font-size: large;">Entonces, necesitamos calcular <span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»fĀ«/miĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«/mathĀ»</span></span></em></div> <div style="text-align: left;" align="justify"><em style="text-align: center;"><span style="font-size: large;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«miĀ»fĀ«/miĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#fĀ«/miĀ»Ā«moĀ»Ā§#8658;Ā«/moĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»fĀ«/miĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#dfĀ«/miĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></span></em></div> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: left;" align="justify"><em style="font-family: 'times new roman', times, serif; font-size: large;"><span style="font-size: large;">Por lo tanto, debemos encontrar la soluciĆ³n de la siguiente inecuaciĆ³n:</span></em></div> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: center;" align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large;"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«miĀ»#dfĀ«/miĀ»Ā«miĀ»#desĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«/mathĀ»</span></span></span></span></span></span> </em></span></div> <div style="text-align: left;" align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large;"><em>Para esto debemosĀ encontrar los </em><strong style="font-style: italic;">puntos crĆticos </strong><span style="font-style: italic;">de</span></span><em style="text-align: center; font-family: 'times new roman', times, serif; font-size: large;"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»fĀ«/miĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«/mathĀ»</span><span style="font-size: large;">, que se obtienen</span></span></em></div> <div style="text-align: left;" align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large;"><span style="font-style: italic;">resolviendo la siguiente ecuaciĆ³n de segundo grado:</span></span></div> <div style="text-align: center;" align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large;"><span style="font-style: italic;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»fĀ«/miĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#dfĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«/mathĀ»</span></span></span></span></span></span></span></span></div> <div style="text-align: left;" align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large;"><span style="font-style: italic;">Para resolverla utilizamos la fĆ³rmula:</span></span></div> <div style="text-align: left;" align="justify">Ā </div> <div style="text-align: center;" align="justify"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«mtable columnalign=ĀØleftĀØ rowspacing=ĀØ0ĀØĀ»Ā«mtrĀ»Ā«mtdĀ»Ā«miĀ»aĀ«/miĀ»Ā«msupĀ»Ā«miĀ»xĀ«/miĀ»Ā«mnĀ»2Ā«/mnĀ»Ā«/msupĀ»Ā«moĀ»+Ā«/moĀ»Ā«miĀ»bĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»+Ā«/moĀ»Ā«miĀ»cĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§#8658;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«moĀ»-Ā«/moĀ»Ā«miĀ»bĀ«/miĀ»Ā«moĀ»Ā±Ā«/moĀ»Ā«msqrtĀ»Ā«mrowĀ»Ā«msupĀ»Ā«miĀ»bĀ«/miĀ»Ā«mnĀ»2Ā«/mnĀ»Ā«/msupĀ»Ā«moĀ»-Ā«/moĀ»Ā«mnĀ»4Ā«/mnĀ»Ā«miĀ»aĀ«/miĀ»Ā«miĀ»cĀ«/miĀ»Ā«/mrowĀ»Ā«/msqrtĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«mnĀ»2Ā«/mnĀ»Ā«miĀ»aĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«mtrĀ»Ā«mtd/Ā»Ā«/mtrĀ»Ā«mtrĀ»Ā«mtdĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«/mtableĀ»Ā«/mathĀ»</span></span></span></span></span></span></div> <div style="text-align: center;" align="justify"><em><span style="font-family: 'Times New Roman'; font-size: large;">AsĆ, de</span></em>Ā <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»fĀ«/miĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#dfĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«/mathĀ»</span></span></span></span></span><span style="font-family: 'times new roman', times, serif; font-size: large;"><em>obtenemos los parĆ”metros:</em></span></span></div> <div style="text-align: center;" align="justify"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«miĀ»aĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#apĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»,Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»bĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#bpĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»,Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»cĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#cĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«/mathĀ»</span></span></span></span></span></span></div> <div style="text-align: left;" align="justify"><span style="font-style: italic; font-family: 'times new roman', times, serif; font-size: large;"><span style="font-size: large;">Reemplazando estos valores en la fĆ³rmula obtenemos:</span></span></div> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: center;" align="justify"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«mtable columnalign=ĀØleftĀØ rowspacing=ĀØ0ĀØĀ»Ā«mtrĀ»Ā«mtdĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«moĀ»-Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»#bpĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»Ā±Ā«/moĀ»Ā«msqrtĀ»Ā«mrowĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»#bpĀ«/miĀ»Ā«msupĀ»Ā«moĀ»)Ā«/moĀ»Ā«mnĀ»2Ā«/mnĀ»Ā«/msupĀ»Ā«moĀ»-Ā«/moĀ»Ā«mnĀ»4Ā«/mnĀ»Ā«moĀ»Ā·Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»#apĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»Ā·Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»#cĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«/mrowĀ»Ā«/msqrtĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«mnĀ»2Ā«/mnĀ»Ā«moĀ»Ā·Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»#apĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«mtrĀ»Ā«mtdĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»#mbpĀ«/miĀ»Ā«moĀ»Ā±Ā«/moĀ»Ā«msqrtĀ»Ā«miĀ»#discĀ«/miĀ»Ā«/msqrtĀ»Ā«/mrowĀ»Ā«miĀ»#deĀ«/miĀ»Ā«/mfracĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«mtrĀ»Ā«mtdĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«mfenced close=ĀØĀØ open=ĀØ{ĀØĀ»Ā«mtableĀ»Ā«mtrĀ»Ā«mtdĀ»Ā«msubĀ»Ā«miĀ»xĀ«/miĀ»Ā«mnĀ»1Ā«/mnĀ»Ā«/msubĀ»Ā«moĀ»=Ā«/moĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»#mbpĀ«/miĀ»Ā«moĀ»+Ā«/moĀ»Ā«msqrtĀ»Ā«miĀ»#discĀ«/miĀ»Ā«/msqrtĀ»Ā«/mrowĀ»Ā«miĀ»#deĀ«/miĀ»Ā«/mfracĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#r6Ā«/miĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«mtrĀ»Ā«mtdĀ»Ā«msubĀ»Ā«miĀ»xĀ«/miĀ»Ā«mnĀ»2Ā«/mnĀ»Ā«/msubĀ»Ā«moĀ»=Ā«/moĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»#mbpĀ«/miĀ»Ā«moĀ»-Ā«/moĀ»Ā«msqrtĀ»Ā«miĀ»#discĀ«/miĀ»Ā«/msqrtĀ»Ā«/mrowĀ»Ā«miĀ»#deĀ«/miĀ»Ā«/mfracĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#r4Ā«/miĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«/mtableĀ»Ā«/mfencedĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«/mtableĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></em> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: left;" align="justify"><em style="font-family: 'times new roman', times, serif; font-size: large;"><span style="font-size: large;">Por lo tanto, podemos escribir la inecuaciĆ³n de la siguiente manera:</span></em></div> <div style="text-align: left;" align="justify">Ā </div> <div style="text-align: center;" align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large;"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«mtable columnalign=ĀØleftĀØ rowspacing=ĀØ0ĀØĀ»Ā«mtrĀ»Ā«mtdĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»fĀ«/miĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»+Ā«/moĀ»Ā«miĀ»#p1Ā«/miĀ»Ā«miĀ»#opr4Ā«/miĀ»Ā«miĀ»#p2Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»+Ā«/moĀ»Ā«miĀ»#p3Ā«/miĀ»Ā«miĀ»#opr6Ā«/miĀ»Ā«miĀ»#p4Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»#desĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«mtrĀ»Ā«mtd/Ā»Ā«/mtrĀ»Ā«/mtableĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></em></span> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: left;" align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large;"><em>Para que este producto sea #des 0 se debe cumplir que ambos factores sean de #comentario signo, es decir:</em></span></div> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: center;" align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«mfenced close=ĀØ]ĀØ open=ĀØ[ĀØĀ»Ā«mrowĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#s1Ā«/miĀ»Ā«miĀ»#opr4Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«miĀ»#des1Ā«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§#8743;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#s2Ā«/miĀ»Ā«miĀ»#opr6Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«miĀ»#des2Ā«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«/mrowĀ»Ā«/mfencedĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></span> <div style="text-align: center;" align="justify"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«miĀ»#opĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«/mathĀ»</span></span></span></span></span></span></div> <div style="text-align: center;" align="justify"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«mfenced close=ĀØ]ĀØ open=ĀØ[ĀØĀ»Ā«mrowĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#s1Ā«/miĀ»Ā«miĀ»#opr4Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«miĀ»#des3Ā«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§#8743;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#s2Ā«/miĀ»Ā«miĀ»#opr6Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«miĀ»#des4Ā«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«/mrowĀ»Ā«/mfencedĀ»Ā«/mathĀ»</span></span></span></span></span></span></div> <div style="text-align: left;" align="justify"><em style="font-family: 'times new roman', times, serif; font-size: large;"><span style="font-size: large;">Resolviendo cada inecuaciĆ³n:</span></em></div> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: center;" align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#des1Ā«/miĀ»Ā«miĀ»#r4Ā«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§#8743;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#des2Ā«/miĀ»Ā«miĀ»#r6Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»#opĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#des3Ā«/miĀ»Ā«miĀ»#r4Ā«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§#8743;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#des4Ā«/miĀ»Ā«miĀ»#r6Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></span> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: left;" align="justify"><em style="font-family: 'times new roman', times, serif; font-size: large;"><span style="font-size: large;">Escribiendo como intervalos:</span></em></div> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: center;" align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«moĀ»(Ā«/moĀ»Ā«moĀ»]Ā«/moĀ»Ā«miĀ»#in1Ā«/miĀ»Ā«moĀ»,Ā«/moĀ»Ā«miĀ»#in2Ā«/miĀ»Ā«moĀ»[Ā«/moĀ»Ā«moĀ»Ā§#8745;Ā«/moĀ»Ā«moĀ»]Ā«/moĀ»Ā«miĀ»#in3Ā«/miĀ»Ā«moĀ»,Ā«/moĀ»Ā«miĀ»#in4Ā«/miĀ»Ā«moĀ»[Ā«/moĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»#cjĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«moĀ»]Ā«/moĀ»Ā«miĀ»#in5Ā«/miĀ»Ā«moĀ»,Ā«/moĀ»Ā«miĀ»#in6Ā«/miĀ»Ā«moĀ»[Ā«/moĀ»Ā«moĀ»Ā§#8745;Ā«/moĀ»Ā«moĀ»]Ā«/moĀ»Ā«miĀ»#in7Ā«/miĀ»Ā«moĀ»,Ā«/moĀ»Ā«miĀ»#in8Ā«/miĀ»Ā«moĀ»[Ā«/moĀ»Ā«moĀ»)Ā«/moĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></span> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: left;" align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large;"><em><span style="font-size: large;">Resolviendo, obtenemos</span>:</em></span></div> <div style="text-align: left;" align="justify">Ā </div> <div style="text-align: center;" align="justify"> <table style="text-align: center; width: 100%;" border="1"> <tbody> <tr> <td valign="top" width="100%"><em style="text-align: center; font-family: 'times new roman', times, serif; font-size: large;">x#pert#r1#r2#r3#r4#r5#r6#r7</em></td> </tr> </tbody> </table> </div> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: left;" align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large;"><em>Observemos el grĆ”fico de <span class="nolink">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«miĀ»fĀ«/miĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#fĀ«/miĀ»Ā«/mathĀ»</span></em></span></div> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: center;" align="justify">Ā </div> <div style="text-align: center;" align="justify">#t1</div> <div style="text-align: center;" align="justify"><span style="font-family: 'times new roman', times, serif;"><span style="font-size: large;"><em>Si observas el grĆ”fico, en rojo estĆ” marcada la parte #cr, que coincide con el resultado obtenido.</em><br /></span></span></div> </div> </div> </div> </div> </div>
One or multiple answers?
Multiple answers allowed
One answer only
Shuffle the choices?
Number the choices?
a., b., c., ...
A., B., C., ...
1., 2., 3., ...
i., ii., iii., ...
I., II., III., ...
No numbering
WIRIS variables
Algorithm
Choice 1
Answer
<p>#x1#pert#r1#r2#r3#r4#r5#r6#r7</p>
Grade
None
100%
90%
83.33333%
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Feedback
<div style="text-align: left;" align="left"><span style="font-size: large;"><em><span style="font-family: 'times new roman', times, serif;">Ā”Excelente!</span> </em></span></div>
Choice 2
Answer
<p>#x1#pert#w1#w2#w3#w4#w5#w6#w7</p>
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
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Feedback
<div style="text-align: left;">Ā </div> <div style="text-align: left;" align="left"><em><span style="font-family: 'times new roman', times, serif; font-size: large;">Revisa el desarrollo para identificar tus errores.</span></em></div>
Choice 3
Answer
<p>#x1#pert#q1#q2#q3#q4#q5</p>
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
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50%
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33.33333%
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Feedback
<div style="text-align: left;"> <div style="text-align: left;"><em><span style="font-family: 'times new roman', times, serif; font-size: large;">Revisa el desarrollo para identificar tus errores.</span></em></div> </div>
Choice 4
Answer
<p>#x1#pert#k1#k2#k3#k4#k5</p>
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
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Feedback
<div style="text-align: left;"> <div style="text-align: left;"><em><span style="font-family: 'times new roman', times, serif; font-size: large;">Revisa el desarrollo para identificar tus errores.</span></em></div> </div>
Choice 5
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
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33.33333%
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Feedback
Choice 6
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
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33.33333%
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Feedback
Choice 7
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
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20%
16.66667%
14.28571%
12.5%
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Feedback
Combined feedback
For any correct response
For any partially correct response
Options
Show the number of correct responses once the question has finished
For any incorrect response
Settings for multiple tries
Penalty for each incorrect try
100%
50%
33.33333%
25%
20%
10%
0%
Hint 1
Hint text
Options
Clear incorrect responses
Show the number of correct responses
Hint 2
Hint text
Options
Clear incorrect responses
Show the number of correct responses
Created / last saved
Created
by
Admin User
on
Friday, 6 February 2015, 4:35 PM
Last saved
by
Admin User
on
Friday, 6 February 2015, 4:35 PM
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