<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/e31e6a7f-4780-4e57-a859-ca766b267606/bg1.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls4 ws9">MATEMÁTICA (6<span class="ls5 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM </span></div><div class="t m0 x1 h2 y3 ff1 fs0 fc0 sc0 ls4 ws9">FINAL </div><div class="t m0 x2 h2 y4 ff1 fs0 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h2 y5 ff2 fs0 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h3 y6 ff2 fs1 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h2 y7 ff2 fs0 fc0 sc0 ls4 ws1">12/07/2023<span class="ff1 ws9"> <span class="blank _0"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span>TEMA 4 </span></div><div class="t m0 x3 h2 y8 ff2 fs0 fc0 sc0 ls4 ws9"> Hoja 1 de 4 </div><div class="t m0 x3 h2 y9 ff2 fs0 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h3 ya ff2 fs1 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h3 yb ff2 fs1 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h4 yc ff3 fs2 fc0 sc0 ls4 ws9">Tabla de uso exclusivo para el docente </div></div><div class="c x4 yd w3 h5"><div class="t m0 x5 h6 ye ff3 fs3 fc0 sc0 ls4 ws9"> </div></div><div class="c x6 yd w4 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls4 ws9">1 </div></div><div class="c x8 yd w5 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls4 ws9">2 </div></div><div class="c x9 yd w6 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls4 ws9">3 </div></div><div class="c xa yd w7 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls4 ws9">4 </div></div><div class="c x4 yf w3 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls4 ws9"> </div></div><div class="c x6 yf w4 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls4 ws9"> </div></div><div class="c x8 yf w5 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls4 ws9"> </div></div><div class="c x9 yf w6 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls4 ws9"> </div></div><div class="c xa yf w7 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls4 ws9"> </div></div><div class="c x4 y11 w5 h9"><div class="t m0 xb ha y12 ff4 fs4 fc0 sc0 ls4 ws9">Puntaje de cada </div><div class="t m0 xb ha y13 ff4 fs4 fc0 sc0 ls4 ws9">ejercicio </div></div><div class="c x6 y11 w4 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls4 ws9">2,50 </div></div><div class="c x8 y11 w5 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls4 ws9">2,50 </div></div><div class="c x9 y11 w6 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls4 ws9">2,50 </div></div><div class="c xa y11 w7 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls4 ws9">2,50 </div></div><div class="c x0 y1 w2 h0"><div class="t m0 x1 hb y15 ff5 fs5 fc0 sc0 ls4 ws9">Duración del exam<span class="blank _2"> </span>en: 1h <span class="ff6 ws2">40\u2019.</span> Com<span class="blank _2"> </span>pletar los datos<span class="blank _2"> </span> personales<span class="blank _2"> </span> con letra clara, m<span class="blank _2"> </span>ayúscula e imprenta. <span class="blank _2"> </span> </div><div class="t m0 xd hc y16 ff3 fs5 fc0 sc0 ls4 ws9">No se aceptarán respue<span class="blank _2"> </span>stas en lápiz.<span class="blank _2"> </span> </div><div class="t m0 xe hd y17 ff2 fs6 fc0 sc0 ls0 ws9"> <span class="ff3 fs2 ls4 v1">1. <span class="blank _3"> </span>¿Cuántas <span class="blank _3"> </span>palabra<span class="blank _4"></span>s <span class="blank _3"> </span>se <span class="blank _3"> </span>pueden<span class="blank _4"></span> <span class="blank _3"> </span>formar, <span class="blank _3"> </span>con <span class="blank _3"> </span>o <span class="blank"> </span>s<span class="blank _2"> </span>in <span class="blank _3"> </span>sentido<span class="blank _4"></span>, <span class="blank _3"> </span>con <span class="blank _3"> </span>l<span class="blank _4"></span>as <span class="blank _3"> </span>letras <span class="blank _3"> </span>de <span class="blank"> </span>la <span class="blank _3"> </span>palabra </span></div><div class="t m0 x1 h4 y18 ff7 fs2 fc0 sc0 ls4 ws9">\u201cPALACIOS\u201d si deben comenzar con \u201cS\u201d y<span class="blank _4"></span> terminar c<span class="blank _2"> </span>on \u201cO\u201d?<span class="ff3"> </span></div><div class="t m0 x1 h4 y19 ff3 fs2 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 he y1a ff8 fs3 fc0 sc0 ls4 ws9">Buscamos <span class="blank _2"> </span>utilizar <span class="blank _2"> </span>las <span class="blank _5"> </span>8 <span class="blank _2"> </span>letras <span class="blank _2"> </span>de <span class="blank _5"> </span>la <span class="blank _2"> </span>palabra <span class="blank _2"> </span>\u201cP<span class="blank _2"> </span>ALACIO<span class="blank _4"></span>S\u201d <span class="blank _2"> </span>para <span class="blank _5"> </span>armar <span class="blank _2"> </span>los <span class="blank _2"> </span>nuevos <span class="blank _2"> </span>vocablos <span class="blank _5"> </span>(independiente<span class="blank _4"></span>mente <span class="blank _2"> </span>de <span class="blank _2"> </span>si <span class="blank _5"> </span>éstos </div><div class="t m0 x1 he y1b ff4 fs3 fc0 sc0 ls4 ws9">tienen <span class="blank _5"> </span>o <span class="blank _6"> </span>no <span class="blank _5"> </span>sentido <span class="blank _5"> </span>en <span class="blank _6"> </span>nu<span class="blank _4"></span>estro <span class="blank _5"> </span>idioma). <span class="blank _5"> </span>Por <span class="blank _6"> </span>otra <span class="blank _5"> </span>parte, <span class="blank _5"> </span>importa <span class="blank _5"> </span>el <span class="blank _5"> </span>orden <span class="blank _6"> </span>en <span class="blank _5"> </span>que <span class="blank _5"> </span>se <span class="blank _6"> </span>eligen <span class="blank _5"> </span>las <span class="blank _5"> </span>letras <span class="blank _5"> </span>para <span class="blank _5"> </span>formar <span class="blank _6"> </span>dichos </div><div class="t m0 x1 he y1c ff4 fs3 fc0 sc0 ls4 ws9">términos. Lueg<span class="blank _4"></span>o, estamos ante un cas<span class="blank _4"></span>o de permutaci<span class="blank _4"></span>ón o reordenamient<span class="blank _4"></span>o de elementos.<span class="blank _4"></span> </div><div class="t m0 x1 he y1d ff8 fs3 fc0 sc0 ls4 ws9">Siendo <span class="blank _2"> </span>además <span class="blank _2"> </span>que <span class="blank _2"> </span>buscamos palabras <span class="blank _2"> </span>que <span class="blank _2"> </span>comienzan <span class="blank _2"> </span>con <span class="blank _2"> </span>\u201cS\u201d <span class="blank _2"> </span>y <span class="blank _2"> </span>finalizan <span class="blank _2"> </span>con <span class="blank _2"> </span>\u201cO\u201d, <span class="blank _2"> </span>en <span class="blank _2"> </span>lugar <span class="blank _2"> </span>de <span class="blank _2"> </span>permutar <span class="blank _2"> </span>los <span class="blank _2"> </span>8 <span class="blank _2"> </span>caracteres </div><div class="t m0 x1 he y1e ff4 fs3 fc0 sc0 ls4 ws9">disponibles, <span class="blank _4"></span>debemos <span class="blank _4"></span>reor<span class="blank _4"></span>denar <span class="blank _4"></span>solo <span class="blank _4"></span>6 de <span class="blank _4"></span>ellos, <span class="blank _4"></span>aquel<span class="blank _4"></span>los que <span class="blank _4"></span>justamente <span class="blank _4"></span>ocupan <span class="blank _4"></span>las <span class="blank _4"></span>posici<span class="blank _4"></span>ones 2 <span class="blank _4"></span>a <span class="blank _4"></span>7 <span class="blank _4"></span>dentro <span class="blank _4"></span>de <span class="blank _4"></span>cada n<span class="blank _4"></span>ueva </div><div class="t m0 x1 he y1f ff4 fs3 fc0 sc0 ls4 ws9">palabra. </div><div class="t m0 x1 he y20 ff4 fs3 fc0 sc0 ls4 ws9">Por otra parte, re<span class="blank _4"></span>cordemos que: </div><div class="t m0 xf he y21 ff4 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 he y22 ff8 fs3 fc0 sc0 ls4 ws9">Luego,como hay 2 l<span class="blank _4"></span>etras \u201cA\u201d disponibles<span class="blank _4"></span> entre las <span class="blank _4"></span>6 a reordenar,<span class="blank _4"></span> tendremos: <span class="ff4"> </span></div><div class="t m0 x10 hf y23 ff9 fs3 fc0 sc0 ls4">\ued32</div><div class="t m0 x11 h10 y24 ff9 fs0 fc0 sc0 ls4">\uf13a</div><div class="t m0 x12 h11 y25 ff9 fs0 fc0 sc0 ls4 ws3">\uf136\ue7e1\uf135\ue7e1\uf135\ue7e1\uf135\ue7e1\uf135<span class="blank"> </span><span class="fs3 ls1 v2">\uf34c</span><span class="fs3 ws4 v3">\ue978\ue7e8</span></div><div class="t m0 x13 h12 y26 ff9 fs3 fc0 sc0 ls4 ws5">\ue974\ue7e8<span class="blank"> </span>\ue973\ue7e8<span class="blank"> </span>\ue973\ue7e8<span class="blank"> </span>\ue973\ue7e8<span class="blank"> </span>\ue973\ue7e8<span class="blank _7"> </span><span class="ls2 v4">\uf34c</span><span class="ws4 v5">\ue978\ue7e4\ue977\ue7e4\ue976\ue7e4\ue975\ue7e4\ue974\ue7e8</span></div><div class="t m0 x14 h13 y26 ff9 fs3 fc0 sc0 ls4 ws6">\ue974\ue7e8<span class="blank"> </span><span class="ws7 v4">\uf34c<span class="blank"> </span>\ue978\ue7e4\ue977\ue7e4\ue976\ue7e4\ue975<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="ls3 ws8">\ue975\ue978\ue972<span class="ff4 ls4 ws9"> </span></span></span></div><div class="t m0 x1 he y27 ff4 fs3 fc0 sc0 ls4 ws9">palabras <span class="blank _6"> </span>distintas <span class="blank _8"> </span>que <span class="blank _6"> </span>pu<span class="ff8">eden <span class="blank _6"> </span>fo<span class="blank _2"> </span>rmarse<span class="blank _4"></span> <span class="blank _8"> </span>con <span class="blank _6"> </span>las <span class="blank _8"> </span>8 <span class="blank _6"> </span>letras <span class="blank _6"> </span>de <span class="blank _8"> </span>la <span class="blank _8"> </span>palabra <span class="blank _6"> </span>\u201cPALACIOS\u201d <span class="blank _6"> </span>y <span class="blank _8"> </span>que <span class="blank _6"> </span>además <span class="blank _8"> </span>comien<span class="blank _4"></span>zan <span class="blank _6"> </span>con <span class="blank _8"> </span>\u201cS\u201d <span class="blank _6"> </span>y </span></div><div class="t m0 x1 he y28 ff8 fs3 fc0 sc0 ls4 ws9">terminan con \u201cO<span class="blank _4"></span>\u201d.<span class="ff4"> </span></div><div class="t m0 x1 h4 y29 ff3 fs2 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h4 y2a ff3 fs2 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h6 y2b ff3 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h6 y2c ff3 fs3 fc0 sc0 ls4 ws9"> <span class="blank _9"> </span> </div></div><div class="c x1 y2d w8 h14"><div class="t m0 x15 h2 y2e ff2 fs0 fc0 sc0 ls4 ws9">APELLIDO: </div></div><div class="c x16 y2f w9 h15"><div class="t m0 xb h2 y30 ff2 fs0 fc0 sc0 ls4 ws9">CALIFICACIÓN:<span class="blank _4"></span> </div></div><div class="c x1 y31 w8 h16"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls4 ws9">NOMBRE: </div></div><div class="c x1 y2f w8 h16"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls4 ws9">DNI (registrado en S<span class="blank _4"></span>IU Guaraní<span class="blank _4"></span>): </div></div><div class="c x1 y32 w8 h17"><div class="t m0 xb h2 y10 ff2 fs0 fc0 sc0 ls4 ws9">E-MAIL: </div></div><div class="c x16 y33 w9 h18"><div class="t m0 xb h2 y34 ff2 fs0 fc0 sc0 ls4 ws9">DOCENTE (nombre<span class="blank _4"></span> y apellido<span class="blank _4"></span>): </div></div><div class="c x1 y35 w8 h16"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls4 ws9">TEL: </div></div><div class="c x1 y33 w8 h16"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls4 ws9">AULA: </div></div><div class="c x0 y36 wa h19"><div class="t m0 x15 he y37 ff4 fs3 fc1 sc0 ls4 ws9"><span class="fc2 sc0"> </span></div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y38 wb h1a" alt="" src="https://files.passeidireto.com/e31e6a7f-4780-4e57-a859-ca766b267606/bg2.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls4 ws9">MATEMÁTICA (6<span class="ls5 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls6"> <span class="ls7"> </span></span>FINAL </div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 ls4 ws9">APELLIDO Y NOMB<span class="blank _4"></span>RE: <span class="blank _4"></span> <span class="blank _4"></span> <span class="blank _4"></span> <span class="blank _4"></span> DNI<span class="blank _4"></span>:<span class="ff1"> <span class="blank _a"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span>TEMA 4 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 ls4 ws9">Hoja 2 de 4 </div><div class="t m0 x3 h2 y39 ff2 fs0 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h1b y3a ff3 fs2 fc0 sc0 ls4 ws9">2. Calcular la siguiente integral <span class="ff9 ls8 v6">\uebec</span><span class="ff9 wsa">\uf36b\ue603\uee9e\ue7e4<span class="blank"> </span><span class="ls9 v6">\ue9be</span><span class="wsb">\uee9e<span class="blank"> </span>\uf345<span class="blank _b"> </span>\uf0db\ue603\uf36f<span class="ls1c wsc">\uee8a\uee9e</span></span></span><span class="ff5"> </span></div><div class="t m0 x1 h6 y3b ff3 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 he y3c ff4 fs3 fc0 sc0 ls4 ws9">Para <span class="blank"> </span>resolver <span class="blank"> </span>est<span class="blank _4"></span>os <span class="blank"> </span>ejercicios <span class="blank"> </span>se <span class="blank"> </span>tendrán <span class="blank"> </span>en <span class="blank"> </span>cuent<span class="blank _4"></span>a <span class="blank"> </span>los <span class="blank"> </span>temas <span class="blank"> </span>abordad<span class="blank _4"></span>os <span class="blank"> </span>durante <span class="blank"> </span>todo <span class="blank"> </span>el <span class="blank"> </span>cuatrimest<span class="blank _4"></span>re: <span class="blank"> </span>Funciones<span class="blank _2"> </span>- </div><div class="t m0 x1 he y3d ff4 fs3 fc0 sc0 ls4 ws9">Operaciones con p<span class="blank _4"></span>olinomios- Integrales<span class="blank _4"></span> inmediatas- Integral<span class="blank _4"></span>es por sustituci<span class="blank _4"></span>ón. </div><div class="t m0 x1 he y3e ff4 fs3 fc0 sc0 ls4 ws9">Designamos: </div><div class="t m0 x1 hf y3f ff9 fs3 fc0 sc0 ls4 wsd">\ued51<span class="blank _7"> </span>\uf34c<span class="blank _7"> </span>\ued54<span class="blank"> </span>\uf345<span class="blank"> </span>\ue974<span class="ff4 lsa ws9"> </span><span class="wse">\ueb5c<span class="blank _7"> </span>\ued51<span class="blank _c"> </span>\uf346<span class="blank _c"> </span>\ue974<span class="blank _b"> </span>\uf34c<span class="blank _7"> </span>\ued54<span class="blank"> </span><span class="ff4 ws9"> </span></span></div><div class="t m0 x1 hf y40 ff4 fs3 fc0 sc0 lsa ws9"> <span class="ff9 ls1d wsf">\ued40\ued51<span class="blank"> </span><span class="lsb">\uf34c</span><span class="ws10">\ued40\ued54</span></span><span class="ls4"> </span></div><div class="t m0 x1 he y41 ff4 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 he y42 ff4 fs3 fc0 sc0 ls4 ws9">Nos queda que:<span class="blank _4"></span> </div><div class="t m0 x13 h1c y43 ff9 fs3 fc0 sc0 ls4 ws4">\uf3b1<span class="v0">\uf36b</span><span class="wse">\ued54<span class="blank"> </span>\ue7e4<span class="blank _d"> </span></span><span class="v0">\ue9be</span><span class="wsd">\ued54<span class="blank _c"> </span>\uf345<span class="blank"> </span>\ue974\ue603</span><span class="v0">\uf36f</span><span class="ls1d ws11">\ued40\ued54<span class="blank"> </span></span><span class="ws7">\uf34c<span class="blank"> </span>\uf3b1<span class="lsc v0">\uf363</span></span><span class="v7">\udb80\udddb</span><span class="wsd">\ued51<span class="blank _c"> </span>\uf346<span class="blank"> </span>\ue974</span><span class="v7">\udb80\udddc<span class="v8">\ue9be</span></span><span class="lsd">\ued51<span class="lsc v0">\uf367</span></span>\ue603<span class="ls1d ws12">\ued40\ued51<span class="blank"> </span></span><span class="ff4 ws9"> </span></div><div class="t m0 x17 he y44 ff4 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x17 h1d y45 ff4 fs3 fc0 sc0 ls4 ws9">Recordemos que <span class="blank _4"></span><span class="ff9 ws4 v6">\ue9be<span class="ws13 v9">\ued51<span class="blank _7"> </span>\uf34c<span class="blank _7"> </span>\ued51<span class="fs7 va">\uf22d</span></span></span></div><div class="t m0 x18 h1e y46 ff9 fs7 fc0 sc0 lse">\uf22e<span class="ff4 fs3 ls4 ws9 v8"> </span></div><div class="t m0 x1 he y47 ff4 fs3 fc0 sc0 ls4 ws9">Por lo tanto, aplicand<span class="blank _4"></span>o propiedad distri<span class="blank _4"></span>butiva: </div><div class="t m0 x19 h1f y48 ff9 fs3 fc0 sc0 lsf">\uf3b1<span class="ls10 v0">\uf364<span class="ls4 ws4 v7">\udb80\udddb</span></span><span class="ls4 ws14">\ued51<span class="blank _c"> </span>\uf346<span class="blank"> </span>\ue974<span class="ws4 v7">\udb80\udddc</span><span class="ws15">\ue7e4<span class="blank _d"> </span>\ued51<span class="blank"> </span><span class="fs0 va">\uf135</span></span></span></div><div class="t m0 x1a h20 y49 ff9 fs0 fc0 sc0 ls11">\uf136<span class="fs3 ls12 v8">\uf368<span class="ls4 ws4 v0">\ue603<span class="ls1d ws16">\ued40\ued51<span class="blank"> </span></span><span class="ws15">\uf34c<span class="blank _8"> </span>\ue603<span class="blank _8"> </span>\uf3b1<span class="blank _e"> </span>\uf36c\ued51<span class="fs0 va">\uf137</span></span></span></span></div><div class="t m0 x1b h20 y49 ff9 fs0 fc0 sc0 ls13">\uf136<span class="fs3 ls4 ws17 v8">\uf346<span class="blank _c"> </span>\ue974\ued51</span><span class="ls4 vb">\uf135</span></div><div class="t m0 x1c h20 y49 ff9 fs0 fc0 sc0 ls11">\uf136<span class="fs3 ls4 ws18 v8">\uf370<span class="blank"> </span>\ue603<span class="ls1d wsf">\ued40\ued51<span class="blank"> </span><span class="ls4 ws15">\uf34c<span class="blank _8"> </span>\ue603<span class="blank _8"> </span>\uf3b1<span class="blank _d"> </span>\ued51<span class="blank"> </span><span class="fs0 va">\uf137</span></span></span></span></div><div class="t m0 x1d h20 y49 ff9 fs0 fc0 sc0 ls11">\uf136<span class="fs3 ls4 ws4 v8">\ue603<span class="ls1d ws19">\ued40\ued51<span class="blank"> </span><span class="ls4 ws13">\uf346<span class="blank _c"> </span>\uf3b1<span class="blank _8"> </span>\ue974\ued51<span class="blank"> </span><span class="fs0 va">\uf135</span></span></span></span></div><div class="t m0 x1e h21 y49 ff9 fs0 fc0 sc0 ls11">\uf136<span class="fs3 ls4 ws4 v8">\ue603<span class="ls1d ws16">\ued40\ued51<span class="blank"> </span></span>\uf34c\ue603<span class="ff4 ws9"> </span></span></div><div class="t m0 x1f h22 y4a ff9 fs3 fc0 sc0 ls14">\uf34c<span class="ls4 vc">\ue974</span></div><div class="t m0 x20 h23 y4b ff9 fs3 fc0 sc0 ls15">\ue977<span class="ls4 ws15 v4">\ue603<span class="blank _6"> </span>\ued51<span class="fs0 va">\uf139</span></span></div><div class="t m0 x21 h24 y4c ff9 fs0 fc0 sc0 ls16">\uf136<span class="fs3 ls4 ws1a v8">\uf346<span class="blank _c"> </span>\ue974\ue7e4<span class="blank"> </span><span class="vc">\ue974</span></span></div><div class="t m0 x22 h23 y4b ff9 fs3 fc0 sc0 ls17">\ue975<span class="ls4 ws15 v4">\ue7e4<span class="blank _d"> </span>\ued51<span class="blank"> </span><span class="fs0 va">\uf137</span></span></div><div class="t m0 x23 h21 y4c ff9 fs0 fc0 sc0 ls13">\uf136<span class="fs3 ls4 ws1b v8">\uf345<span class="blank _c"> </span>\ued25<span class="blank"> </span><span class="ff4 ws9"> </span></span></div><div class="t m0 x17 he y4d ff4 fs3 fc0 sc0 ls4 ws9">Realizamos la sustituci<span class="blank _4"></span>ón correspondien<span class="blank _4"></span>te: </div><div class="t m0 x17 he y4e ff4 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x24 h22 y4f ff9 fs3 fc0 sc0 ls4 ws4">\uf3b1<span class="v0">\uf36b</span><span class="wse">\ued54<span class="blank"> </span>\ue7e4<span class="blank _d"> </span></span><span class="v0">\ue9be</span><span class="wsd">\ued54<span class="blank _c"> </span>\uf345<span class="blank"> </span>\ue974\ue603</span><span class="v0">\uf36f</span><span class="ls1d ws1c">\ued40\ued54<span class="blank"> </span></span><span class="ws1d">\uf34c<span class="blank"> </span>\ue603<span class="blank"> </span><span class="vc">\ue974</span></span></div><div class="t m0 x21 h23 y50 ff9 fs3 fc0 sc0 ls18">\ue977<span class="ls19 v4">\ue603</span><span class="ls4 ws4 vd">\udb80\udddb</span><span class="ls4 wsd v4">\ued54<span class="blank _c"> </span>\uf345<span class="blank"> </span>\ue974</span><span class="ls4 ws4 vd">\udb80\udddc<span class="fs0 ve">\uf139</span></span></div><div class="t m0 x25 h24 y51 ff9 fs0 fc0 sc0 ls13">\uf136<span class="fs3 ls1a v8">\uf346<span class="ls4 vc">\ue976</span></span></div><div class="t m0 x26 h23 y50 ff9 fs3 fc0 sc0 ls17">\ue975<span class="ls4 ws1a v4">\ue7e4<span class="blank"> </span>\udb80\udddb\ued54<span class="blank _c"> </span>\uf345<span class="blank _c"> </span>\ue974\udb80\udddc<span class="fs0 va">\uf137</span></span></div><div class="t m0 x27 h21 y51 ff9 fs0 fc0 sc0 ls1b">\uf136<span class="fs3 ls4 ws1b v8">\uf345<span class="blank _c"> </span>\ued25<span class="blank"> </span>\ue603<span class="ff4 ws9"> </span></span></div><div class="t m0 x1 h6 y52 ff3 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h4 y53 ff3 fs2 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h4 y54 ff3 fs2 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h25 y55 ff5 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h25 y56 ff5 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h25 y57 ff5 fs3 fc0 sc0 ls4 ws9"> <span class="blank _9"> </span> </div></div><div class="c x0 y36 wa h19"><div class="t m0 x15 he y37 ff4 fs3 fc1 sc0 ls4 ws9"><span class="fc2 sc0"> </span></div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y58 wb h26" alt="" src="https://files.passeidireto.com/e31e6a7f-4780-4e57-a859-ca766b267606/bg3.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h27 y59 ff5 fs6 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h2 y5a ff1 fs0 fc0 sc0 ls4 ws9">MATEMÁTICA (6<span class="blank _4"></span><span class="ls5 ws0">1)<span class="ff2 ls4 ws9"> Cátedra A: <span class="blank _4"></span>NUÑEZ, MY<span class="blank _4"></span>RIAM<span class="ff1"> FI<span class="blank _4"></span>NAL </span></span></span></div><div class="t m0 x1 h2 y5b ff2 fs0 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h2 y5c ff2 fs0 fc0 sc0 ls4 ws9">APELLIDO Y NOMB<span class="blank _4"></span>RE: <span class="blank _4"></span> <span class="blank _4"></span> <span class="blank _4"></span> <span class="blank _4"></span> DNI<span class="blank _4"></span>:<span class="ff1"> <span class="blank _a"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span>TEMA 4 </span></div><div class="t m0 x3 h2 y5d ff2 fs0 fc0 sc0 ls4 ws9">Hoja 3 de 4 </div><div class="t m0 x3 h2 y3a ff2 fs0 fc0 sc0 ls4 ws9"> </div><div class="t m0 x2 h2 y5e ff1 fs0 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h28 y5f ff3 fs2 fc0 sc0 ls4 ws9">3. <span class="blank _b"> </span>Dada <span class="blank _c"> </span><span class="ff9 ws1e">\uee8c\udb80\udddb<span class="blank _2"> </span>\uee9e\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank"> </span>\uee8b<span class="fs8 ws1f vf">\uf13f<span class="blank _2"> </span>\uee9e</span><span class="fs9 ls1e v4">\uf0dc</span><span class="fs8 ws1f vf">\uf13e<span class="ls37 ws20">\uf0da\uf0db\uee9e<span class="blank"> </span></span></span></span>, <span class="blank _c"> </span>determinar <span class="blank _b"> </span>los <span class="blank _b"> </span>intervalos <span class="blank _b"> </span>de <span class="blank _c"> </span>crecimiento <span class="blank _b"> </span>y <span class="blank _c"> </span>de <span class="blank _b"> </span>decrecimiento, <span class="blank _b"> </span>y <span class="blank _c"> </span>los </div><div class="t m0 x1 h4 y60 ff3 fs2 fc0 sc0 ls4 ws9">máximos y mínimos relativos. </div><div class="t m0 x1 h4 y61 ff3 fs2 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h6 y62 ff3 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h25 y63 ff5 fs3 fc0 sc0 ls4 ws9">Lo primero que necesi<span class="blank _4"></span>tamos conocer<span class="blank _4"></span> es el domin<span class="blank _4"></span>io de la función. Co<span class="blank _4"></span>mo su ex<span class="blank _4"></span>presión no presenta<span class="blank _4"></span> ninguna </div><div class="t m0 x1 h1c y64 ff5 fs3 fc0 sc0 ls4 ws9">restricción, el domini<span class="blank _4"></span>o es <span class="ff9 ws4">\ued26\ued4b\ued49<span class="ls1f v7">\udb80\udddb</span><span class="ls20">\ued42<span class="ls21 v7">\udb80\udddc</span></span><span class="ws7">\uf34c<span class="blank"> </span>\ueb39</span></span>. </div><div class="t m0 x1 h25 y65 ff5 fs3 fc0 sc0 ls4 ws9">Para hallar los<span class="blank _4"></span> intervalos de creci<span class="blank _4"></span>miento y de dec<span class="blank _4"></span>recimiento, analizamos e<span class="blank _4"></span>l signo de la de<span class="blank _4"></span>rivada. </div><div class="t m0 x1 h29 y66 ff9 fs3 fc0 sc0 ls22">\ued42<span class="fs0 ls23 v10">\udb80\udd92</span><span class="ls4 ws4 v7">\udb80\udddb</span><span class="ls24">\ued54<span class="ls25 v7">\udb80\udddc</span><span class="ls4 ws21">\uf34c<span class="blank _8"> </span>\ue603<span class="blank _8"> </span>\ued41<span class="blank"> </span><span class="fs0 ws22 v10">\uf13f\uf1eb<span class="blank"> </span></span><span class="fs7 lse v11">\uf22f</span><span class="fs0 ls26 v10">\uf13e<span class="ls38 ws23">\uf135\uf136<span class="blank _2"> </span><span class="ls27">\uf1eb</span></span></span><span class="ff5 ws9">. (-3</span><span class="ls28">\ued54<span class="fs0 ls1b v10">\uf136</span><span class="ls1a">\uf345<span class="ls3">\ue973\ue974</span></span></span><span class="ff5 ws9">). Notamos <span class="blank _4"></span>que para hall<span class="blank _4"></span>ar la derivad<span class="blank _4"></span>a aplicamos la regla de<span class="blank _4"></span> la cadena por t<span class="blank _4"></span>ratarse </span></span></span></div><div class="t m0 x1 h25 y67 ff5 fs3 fc0 sc0 ls4 ws9">de una función co<span class="blank _4"></span>mpuesta, y<span class="blank _4"></span> que el dominio de esta coincide<span class="blank _4"></span> con el domi<span class="blank _4"></span>nio de la funci<span class="blank _4"></span>ón original. Utili<span class="blank _4"></span>zamos </div><div class="t m0 x1 hf y68 ff5 fs3 fc0 sc0 ls4 ws9">ahora el teorema d<span class="blank _4"></span>e Bolz<span class="blank _4"></span>ano aplicado a <span class="ff9 ws4">\ued42\ueb22</span> para sa<span class="blank _4"></span>ber cómo varí<span class="blank _4"></span>a su signo en su dominio.<span class="blank _4"></span> </div><div class="t m0 x1 hf y69 ff5 fs3 fc0 sc0 ls4 ws9">Calculamos el con<span class="blank _4"></span>junto de ceros<span class="blank _4"></span> de <span class="ff9 ws4">\ued42\ueb22</span>: </div><div class="t m0 x1 h29 y6a ff9 fs3 fc0 sc0 ls29">\ued41<span class="fs0 ls4 ws22 v10">\uf13f\uf1eb<span class="blank"> </span></span><span class="fs7 lse v11">\uf22f</span><span class="fs0 ls2a v10">\uf13e<span class="ls38 ws23">\uf135\uf136<span class="ls2b">\uf1eb</span></span></span><span class="ls4 ws24">\ue7e4<span class="blank _d"> </span>\udb80\udddb\uf346\ue975\ued54<span class="blank"> </span><span class="fs0 ls1b v10">\uf136</span><span class="ls1a">\uf345<span class="ls3">\ue973\ue974</span></span><span class="ws25">\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank"> </span>\ue972<span class="ff5 ws9"> </span></span></span></div><div class="t m0 x1 h25 y6b ff5 fs3 fc0 sc0 ls4 ws9">Como la exponenci<span class="blank _4"></span>al siempre toma v<span class="blank _4"></span>alores positiv<span class="blank _4"></span>os, la ecuación anterior <span class="blank _4"></span>es equival<span class="blank _4"></span>ente a </div><div class="t m0 x1 h2a y6c ff9 fs3 fc0 sc0 ls4 ws24">\uf346\ue975\ued54<span class="blank"> </span><span class="fs0 ls2c v10">\uf136</span><span class="ls1a">\uf345<span class="ls3 ws26">\ue973\ue974<span class="blank"> </span></span></span><span class="ws27">\uf34c<span class="blank"> </span>\ue972<span class="ff5 ws9"> </span></span></div><div class="t m0 x1 h2a y6d ff9 fs3 fc0 sc0 ls4 ws24">\uf346\ued54<span class="blank"> </span><span class="fs0 ls1b v10">\uf136</span><span class="ws28">\uf345<span class="blank"> </span>\ue976<span class="blank _b"> </span>\uf34c<span class="blank _7"> </span>\ue972<span class="ff5 ws9"> </span></span></div><div class="t m0 x1 hf y6e ff9 fs3 fc0 sc0 ls4 ws4">\udb80\udddb<span class="ws29 v6">\ue974<span class="blank _c"> </span>\uf346<span class="blank _c"> </span>\ued54</span>\udb80\udddc<span class="ls2d v6">\ue7e4</span>\udb80\udddb<span class="ws2a v6">\ue974<span class="blank _c"> </span>\uf345<span class="blank _c"> </span>\ued54<span class="blank"> </span></span><span class="ls21">\udb80\udddc</span><span class="ws7 v6">\uf34c<span class="blank"> </span>\ue972<span class="ff5 ws9"> </span></span></div><div class="t m0 x1 hf y6f ff9 fs3 fc0 sc0 ls4 ws7">\ued54<span class="blank _7"> </span>\uf34c<span class="blank"> </span>\ue603\ue974<span class="ff5 ls39 ws9">, </span><span class="ws1d">\ued54<span class="blank _7"> </span>\uf34c<span class="blank"> </span>\ue603<span class="blank"> </span>\uf346<span class="blank _2"> </span>\ue974<span class="ff5 ws9"> </span></span></div><div class="t m0 x1 hf y70 ff5 fs3 fc0 sc0 ls4 ws9">Luego, el conjun<span class="blank _4"></span>to de ceros de<span class="blank _4"></span> la derivada es<span class="blank _4"></span> <span class="ff9">\ued25</span></div><div class="t m0 x28 h2b y71 ff9 fs0 fc0 sc0 ls11">\uf134<span class="fs3 ls4 ws4 v12">\udb80\udddb<span class="ls2e v6">\ued42</span></span><span class="ls23 v13">\udb80\udd92</span><span class="fs3 ls2f v12">\udb80\udddc<span class="ls2 v6">\uf34c<span class="ls30 v7">\udb80\udddd</span><span class="ls4 ws2b">\uf346\ue974\ue7e2<span class="blank"> </span>\ue974<span class="ls30 v7">\udb80\uddde</span><span class="ws4">\ue7e4<span class="ff5 ws9"> </span></span></span></span></span></div><div class="t m0 x1 h1c y72 ff5 fs3 fc0 sc0 ls4 ws9">Evalua<span class="blank _4"></span>mos <span class="ff9 ws4">\ued42\ueb22</span> en algún punto del conjun<span class="blank _4"></span>to <span class="ff9 ws4 v7">\udb80\udddb</span><span class="ff9 ws2c">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346\ue974<span class="ws4 v7">\udb80\udddc</span></span> para v<span class="blank _4"></span>er su signo: </div><div class="t m0 x1 h1c y73 ff9 fs3 fc0 sc0 ls22">\ued42<span class="fs0 ls23 v10">\udb80\udd92</span><span class="ls4 ws4 v7">\udb80\udddb<span class="v6">\uf346\ue975</span><span class="ls2f">\udb80\udddc</span></span><span class="ls4 ws21">\uf34c<span class="blank _b"> </span>\ued41<span class="blank"> </span></span><span class="fs0 ls3a ws2d v10">\uf136\uf13b<span class="ls4 ws2e">\uf13f<span class="ls3a ws2f">\uf137\uf13a<span class="blank"> </span></span></span></span><span class="ls31">\ue7e4<span class="ls4 ws4 v7">\udb80\udddb</span><span class="ls4 ws30">\uf346\ue975\ue7e4\ue97b<span class="blank"> </span>\uf345<span class="blank"> </span><span class="ls3">\ue973\ue974<span class="ls21 v7">\udb80\udddc</span></span><span class="ws31">\uf34f<span class="blank"> </span>\ue972<span class="ff5 ws9">, luego, </span><span class="ws4">\ued42\ueb22<span class="ff5 ws9"> es nega<span class="blank _4"></span>tiva en <span class="ff9 ws4 v7">\udb80\udddb</span><span class="ff9 ws2c">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346\ue974<span class="ws4 v7">\udb80\udddc<span class="blank _4"></span><span class="ff5 ws9 v6">. </span></span></span></span></span></span></span></span></div><div class="t m0 x1 h1c y74 ff5 fs3 fc0 sc0 ls4 ws9">Análogamente, en el<span class="blank _4"></span> interval<span class="blank _4"></span>o <span class="ff9 ws4 v7">\udb80\udddb</span><span class="ff9 ws2c">\uf346\ue974\ue7e2<span class="blank"> </span>\ue974<span class="ws4 v7">\udb80\udddc<span class="v6">\ue7e3</span></span></span> </div><div class="t m0 x1 h1c y75 ff9 fs3 fc0 sc0 ls22">\ued42<span class="fs0 ls23 v10">\udb80\udd92</span><span class="ls4 ws4 v7">\udb80\udddb<span class="v6">\ue972</span><span class="ls25">\udb80\udddc</span></span><span class="ls4 ws21">\uf34c<span class="blank _b"> </span>\ued41<span class="blank"> </span><span class="fs0 ls11 v10">\uf134</span><span class="ls31">\ue7e4</span><span class="ws4 v7">\udb80\udddb</span><span class="ws32">\ue972<span class="blank"> </span>\uf345<span class="blank"> </span><span class="ls3">\ue973\ue974<span class="ls21 v7">\udb80\udddc</span><span class="ls32">\uf34c</span><span class="ws26">\ue973\ue974<span class="blank"> </span></span></span><span class="ws33">\uf350<span class="blank"> </span>\ue972<span class="ff5 ws9">, por lo que </span><span class="ws4">\ued42\ueb22<span class="ff5 ws9"> es positiv<span class="blank _4"></span>a en <span class="ff9 ws4 v7">\udb80\udddb</span><span class="ff9 ws2c">\uf346\ue974\ue7e2<span class="blank"> </span>\ue974<span class="ws4 v7">\udb80\udddc</span></span>. </span></span></span></span></span></div><div class="t m0 x1 h1c y76 ff5 fs3 fc0 sc0 ls4 ws9">En <span class="ff9 ws4 v7">\udb80\udddb</span><span class="ff9 ws2c">\ue974\ue7e2<span class="blank"> </span>\uf345\ue9bb<span class="ws4 v7">\udb80\udddc</span></span> la deriv<span class="blank _4"></span>ada es nuevamente<span class="blank _4"></span> negativa ya que<span class="blank _4"></span>, por ejemplo, </div><div class="t m0 x1 h1c y77 ff9 fs3 fc0 sc0 ls22">\ued42<span class="fs0 ls23 v10">\udb80\udd92</span><span class="ls4 ws4 v7">\udb80\udddb<span class="v6">\ue975</span><span class="ls25">\udb80\udddc</span></span><span class="ls4 ws21">\uf34c<span class="blank _b"> </span>\ued41<span class="blank"> </span><span class="fs0 ls33 v10">\uf13f<span class="ls38 ws23">\uf136\uf13b<span class="ls4 ws2e">\uf13e<span class="ls3a ws2f">\uf137\uf13a<span class="blank"> </span></span></span></span></span><span class="ls31">\ue7e4</span><span class="ws4 v7">\udb80\udddb</span><span class="ws30">\uf346\ue975\ue7e4\ue97b<span class="blank"> </span>\uf345<span class="blank"> </span><span class="ls3">\ue973\ue974<span class="ls21 v7">\udb80\udddc</span></span><span class="ws31">\uf34f<span class="blank"> </span>\ue972<span class="ff5 ws9">. </span></span></span></span></div><div class="t m0 x1 h1c y78 ff5 fs3 fc0 sc0 ls4 ws9">De esta forma<span class="blank _4"></span>, por el criterio<span class="blank _4"></span> de la derivad<span class="blank _4"></span>a el intervalo de crecimien<span class="blank _4"></span>to de la función <span class="ff9 ls34">\ued42</span> es <span class="ff9 ws4 v7">\udb80\udddb</span><span class="ff9 ws2b">\uf346\ue974\ue7e2<span class="blank"> </span>\ue974<span class="ls35 v7">\udb80\udddc</span></span><span class="ls2a"> <span class="ls3b">y </span></span>los interv<span class="blank _4"></span>alos </div><div class="t m0 x1 h1c y79 ff5 fs3 fc0 sc0 ls4 ws9">de decrecimiento son<span class="blank _4"></span> <span class="ff9 ws4 v7">\udb80\udddb</span><span class="ff9 ws2c">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346\ue974<span class="ws4 v7">\udb80\udddc</span></span><span class="ls2a"> <span class="ls3b">y </span></span><span class="ff9 ws4 v7">\udb80\udddb</span><span class="ff9 ws2c">\ue974\ue7e2<span class="blank"> </span>\uf345\ue9bb<span class="ws4 v7">\udb80\udddc</span><span class="ls36">\ue7e4</span></span> Además, co<span class="blank _4"></span>mo la funció<span class="blank _4"></span>n decrece a la iz<span class="blank _4"></span>quierda de -2 y crece a su<span class="blank _4"></span> </div><div class="t m0 x1 hf y7a ff5 fs3 fc0 sc0 ls4 ws9">derecha, entonces <span class="blank _4"></span><span class="ff9 ws7">\ued54<span class="blank _7"> </span>\uf34c<span class="blank"> </span>\uf346\ue974<span class="ff5 ws9"> es un mínimo relativo; y<span class="blank _4"></span> como <span class="ff9 ls34">\ued42</span> crece a l<span class="blank _4"></span>a izquierda d<span class="blank _4"></span>e 2 y decrece a<span class="blank _4"></span> su derecha, la </span></span></div><div class="t m0 x1 hf y7b ff5 fs3 fc0 sc0 ls4 ws9">abscisa <span class="ff9 ws7">\ued54<span class="blank"> </span>\uf34c<span class="blank"> </span>\ue974</span> es un máximo relativ<span class="blank _4"></span>o. </div><div class="t m0 x1 h6 y7c ff3 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h2c y7d ffa fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h4 y7e ff3 fs2 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h6 y7f ff3 fs3 fc0 sc0 ls4 ws9"> <span class="blank _9"> </span> </div></div><div class="c x0 y80 wa h2d"><div class="t m0 x15 he y37 ff4 fs3 fc1 sc0 ls4 ws9"><span class="fc2 sc0"> </span></div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y81 wb h2e" alt="" src="https://files.passeidireto.com/e31e6a7f-4780-4e57-a859-ca766b267606/bg4.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls4 ws9">MATEMÁTICA (6<span class="ls5 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls6"> <span class="ls7"> </span></span>FINAL </div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 ls4 ws9">APELLIDO Y NOMB<span class="blank _4"></span>RE: <span class="blank _4"></span> <span class="blank _4"></span> <span class="blank _4"></span> <span class="blank _4"></span> D<span class="blank _4"></span>NI:<span class="ff1"> <span class="blank _a"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span>TEMA 4 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 ls4 ws9">Hoja 4 de 4 </div><div class="t m0 x3 h2 y39 ff2 fs0 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 he y82 ff4 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h1c y83 ff3 fs2 fc0 sc0 ls8">4<span class="ls3c ws9">. <span class="fs3 ls4">Determinar e<span class="blank _4"></span>l/los valores<span class="blank _4"></span> de <span class="ff9 ws34">\uee91<span class="blank"> </span>\uebd0<span class="blank"> </span>\uee7e</span> para que e<span class="blank _4"></span>l <span class="ff9 ws4 v7">\ue801</span><span class="ff9 ls3d">\uee6d<span class="ls3e v7">\ue801</span><span class="ls1a">\uf345<span class="ls4 ws4 v7">\ue801</span><span class="ls3f">\uee6e<span class="ls40 v7">\ue801</span><span class="ls32">\uf34c<span class="ls48 ws35">\uf0da\uf0d9</span></span></span></span></span> s<span class="blank _4"></span>i se sabe que </span></span></div><div class="t m0 x17 h6 y84 ff3 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x17 h2f y85 ff3 fs3 fc0 sc0 ls4 ws9"> <span class="ff9 ws7">\uee6d<span class="blank"> </span>\uf34c<span class="blank"> </span>\udb80\udde1<span class="blank _f"> </span><span class="ws36 v14">\uf0da<span class="blank"> </span>\uf0dc</span></span></div><div class="t m0 x29 h30 y86 ff9 fs3 fc0 sc0 ls4 ws37">\uf346\uee91<span class="blank"> </span><span class="ls48 ws35">\uf0db\uee91</span><span class="ws4 v11">\udb80\udde2<span class="ff3 ls39 ws9"> <span class="ls4">y<span class="blank _4"></span> <span class="ff9 ws38">\uee6e<span class="blank"> </span>\uf34c<span class="blank"> </span>\udb80\udde1<span class="blank _f"> </span><span class="ws39 v14">\uee91<span class="blank"> </span>\uf346\uf0da</span></span></span></span></span></div><div class="t m0 x11 h24 y87 ff9 fs3 fc0 sc0 ls4 ws3a">\uf346\uf0dd<span class="blank _10"> </span>\uee91<span class="blank"> </span><span class="ws4 v11">\udb80\udde2<span class="ff3 ws9"> </span></span></div><div class="t m0 x1 h4 y88 ff3 fs2 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h4 y89 ff3 fs2 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h1c y8a ff5 fs3 fc0 sc0 ls4 ws9">Hallamos <span class="ff9 ws4 v7">\ue801</span><span class="ff9 ls41">\ued23<span class="ls42 v7">\ue801</span><span class="ls4 ws3b">\uf34c<span class="blank _b"> </span>\ue974\ued47<span class="blank _b"> </span>\uf345<span class="blank _c"> </span>\ue975\ued47\ue7e1<span class="blank _d"> </span><span class="ws4 v7">\ue801</span><span class="ls43">\ued24<span class="ls44 v7">\ue801</span></span><span class="ws3c">\uf34c<span class="blank _7"> </span>\ued47<span class="blank"> </span><span class="fs0 ls1b v10">\uf136</span><span class="wsd">\uf346<span class="blank"> </span>\ue976</span></span></span></span> </div><div class="t m0 x2a hf y8b ff9 fs3 fc0 sc0 ls4 ws4">\ue801<span class="ls41 v6">\ued23</span><span class="ls45">\ue801<span class="ls1a v6">\uf345</span><span class="ls46">\ue801<span class="ls43 v6">\ued24</span><span class="ls44">\ue801<span class="ls32 v6">\uf34c<span class="ls3">\ue973\ue972<span class="ff5 ls4 ws9"> </span></span></span></span></span></span></div><div class="t m0 x2b h2a y8c ff9 fs3 fc0 sc0 ls4 ws3d">\ue974\ued47<span class="blank"> </span>\uf345<span class="blank"> </span>\ue975\ued47<span class="blank"> </span>\uf345<span class="blank _e"> </span>\ued47<span class="blank _5"> </span><span class="fs0 ls1b v10">\uf136</span><span class="wsd">\uf346<span class="blank"> </span>\ue976<span class="blank _7"> </span>\uf34c<span class="blank _b"> </span><span class="ls3">\ue973\ue972</span><span class="ff5 ws9"> </span></span></div><div class="t m0 x28 h31 y8d ff9 fs3 fc0 sc0 ls47">\ued47<span class="fs0 ls1b v10">\uf136</span><span class="ls4 wsd">\uf345<span class="blank"> </span>\ue977\ued47<span class="blank _c"> </span>\uf346<span class="blank"> </span></span><span class="ls3 ws26">\ue973\ue976<span class="blank"> </span></span><span class="ls4 ws7">\uf34c<span class="blank"> </span>\ue972<span class="ff5 ws9"> </span></span></div><div class="t m0 x1f hf y8e ff9 fs3 fc3 sc0 ls4 ws7">\ued47<span class="blank _7"> </span>\uf34c<span class="blank"> </span>\ue974\ue7e1<span class="blank _e"> </span>\ued47<span class="blank"> </span>\uf34c<span class="blank"> </span>\uf346<span class="blank _2"> </span>\ue979<span class="ff5 ws9"> </span></div><div class="t m0 x17 h25 y8f ff5 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h6 y90 ff3 fs3 fc0 sc0 ls4 ws9">Referencia: Un<span class="blank _4"></span>idad 9: Sistema<span class="blank _4"></span> de ecuaciones<span class="blank _4"></span> y matrices </div><div class="t m0 x1 h25 y91 ff5 fs3 fc3 sc0 ls4 ws9"> </div><div class="t m0 x1 h25 y92 ff5 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h4 y93 ff3 fs2 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h4 y94 ff3 fs2 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h4 y95 ff3 fs2 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h6 y96 ff3 fs3 fc0 sc0 ls4 ws9"> </div><div class="t m0 x1 h2c y97 ffa fs3 fc0 sc0 ls4 ws9"> </div></div><div class="c x0 y36 wa h19"><div class="t m0 x15 he y37 ff4 fs3 fc1 sc0 ls4 ws9"><span class="fc2 sc0"> </span></div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div>
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