<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/24520f46-6f07-474d-a495-058b31d7b02f/bg1.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls11 ws19">MATEMÁTICA (6<span class="ls12 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM </span></div><div class="t m0 x1 h2 y3 ff1 fs0 fc0 sc0 ls11 ws19">FINAL </div><div class="t m0 x2 h2 y4 ff1 fs0 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h2 y5 ff2 fs0 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h3 y6 ff2 fs1 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h2 y7 ff2 fs0 fc0 sc0 ls11 ws1">12/07/2023<span class="ff1 ws19"> <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 1 </span></div><div class="t m0 x3 h2 y8 ff2 fs0 fc0 sc0 ls11 ws19"> Hoja 1 de 4 </div><div class="t m0 x3 h2 y9 ff2 fs0 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h3 ya ff2 fs1 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h3 yb ff2 fs1 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h4 yc ff3 fs2 fc0 sc0 ls11 ws19">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 ls11 ws19"> </div></div><div class="c x6 yd w4 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls11 ws19">1 </div></div><div class="c x8 yd w5 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls11 ws19">2 </div></div><div class="c x9 yd w6 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls11 ws19">3 </div></div><div class="c xa yd w7 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls11 ws19">4 </div></div><div class="c x4 yf w3 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls11 ws19"> </div></div><div class="c x6 yf w4 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls11 ws19"> </div></div><div class="c x8 yf w5 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls11 ws19"> </div></div><div class="c x9 yf w6 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls11 ws19"> </div></div><div class="c xa yf w7 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls11 ws19"> </div></div><div class="c x4 y11 w5 h9"><div class="t m0 xb ha y12 ff4 fs4 fc0 sc0 ls11 ws19">Puntaje de cada </div><div class="t m0 xb ha y13 ff4 fs4 fc0 sc0 ls11 ws19">ejercicio </div></div><div class="c x6 y11 w4 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls11 ws19">2,50 </div></div><div class="c x8 y11 w5 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls11 ws19">2,50 </div></div><div class="c x9 y11 w6 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls11 ws19">2,50 </div></div><div class="c xa y11 w7 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls11 ws19">2,50 </div></div><div class="c x0 y1 w2 h0"><div class="t m0 x1 hb y15 ff5 fs5 fc0 sc0 ls11 ws19">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 ls11 ws19">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 ls11 ws19"> </div><div class="t m0 x1 he y18 ff3 fs2 fc0 sc0 ls11 ws19">1. Calcular la siguiente integral<span class="ff7 ws3 v1">\uebec</span><span class="ff7 ws4">\uf36b\uee9e\ue7e4<span class="blank"> </span><span class="ls0 v0">\ue9be<span class="v0">\uee9e<span class="fs7 ls1 v2">\uf0db</span></span></span><span class="ws5">\uf345<span class="blank _3"> </span>\uf0de\uf36f<span class="blank"> </span><span class="ls13 ws6">\uee8a\uee9e</span></span></span> </div><div class="t m0 x1 h6 y19 ff3 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 hf y1a ff4 fs3 fc0 sc0 ls11 ws19">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>cuen<span class="blank _4"></span>ta <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>cuatrim<span class="blank _4"></span>estre: <span class="blank"> </span>Funciones- </div><div class="t m0 x1 hf y1b ff4 fs3 fc0 sc0 ls11 ws19">Operaciones con p<span class="blank _4"></span>olinomios- Integrales<span class="blank _4"></span> inmediatas- In<span class="blank _4"></span>tegrales por sus<span class="blank _4"></span>titución. </div><div class="t m0 xf h10 y1c ff4 fs3 fc0 sc0 ls11 ws19">Designamos a: <span class="blank _4"></span><span class="ff7 ws7">\ued50<span class="blank"> </span>\uf34c<span class="blank"> </span>\uee9e<span class="fs0 ls2 v3">\uf0db</span><span class="ws8">\uf345<span class="blank"> </span>\uf0de<span class="ff8 ls3 ws19"> <span class="ff4 ls11">y luego derivamos la expresi<span class="blank _4"></span>ón<span class="ff8">: </span></span></span></span></span></div><div class="t m0 x10 h11 y1d ff7 fs3 fc0 sc0 ls14 ws9">\ued40\ued50<span class="blank"> </span><span class="ls11 wsa">\uf34c<span class="blank _5"> </span>\ue974\ued54<span class="blank"> </span>\ue603</span><span class="wsb">\ued40\ued54<span class="blank"> </span><span class="ff4 ls11 ws19"> </span></span></div><div class="t m0 x11 h11 y1e ff7 fs3 fc0 sc0 ls14">\ued40\ued50</div><div class="t m0 x12 h12 y1f ff7 fs3 fc0 sc0 ls4">\ue974<span class="ls11 wsc v4">\uf34c<span class="blank _5"> </span>\ued54<span class="blank"> </span>\ue603</span><span class="ls14 wsd v4">\ued40\ued54<span class="blank"> </span></span><span class="ff4 ls11 ws19 v4"> </span></div><div class="t m0 xf h13 y20 ff8 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 xf hf y21 ff4 fs3 fc0 sc0 ls11 ws19">Vemos que: </div><div class="t m0 x13 h14 y22 ff7 fs3 fc0 sc0 ls11 wsc">\uf3b1<span class="blank _6"> </span>\ued54<span class="blank"> </span>\ue7e4<span class="blank _6"> </span><span class="wse v5">\uf3a5</span><span class="ls5">\ued54<span class="fs0 ls6 v2">\uf136</span></span><span class="ws8">\uf345<span class="blank"> </span>\ue977\ue603<span class="ls14 wsf">\ued40\ued54<span class="blank"> </span></span><span class="ws10">\uf34c<span class="blank _5"> </span>\uf3b1<span class="blank"> </span><span class="wse v1">\ue9be</span><span class="ws11">\ued50<span class="blank _7"> </span>\ue603<span class="blank"> </span><span class="ls14 v6">\ued40\ued50</span></span></span></span></div><div class="t m0 x14 h15 y23 ff7 fs3 fc0 sc0 ls7">\ue974<span class="ff4 ls11 ws19 v4"> </span></div><div class="t m0 x15 h14 y24 ff7 fs3 fc0 sc0 ls11 wsa">\uf3b1<span class="blank _6"> </span>\ued54<span class="blank"> </span>\ue7e4<span class="blank _6"> </span><span class="wse v5">\uf3a5</span><span class="ls5">\ued54<span class="fs0 ls8 v2">\uf136</span></span><span class="ws12">\uf345<span class="blank"> </span>\ue977\ue603<span class="ls14 wsf">\ued40\ued54<span class="blank"> </span><span class="ls9">\uf34c</span></span><span class="v6">\ue973</span></span></div><div class="t m0 x16 h16 y25 ff7 fs3 fc0 sc0 lsa">\ue974<span class="ls11 ws13 v4">\uf3b1<span class="blank _6"> </span>\ued50<span class="blank"> </span></span><span class="fs0 ls11 ws14 v7">\uf135\ue800\uf136<span class="blank"> </span></span><span class="ls11 wse v4">\ue603</span><span class="ls14 ws15 v4">\ued40\ued50</span><span class="ff4 ls11 ws19 v4"> </span></div><div class="t m0 x17 h14 y26 ff7 fs3 fc0 sc0 ls11 wsa">\uf3b1<span class="blank _6"> </span>\ued54\ue7e4<span class="blank _8"> </span><span class="lsb v5">\uf3a5</span><span class="ls5">\ued54<span class="fs0 lsc v2">\uf136</span></span><span class="ws12">\uf345<span class="blank"> </span>\ue977\ue603<span class="ls14 wsf">\ued40\ued54<span class="blank"> </span><span class="ls9">\uf34c</span></span><span class="v6">\ue973</span></span></div><div class="t m0 x18 h17 y27 ff7 fs3 fc0 sc0 lsa">\ue974<span class="lsd v4">\ue7e4</span><span class="lse v8">\ued50</span><span class="fs0 ls11 ws16 v9">\uf137\ue800\uf136</span></div><div class="t m0 x19 h11 y28 ff7 fs3 fc0 sc0 ls11">\ue975</div><div class="t m0 x19 h18 y29 ff7 fs3 fc0 sc0 lsf">\ue974<span class="ls11 ws17 va">\uf345<span class="blank _9"> </span>\ued25<span class="blank"> </span><span class="ff4 ws19"> </span></span></div><div class="t m0 xf hf y2a ff4 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 hf y2b ff4 fs3 fc0 sc0 ls11 ws19">Volvemos a realizar la<span class="blank _4"></span> sustitución c<span class="blank _4"></span>orrespondient<span class="blank _4"></span>e y nos queda<span class="blank _4"></span>: </div><div class="t m0 x1a h14 y2c ff7 fs3 fc0 sc0 ls11 wsc">\uf3b1<span class="blank _6"> </span>\ued54<span class="blank"> </span>\ue7e4<span class="blank _6"> </span><span class="wse v5">\uf3a5</span><span class="ls5">\ued54<span class="fs0 lsc v2">\uf136</span></span><span class="ws8">\uf345<span class="blank"> </span>\ue977\ue603<span class="ls14 ws18">\ued40\ued54<span class="blank"> </span><span class="ls9">\uf34c</span></span><span class="v6">\ue973</span></span></div><div class="t m0 x1b h19 y2d ff7 fs3 fc0 sc0 lsa">\ue974<span class="ls10 v4">\ue7e4</span><span class="ls11 v8">\ue974</span></div><div class="t m0 x1c h1a y2d ff7 fs3 fc0 sc0 lsa">\ue975<span class="ls11 wse vb">\udb80\udddb</span><span class="ls5 v4">\ued54</span><span class="fs0 ls8 v7">\uf136</span><span class="ls11 ws8 v4">\uf345<span class="blank"> </span>\ue977</span><span class="ls11 wse vb">\udb80\udddc<span class="fs0 vc">\uf137</span></span></div><div class="t m0 x1d h1b y2e ff7 fs0 fc0 sc0 lsc">\uf136<span class="fs3 ls11 ws17 vd">\uf345<span class="blank _9"> </span>\ued25<span class="blank"> </span><span class="ff4 ws19"> </span></span></div><div class="t m0 x1 hf y2f ff4 fs3 fc0 sc0 ls11 ws19">Por lo tanto: </div><div class="t m0 x1e h14 y30 ff7 fs3 fc0 sc0 ls11 wsc">\uf3b1<span class="blank _6"> </span>\ued54<span class="blank"> </span>\ue7e4<span class="blank _6"> </span><span class="wse v5">\uf3a5</span><span class="ls5">\ued54<span class="fs0 lsc v2">\uf136</span></span><span class="ws8">\uf345<span class="blank"> </span>\ue977\ue603<span class="ls14 wsf">\ued40\ued54<span class="blank"> </span><span class="ls9">\uf34c</span></span><span class="v6">\ue973</span></span></div><div class="t m0 x1f h1a y31 ff7 fs3 fc0 sc0 lsa">\ue975<span class="ls10 v4">\ue7e4</span><span class="ls11 wse vb">\udb80\udddb</span><span class="ls5 v4">\ued54</span><span class="fs0 ls8 v7">\uf136</span><span class="ls11 ws8 v4">\uf345<span class="blank"> </span>\ue977</span><span class="ls11 wse vb">\udb80\udddc<span class="fs0 vc">\uf137</span></span></div><div class="t m0 x20 h1b y32 ff7 fs0 fc0 sc0 lsc">\uf136<span class="fs3 ls11 ws17 vd">\uf345<span class="blank _9"> </span>\ued25<span class="blank"> </span><span class="ff5 ws19"> </span></span></div><div class="t m0 x1 h6 y33 ff3 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h1c y34 ff5 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h1c y35 ff5 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h1c y36 ff5 fs3 fc0 sc0 ls11 ws19"> <span class="blank _a"> </span> </div></div><div class="c x1 y37 w8 h1d"><div class="t m0 x21 h2 y38 ff2 fs0 fc0 sc0 ls11 ws19">APELLIDO: </div></div><div class="c x22 y39 w9 h1e"><div class="t m0 xb h2 y3a ff2 fs0 fc0 sc0 ls11 ws19">CALIFICACIÓN:<span class="blank _4"></span> </div></div><div class="c x1 y3b w8 h1f"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls11 ws19">NOMBRE: </div></div><div class="c x1 y39 w8 h1f"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls11 ws19">DNI (registrado en S<span class="blank _4"></span>IU Guaran<span class="blank _4"></span>í): </div></div><div class="c x1 y3c w8 h20"><div class="t m0 xb h2 y10 ff2 fs0 fc0 sc0 ls11 ws19">E-MAIL: </div></div><div class="c x22 y3d w9 h21"><div class="t m0 xb h2 y3e ff2 fs0 fc0 sc0 ls11 ws19">DOCENTE (nombre<span class="blank _4"></span> y apelli<span class="blank _4"></span>do): </div></div><div class="c x1 y3f w8 h1f"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls11 ws19">TEL: </div></div><div class="c x1 y3d w8 h1f"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls11 ws19">AULA: </div></div><div class="c x0 y40 wa h22"><div class="t m0 x21 hf y41 ff4 fs3 fc1 sc0 ls11 ws19"><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 y42 wb h23" alt="" src="https://files.passeidireto.com/24520f46-6f07-474d-a495-058b31d7b02f/bg2.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls11 ws19">MATEMÁTICA (6<span class="ls12 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls15"> <span class="ls16"> </span></span> FINAL </div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 ls11 ws19">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> <span class="blank _4"></span> DNI<span class="blank _4"></span>:<span class="ff1"> <span class="blank _b"> </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 1 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 ls11 ws19">Hoja 2 de 4 </div><div class="t m0 x3 h2 y43 ff2 fs0 fc0 sc0 ls11 ws19"> </div><div class="t m0 x2 h2 y44 ff1 fs0 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h24 y45 ff3 fs2 fc0 sc0 ls11 ws19">2. <span class="fs3">Encontrar el/los<span class="blank _4"></span> valores de <span class="ff7 ws1a">\uee91<span class="blank"> </span>\uebd0<span class="blank"> </span>\uee7e<span class="blank _4"></span><span class="ff3 ws19"> para que e<span class="blank _4"></span>l <span class="ff7 wse ve">\ue801</span><span class="ff7 ls17">\uee6d<span class="ls18 ve">\ue801</span><span class="ls11 ws1b">\uf34c<span class="blank"> </span>\uf0e0</span></span> si <span class="ff7 ws1c">\uee6d<span class="blank"> </span>\uf34c<span class="blank"> </span>\udb80\udde1<span class="ws1d vf">\uee91<span class="blank"> </span>\uf0dc</span></span></span></span></span></div><div class="t m0 x23 h25 y46 ff7 fs3 fc0 sc0 ls11 ws8">\uf0da<span class="blank _c"> </span>\uee91<span class="blank"> </span>\uf345<span class="blank"> </span>\uf0dc<span class="wse v10">\udb80\udde2<span class="ff3 ws19"> </span></span></div><div class="t m0 x1 h26 y47 ff8 fs2 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h4 y48 ff3 fs2 fc0 sc0 ls11 ws19"> </div><div class="t m0 xf h27 y49 ff5 fs3 fc0 sc0 ls11 ws19">Hallamos el dete<span class="blank _4"></span>rminant<span class="blank _4"></span>e de <span class="ff7 ws1e">\ued23<span class="blank _5"> </span>\uf34c<span class="blank _5"> </span>\ued47<span class="blank"> </span><span class="wse ve">\udb80\udddb</span><span class="ws1f">\ued47<span class="blank _3"> </span>\uf345<span class="blank"> </span>\ue975<span class="ls19 ve">\udb80\udddc</span><span class="ws20">\uf346<span class="blank _9"> </span>\ue975<span class="blank _5"> </span>\uf34c<span class="blank _5"> </span>\ued47<span class="blank"> </span><span class="fs0 ls1a v3">\uf136</span><span class="ws8">\uf345<span class="blank"> </span>\ue975\ued47<span class="blank _5"> </span>\uf346<span class="blank"> </span>\ue975</span></span></span></span> </div><div class="t m0 x24 h10 y4a ff7 fs3 fc0 sc0 ls11 ws20">\udb80\udddb\ued47<span class="blank"> </span><span class="fs0 lsc v3">\uf136</span><span class="ws8">\uf345<span class="blank"> </span>\ue975\ued47<span class="blank"> </span>\uf346<span class="blank"> </span>\ue975<span class="blank _5"> </span>\uf34c<span class="blank _5"> </span>\ue979\udb80\udddc<span class="blank _d"> </span>\ueb5c<span class="blank _5"> </span>\udb80\udddb\ued47<span class="blank _e"> </span><span class="fs0 ls6 v3">\uf136</span>\uf345<span class="blank"> </span>\ue975\ued47<span class="blank"> </span>\uf346<span class="blank"> </span><span class="ls1b ws21">\ue973\ue972<span class="blank"> </span></span><span class="ws22">\uf34c<span class="blank _5"> </span>\ue972\udb80\udddc<span class="blank"> </span>\ueb5c<span class="blank _5"> </span><span class="fc3 ws23">\ued47<span class="blank"> </span>\uf34c<span class="blank"> </span>\ue974\ue7e1<span class="blank _6"> </span>\ued47<span class="blank"> </span>\uf34c<span class="blank _3"> </span>\uf346\ue977<span class="ff5 ws19"> </span></span></span></span></div><div class="t m0 xf h1c y4b ff5 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h6 y4c ff3 fs3 fc0 sc0 ls11 ws19">Referencia: Un<span class="blank _4"></span>idad 9: Sistema<span class="blank _4"></span> de ecuaciones<span class="blank _4"></span> y<span class="blank _4"></span> matrices </div><div class="t m0 x1 h6 y4d ff3 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h6 y4e ff3 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h6 y4f ff3 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 xf h1c y50 ff5 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 xf hf y51 ff4 fs3 fc0 sc0 ls11 ws19"> <span class="blank _f"> </span> </div></div><div class="c x0 y40 wa h22"><div class="t m0 x21 hf y41 ff4 fs3 fc1 sc0 ls11 ws19"><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 y52 wc h28" alt="" src="https://files.passeidireto.com/24520f46-6f07-474d-a495-058b31d7b02f/bg3.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls11 ws19">MATEMÁTICA (6<span class="ls12 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls15"> <span class="ls16"> </span></span>FINAL </div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 ls11 ws19">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> <span class="blank _4"></span> DNI<span class="blank _4"></span>:<span class="ff1"> <span class="blank _b"> </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 1 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 ls11 ws19">Hoja 3 de 4 </div><div class="t m0 x3 h2 y43 ff2 fs0 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 hf y53 ff4 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h29 y54 ff3 fs2 fc0 sc0 ls23 ws24">3.<span class="ls11 ws19"> <span class="blank _3"> </span>Dada <span class="blank _9"> </span><span class="ff7 ws25">\uee8c<span class="blank _2"> </span>\udb80\udddb\uee9e\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank _d"> </span>\uee8b<span class="fs7 ws26 v11">\uf13f<span class="blank _2"> </span>\uee9e</span><span class="fs8 ls1c v4">\uf0dc</span><span class="fs7 ws26 v11">\uf13e<span class="ls37 ws27">\uf0db\uf0da\uee9e<span class="blank"> </span></span></span></span>, <span class="blank _9"> </span>de<span class="blank _2"> </span>terminar <span class="blank _3"> </span>los <span class="blank _3"> </span>intervalos <span class="blank _3"> </span>de <span class="blank _9"> </span>crec<span class="blank _2"> </span>imiento <span class="blank _3"> </span>y<span class="blank _4"></span> <span class="blank _3"> </span>de <span class="blank _3"> </span>decrec<span class="blank _2"> </span>imiento, <span class="blank _9"> </span>y <span class="blank _9"> </span>los<span class="blank _2"> </span> </span></div><div class="t m0 x1 h4 y55 ff3 fs2 fc0 sc0 ls11 ws19">máximos y mínimos relativos. </div><div class="t m0 x1 h26 y56 ff8 fs2 fc0 sc0 ls11 ws19"> </div><div class="t m0 xf hf y57 ff4 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 hf y58 ff4 fs3 fc0 sc0 ls11 ws19">Lo primero que nec<span class="blank _4"></span>esitamos con<span class="blank _4"></span>ocer es el d<span class="blank _4"></span>ominio de <span class="blank _4"></span>la función. Como su<span class="blank _4"></span> expresi<span class="blank _4"></span>ón no presenta ning<span class="blank _4"></span>una restricción,<span class="blank _4"></span> <span class="blank _2"> </span>el </div><div class="t m0 x1 h27 y59 ff4 fs3 fc0 sc0 ls11 ws19">dominio es <span class="ff7 wse">\ued26\ued4b\ued49<span class="ve">\udb80\udddb</span><span class="ls1d">\ued42<span class="ls1e ve">\udb80\udddc</span></span><span class="ws7">\uf34c<span class="blank"> </span>\ueb39</span></span>. </div><div class="t m0 x1 hf y5a ff4 fs3 fc0 sc0 ls11 ws19">Para hallar los in<span class="blank _4"></span>tervalos de crecimi<span class="blank _4"></span>ento y de decr<span class="blank _4"></span>ecimient<span class="blank _4"></span>o, analizam<span class="blank _4"></span>os el signo de la deri<span class="blank _4"></span>vada. </div><div class="t m0 x1 h2a y5b ff7 fs3 fc0 sc0 ls1f">\ued42<span class="fs0 ls20 v3">\udb80\udd92</span><span class="ls11 wse ve">\udb80\udddb</span><span class="ls21">\ued54<span class="ls22 ve">\udb80\udddc</span><span class="ls11 ws28">\uf34c<span class="blank"> </span>\ue603<span class="blank"> </span><span class="fs2 ls23">\ued41</span><span class="fs7 ws26 v3">\uf346\ued54</span><span class="fs8 ls24 v10">\ue975</span><span class="fs7 ws26 v3">\uf345<span class="ls38 ws29">\ue974\ue973<span class="ls25">\ued54</span></span></span><span class="ff4 ws19">. (-3</span><span class="ls5">\ued54<span class="fs0 ls8 v3">\uf136</span><span class="ls26">\uf345</span></span></span><span class="ls1b ws2a">\ue974\ue973</span><span class="ff4 ls11 ws19">). Notamos qu<span class="blank _4"></span>e para hallar<span class="blank _4"></span> la derivada aplica<span class="blank _4"></span>mos la regla de l<span class="blank _4"></span>a cadena por <span class="blank _4"></span>tratarse de<span class="blank _4"></span> una </span></span></div><div class="t m0 x1 hf y5c ff4 fs3 fc0 sc0 ls11 ws19">función compuesta, <span class="blank _4"></span>y que el dominio de e<span class="blank _4"></span>sta coincide<span class="blank _4"></span> con el domini<span class="blank _4"></span>o de la funci<span class="blank _4"></span>ón original. Utilizamos ahor<span class="blank _4"></span>a el teore<span class="blank _4"></span>ma </div><div class="t m0 x1 h11 y5d ff4 fs3 fc0 sc0 ls11 ws19">de Bolzano aplicad<span class="blank _4"></span>o a <span class="ff7 wse">\ued42\ueb22</span> para<span class="blank _4"></span> saber cómo varía<span class="blank _4"></span> su signo en <span class="ls39 ws2b">su</span> do<span class="blank _4"></span>minio. </div><div class="t m0 x1 h11 y5e ff4 fs3 fc0 sc0 ls11 ws19">Calculamos el c<span class="blank _4"></span>onjunto de ceros de <span class="ff7 wse">\ued42\ueb22<span class="blank _4"></span><span class="ff4 ws19">: </span></span></div><div class="t m0 x1 h29 y5f ff7 fs2 fc0 sc0 ls27">\ued41<span class="fs7 ls11 ws2c v11">\uf13f\uf1eb<span class="blank"> </span></span><span class="fs8 ls28 v4">\uf22f</span><span class="fs7 ls29 v11">\uf13e<span class="ls3a ws2d">\uf136\uf135<span class="ls2a">\uf1eb</span></span></span><span class="fs3 ls11 ws2e">\ue7e4<span class="blank"> </span>\udb80\udddb\uf346\ue975\ued54<span class="fs0 ls2b v11">\ue974</span><span class="ls2c">\uf345<span class="ls1b">\ue974\ue973</span></span><span class="ws2f">\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank"> </span>\ue972<span class="ff4 ws19"> </span></span></span></div><div class="t m0 x1 hf y60 ff4 fs3 fc0 sc0 ls11 ws19">Como la exponencial<span class="blank _4"></span> siemp<span class="blank _4"></span>re toma valor<span class="blank _4"></span>es positivos, l<span class="blank _4"></span>a ecuación ante<span class="blank _4"></span>rior es equivalent<span class="blank _4"></span>e a </div><div class="t m0 x1 h10 y61 ff7 fs3 fc0 sc0 ls11 ws30">\uf346\ue975\ued54<span class="blank"> </span><span class="fs0 ls2d v3">\uf136</span><span class="ls26">\uf345<span class="ls1b ws21">\ue974\ue973<span class="blank"> </span></span></span><span class="ws31">\uf34c<span class="blank"> </span>\ue972<span class="ff4 ws19"> </span></span></div><div class="t m0 x1 h10 y62 ff7 fs3 fc0 sc0 ls11 ws30">\uf346\ued54<span class="blank"> </span><span class="fs0 lsc v3">\uf136</span><span class="ws32">\uf345<span class="blank"> </span>\ue979<span class="blank _5"> </span>\uf34c<span class="blank _5"> </span>\ue972<span class="ff4 ws19"> </span></span></div><div class="t m0 x1 h11 y63 ff7 fs3 fc0 sc0 ls11 wsc">\ue801\ued54<span class="blank"> </span>\ue801<span class="blank _5"> </span>\uf34c<span class="blank _5"> </span><span class="wse v1">\ue9be</span><span class="ls1b">\ue979</span><span class="ff4 ws19"> </span></div><div class="t m0 x1 h11 y64 ff7 fs3 fc0 sc0 ls11 ws28">\ued54<span class="blank _d"> </span>\uf34c<span class="blank"> </span>\ue603<span class="blank"> </span><span class="wse v1">\ue9be</span><span class="ls1b">\ue979</span><span class="ff4 ws19">, </span>\ued54<span class="blank _d"> </span>\uf34c<span class="blank"> </span>\ue603<span class="blank _6"> </span>\uf346<span class="wse v1">\ue9be</span><span class="ls1b">\ue979</span><span class="ff4 ws19"> </span></div><div class="t m0 x1 h11 y65 ff4 fs3 fc0 sc0 ls11 ws19">Luego, el conjunt<span class="blank _4"></span>o de ceros de la d<span class="blank _4"></span>erivada es <span class="ff7">\ued25</span></div><div class="t m0 x25 h2b y66 ff7 fs0 fc0 sc0 ls2e">\uf134<span class="fs3 ls11 wse v12">\udb80\udddb<span class="ls27 v1">\ued42</span></span><span class="ls2f v13">\udb80\udd92</span><span class="fs3 ls1e v12">\udb80\udddc<span class="ls9 v1">\uf34c<span class="ls30 v0">\uf35b<span class="ls31 v0">\uf346<span class="ls11 wse v1">\ue9be</span><span class="ls11 ws33">\ue979\ue7e2<span class="blank"> </span><span class="wse v1">\ue9be</span><span class="ls1b">\ue979</span></span></span>\uf35f<span class="ls11 wse v0">\ue7e4<span class="ff4 ws19"> </span></span></span></span></span></div><div class="t m0 x1 h11 y67 ff4 fs3 fc0 sc0 ls11 ws19">Evaluamos <span class="ff7 wse">\ued42\ueb22</span> en alg<span class="blank _4"></span>ún punto del c<span class="blank _4"></span>onjunto <span class="ff7 wse v0">\uf36b<span class="ws34 v0">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346</span><span class="v1">\ue9be</span><span class="ls1b v0">\ue979</span>\uf36f</span> para <span class="blank _4"></span>ver su sig<span class="blank _4"></span>no: </div><div class="t m0 x1 h2c y68 ff7 fs3 fc0 sc0 ls1f">\ued42<span class="fs0 ls20 v3">\udb80\udd92</span><span class="ls11 wse ve">\udb80\udddb<span class="v1">\uf346\ue975</span><span class="ls32">\udb80\udddc</span></span><span class="ls9">\uf34c<span class="fs2 ls23">\ued41<span class="fs7 ls38 ws29 v3">\ue974\ue979<span class="ls11 ws26">\uf346<span class="ls38 ws35">\ue978\ue975<span class="blank"> </span></span></span></span></span><span class="ls10">\ue7e4<span class="ls11 wse ve">\udb80\udddb</span><span class="ls11 ws36">\uf346\ue975\ue7e4\ue97b<span class="blank"> </span>\uf345<span class="blank"> </span><span class="ls1b">\ue974\ue973<span class="ls1e ve">\udb80\udddc</span></span><span class="ws37">\uf34f<span class="blank"> </span>\ue972<span class="ff4 ws19">, luego, </span><span class="wse">\ued42\ueb22<span class="ff4 ws19"> es negati<span class="blank _4"></span>va en <span class="ff7 wse v0">\uf36b<span class="ws34 v0">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346</span><span class="v1">\ue9be</span><span class="ls1b v0">\ue979</span>\uf36f</span>. </span></span></span></span></span></span></div><div class="t m0 x1 h11 y69 ff4 fs3 fc0 sc0 ls11 ws19">Análogamente, en el<span class="blank _4"></span> interv<span class="blank _4"></span>alo <span class="ff7 wse v0">\uf36b<span class="ls33 v0">\uf346</span><span class="v1">\ue9be</span><span class="ws34 v0">\ue979\ue7e2<span class="blank"> </span></span><span class="v1">\ue9be</span><span class="ls1b v0">\ue979</span>\uf36f<span class="v0">\ue7e3</span></span> </div><div class="t m0 x1 h2c y6a ff7 fs3 fc0 sc0 ls1f">\ued42<span class="fs0 ls20 v3">\udb80\udd92</span><span class="ls11 wse ve">\udb80\udddb<span class="v1">\ue972</span><span class="ls22">\udb80\udddc</span></span><span class="ls9">\uf34c<span class="fs2 ls23">\ued41<span class="fs7 ls34 v3">\ue972</span></span><span class="ls10">\ue7e4<span class="ls11 wse ve">\udb80\udddb</span><span class="ls11 ws38">\ue972<span class="blank"> </span>\uf345<span class="blank"> </span><span class="ls1b">\ue974\ue973<span class="ls1e ve">\udb80\udddc</span></span></span></span>\uf34c<span class="ls1b ws39">\ue974\ue973<span class="blank"> </span></span><span class="ls11 ws3a">\uf350<span class="blank"> </span>\ue972<span class="ff4 ws19">, por l<span class="blank _4"></span>o que <span class="ff7 wse">\ued42\ueb22</span> es positi<span class="blank _4"></span>va en <span class="ff7 wse v0">\uf36b<span class="ls31 v0">\uf346</span><span class="v1">\ue9be<span class="blank _4"></span><span class="ws34 ve">\ue979\ue7e2<span class="blank"> </span><span class="wse v1">\ue9be</span><span class="ls1b">\ue979<span class="ls11 wse v0">\uf36f<span class="ff4 ws19 v0">. </span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h11 y6b ff4 fs3 fc0 sc0 ls11 ws19">En <span class="ff7 wse v0">\uf36b<span class="v1">\ue9be</span><span class="ws34 v0">\ue979\ue7e2<span class="blank"> </span>\uf345\ue9bb</span>\uf36f</span> la derivada e<span class="blank _4"></span>s nuevame<span class="blank _4"></span>nte negativa <span class="blank _4"></span>ya que, por ej<span class="blank _4"></span>emplo, </div><div class="t m0 x1 h2c y6c ff7 fs3 fc0 sc0 ls1f">\ued42<span class="fs0 ls20 v3">\udb80\udd92</span><span class="ls11 wse ve">\udb80\udddb<span class="v1">\ue975</span><span class="ls22">\udb80\udddc</span></span><span class="ls9">\uf34c<span class="fs2 ls23">\ued41<span class="fs7 ls11 ws26 v3">\uf346<span class="ls38 ws29">\ue974\ue979</span>\uf345<span class="ls38 ws3b">\ue978\ue975<span class="blank"> </span></span></span></span><span class="ls10">\ue7e4<span class="ls11 wse ve">\udb80\udddb</span><span class="ls11 ws36">\uf346\ue975\ue7e4\ue97b<span class="blank"> </span>\uf345<span class="blank"> </span><span class="ls1b">\ue974\ue973<span class="ls1e ve">\udb80\udddc</span></span><span class="ws37">\uf34f<span class="blank"> </span>\ue972<span class="ff4 ws19">. </span></span></span></span></span></div><div class="t m0 x1 h11 y6d ff4 fs3 fc0 sc0 ls11 ws19">De esta forma, p<span class="blank _4"></span>or el criter<span class="blank _4"></span>io de la deri<span class="blank _4"></span>vada el inter<span class="blank _4"></span>valo de creci<span class="blank _4"></span>miento de la func<span class="blank _4"></span>ión <span class="ff7 ls35">\ued42</span> es <span class="ff7 ls36 v0">\uf36b<span class="ls31 v0">\uf346<span class="ls11 wse v1">\ue9be</span><span class="ls11 ws33">\ue979\ue7e2<span class="blank"> </span><span class="wse v1">\ue9be</span><span class="ls1b">\ue979</span><span class="wse v0">\uf36f</span></span></span></span> y los interval<span class="blank _4"></span>os de </div><div class="t m0 x1 h11 y6e ff4 fs3 fc0 sc0 ls11 ws19">decrecimiento s<span class="blank _4"></span>on <span class="ff7 wse v0">\uf36b<span class="ws34 v0">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346</span><span class="v1">\ue9be</span><span class="ls1b v0">\ue979</span>\uf36f</span><span class="ls3"> <span class="ls3b">y <span class="ff7 ls36 v0">\uf36b<span class="ls11 wse v1">\ue9be<span class="blank _4"></span><span class="ws34 ve">\ue979\ue7e2<span class="blank"> </span>\uf345\ue9bb<span class="wse v0">\uf36f<span class="v0">\ue7e4<span class="ff4 ws19"> Ade<span class="blank _4"></span>más, como la funci<span class="blank _4"></span>ón decre<span class="blank _4"></span>ce a la izquierd<span class="blank _4"></span>a de -</span></span></span></span></span></span></span></span></div><div class="t m0 x26 h2d y6f ff7 fs3 fc0 sc0 ls11 wse">\ue9be<span class="ls1b ve">\ue979</span><span class="ff4 ws19 ve"> y crece a su d<span class="blank _4"></span>erecha, </span></div><div class="t m0 x1 h11 y70 ff4 fs3 fc0 sc0 ls11 ws19">entonces <span class="ff7 ws7">\ued54<span class="blank"> </span>\uf34c<span class="blank"> </span>\uf346<span class="wse v1">\ue9be<span class="ve">\ue979</span></span></span> es un mínimo relativ<span class="blank _4"></span>o; y como <span class="ff7 ls35">\ued42</span> crece<span class="blank _4"></span> a la izquierd<span class="blank _4"></span>a de <span class="ff7 wse v1">\ue9be</span><span class="ff7 ls1b">\ue979</span> y decrece<span class="blank _4"></span> a su derecha, la<span class="blank _4"></span> abscisa <span class="ff7 ws7">\ued54<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="wse v1">\ue9be</span><span class="ls1b">\ue979</span></span> </div><div class="t m0 x1 hf y71 ff4 fs3 fc0 sc0 ls11 ws19">es un máximo relati<span class="blank _4"></span>vo. </div><div class="t m0 x1 h1c y72 ff5 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h1c y73 ff5 fs3 fc0 sc0 ls11 ws19"> <span class="blank _a"> </span> </div></div><div class="c x0 y40 wa h22"><div class="t m0 x21 hf y41 ff4 fs3 fc1 sc0 ls11 ws19"><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 y74 wd h2e" alt="" src="https://files.passeidireto.com/24520f46-6f07-474d-a495-058b31d7b02f/bg4.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h1c y75 ff5 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h2 y76 ff1 fs0 fc0 sc0 ls11 ws19">MATEMÁTICA (6<span class="blank _4"></span><span class="ls12 ws0">1)<span class="ff2 ls11 ws19"> Cátedra<span class="blank _4"></span> A: NUÑEZ, <span class="blank _4"></span>MYRIAM<span class="ff1"> <span class="blank _4"></span> FIN<span class="ls3f ws3c">AL</span> </span></span></span></div><div class="t m0 x1 h2 y77 ff2 fs0 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h2 y78 ff2 fs0 fc0 sc0 ls11 ws19">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> <span class="blank _4"></span> DNI<span class="blank _4"></span>:<span class="ff1"> <span class="blank _b"> </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 1 </span></div><div class="t m0 x3 h2 y79 ff2 fs0 fc0 sc0 ls11 ws19">Hoja 4 de 4 </div><div class="t m0 x3 h2 y7a ff2 fs0 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h4 y7b ff3 fs2 fc0 sc0 ls23">4<span class="ls3c ws19">. <span class="fs3 ls11">¿Cuántas<span class="blank _4"></span> palabras dist<span class="blank _4"></span>intas, con o sin sen<span class="blank _4"></span>tido, se pued<span class="blank _4"></span>en formar c<span class="blank _4"></span>on las letras<span class="blank _4"></span> de la pala<span class="blank _4"></span>bra </span></span></div><div class="t m0 x1 h6 y7c ff9 fs3 fc0 sc0 ls11 ws19">\u201cSOMBRA<span class="blank _4"></span>S\u201d si deben termina<span class="blank _4"></span>r con la le<span class="blank _4"></span>tra \u201cO\u201d?<span class="ff3"> </span></div><div class="t m0 x1 h4 y7d ff3 fs2 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h4 y7e ff3 fs2 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 hf y7f ffa fs3 fc0 sc0 ls11 ws19">Buscamos <span class="blank _2"> </span>utilizar <span class="blank _2"> </span>las <span class="blank _2"> </span>7 <span class="blank _e"> </span>letras <span class="blank _2"> </span>de <span class="blank _2"> </span>la <span class="blank _2"> </span>palabra <span class="blank _2"> </span>\u201cSOMBRAS\u201d <span class="blank _2"> </span>para <span class="blank _2"> </span>armar <span class="blank _e"> </span>los <span class="blank _2"> </span>nuevos <span class="blank _2"> </span>vocablos <span class="blank _2"> </span>(independiente<span class="blank _4"></span>mente <span class="blank _2"> </span>de <span class="blank _2"> </span>si <span class="blank _2"> </span>éstos </div><div class="t m0 x1 hf y80 ff4 fs3 fc0 sc0 ls11 ws19">tienen <span class="blank _10"> </span>o <span class="blank _10"> </span>no <span class="blank _10"> </span>sentido <span class="blank _e"> </span>en <span class="blank _10"> </span>nuestro <span class="blank _e"> </span>idioma). <span class="blank _10"> </span>Por <span class="blank _10"> </span>otra <span class="blank _10"> </span>parte, <span class="blank _10"> </span>importa <span class="blank _e"> </span>el <span class="blank _10"> </span>orden <span class="blank _10"> </span>en <span class="blank _10"> </span>que <span class="blank _e"> </span>se <span class="blank _10"> </span>eligen <span class="blank _10"> </span>las <span class="blank _10"> </span>letras <span class="blank _e"> </span>para <span class="blank _10"> </span>formar <span class="blank _10"> </span>dichos </div><div class="t m0 x1 hf y81 ff4 fs3 fc0 sc0 ls11 ws19">términos. Lueg<span class="blank _4"></span>o, estamos ante un cas<span class="blank _4"></span>o de per<span class="blank _4"></span>mutación o reordena<span class="blank _4"></span>miento de el<span class="blank _4"></span>ementos. </div><div class="t m0 x1 hf y82 ffa fs3 fc0 sc0 ls11 ws19">Siendo <span class="blank _e"> </span>además <span class="blank _e"> </span>que <span class="blank _e"> </span>buscamos <span class="blank _e"> </span>palabras <span class="blank _e"> </span>que <span class="blank _e"> </span>finalizan <span class="blank _2"> </span>con <span class="blank _10"> </span>la <span class="blank _e"> </span>letra <span class="blank _e"> </span>\u201cO\u201d, <span class="blank _e"> </span>en <span class="blank _e"> </span>lugar <span class="blank _e"> </span>de <span class="blank _e"> </span>permutar <span class="blank _e"> </span>los <span class="blank _e"> </span>7 <span class="blank _e"> </span>caracteres <span class="blank _e"> </span>disponibles,<span class="blank _4"></span> </div><div class="t m0 x1 hf y83 ff4 fs3 fc0 sc0 ls11 ws19">debemos reordenar<span class="blank _4"></span> solo 6 de ellos, aqu<span class="blank _4"></span>ellos que ju<span class="blank _4"></span>stamente <span class="blank _4"></span>ocupan las posiciones 1 a 6 dentr<span class="blank _4"></span>o de cada nu<span class="blank _4"></span>eva palabra. </div><div class="t m0 x1 hf y84 ff4 fs3 fc0 sc0 ls11 ws19">Por otra parte, re<span class="blank _4"></span>cordemos qu<span class="blank _4"></span>e: </div><div class="t m0 x27 hf y85 ff4 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 hf y86 ffa fs3 fc0 sc0 ls11 ws19">Luego,como hay 2 l<span class="blank _4"></span>etras \u201cS\u201d disponib<span class="blank _4"></span>les entre las <span class="blank _4"></span>6 a reordenar,<span class="blank _4"></span> tendrem<span class="blank _4"></span>os: <span class="ff4"> </span></div><div class="t m0 x24 h11 y87 ff7 fs3 fc0 sc0 ls11">\ued32</div><div class="t m0 x28 h2f y88 ff7 fs0 fc0 sc0 ls11">\uf13a</div><div class="t m0 x29 h30 y89 ff7 fs0 fc0 sc0 ls11 ws3d">\uf136\ue7e1\uf135\ue7e1\uf135\ue7e1\uf135\ue7e1\uf135<span class="blank"> </span><span class="fs3 ls3d v14">\uf34c</span><span class="fs3 wse v15">\ue978\ue7e8</span></div><div class="t m0 x1a h19 y8a ff7 fs3 fc0 sc0 ls11 ws3e">\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 _5"> </span><span class="ls3e v4">\uf34c</span><span class="wse v8">\ue978\ue7e4\ue977\ue7e4\ue976\ue7e4\ue975\ue7e4\ue974\ue7e8</span></div><div class="t m0 x2a h12 y8a ff7 fs3 fc0 sc0 ls11 ws3f">\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="ls1b ws2a">\ue975\ue978\ue972<span class="ff4 ls11 ws19"> </span></span></span></div><div class="t m0 x1 h13 y8b ff4 fs3 fc0 sc0 ls11 ws19">palabras distin<span class="blank _4"></span>tas que <span class="blank _4"></span>pueden <span class="blank _4"></span>formarse <span class="blank _4"></span>con las <span class="blank _4"></span>7 <span class="blank _4"></span>letras d<span class="blank _4"></span>e la p<span class="blank _4"></span>alabra <span class="ffb ws40">\u201cSOMB<span class="blank _4"></span>RAS\u201d<span class="ff4 ws19"> <span class="blank _4"></span>y que ad<span class="blank _4"></span>emás <span class="blank _4"></span>terminan <span class="blank _4"></span>con la <span class="blank _4"></span>letra <span class="ffb ws40">\u201cO\u201d<span class="blank _4"></span>.<span class="blank _4"></span><span class="ff8 ws19"> </span></span></span></span></div><div class="t m0 x1 h6 y8c ff3 fs3 fc0 sc0 ls11 ws19"> </div><div class="t m0 x1 h1c y8d ff5 fs3 fc0 sc0 ls11 ws19"> </div></div><div class="c x0 y8e wa h31"><div class="t m0 x21 hf y41 ff4 fs3 fc1 sc0 ls11 ws19"><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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