<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/2744de54-7512-40cb-a3a1-ab34f88607c1/bg1.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 lse ws15">MATEMÁTICA (6<span class="lsf ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM </span></div><div class="t m0 x1 h2 y3 ff1 fs0 fc0 sc0 lse ws15">RECUPERATORI<span class="blank _0"></span>O 1° PARCIAL </div><div class="t m0 x2 h2 y4 ff1 fs0 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h2 y5 ff2 fs0 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h3 y6 ff2 fs1 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h2 y7 ff2 fs0 fc0 sc0 ls10 ws1">21<span class="lse ws2">/06/2023<span class="ff1 ws15"> <span class="blank _0"></span> <span class="blank _1"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span>TEMA 3 </span></span></div><div class="t m0 x3 h2 y8 ff2 fs0 fc0 sc0 lse ws15"> Hoja 1 de 4 </div><div class="t m0 x3 h2 y9 ff2 fs0 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h3 ya ff2 fs1 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h3 yb ff2 fs1 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h4 yc ff3 fs2 fc0 sc0 lse ws15">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 lse ws15"> </div></div><div class="c x6 yd w4 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lse ws15">1 </div></div><div class="c x8 yd w5 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lse ws15">2 </div></div><div class="c x9 yd w6 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lse ws15">3 </div></div><div class="c xa yd w7 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lse ws15">4 </div></div><div class="c x4 yf w3 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lse ws15"> </div></div><div class="c x6 yf w4 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lse ws15"> </div></div><div class="c x8 yf w5 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lse ws15"> </div></div><div class="c x9 yf w6 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lse ws15"> </div></div><div class="c xa yf w7 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lse ws15"> </div></div><div class="c x4 y11 w5 h9"><div class="t m0 xb ha y12 ff4 fs4 fc0 sc0 lse ws15">Puntaje de cada </div><div class="t m0 xb ha y13 ff4 fs4 fc0 sc0 lse ws15">ejercicio </div></div><div class="c x6 y11 w4 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lse ws15">2,50 </div></div><div class="c x8 y11 w5 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lse ws15">2,50 </div></div><div class="c x9 y11 w6 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lse ws15">2,50 </div></div><div class="c xa y11 w7 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lse ws15">2,50 </div></div><div class="c x0 y1 w2 h0"><div class="t m0 x1 hb y15 ff5 fs5 fc0 sc0 lse ws15">Duración del exam<span class="blank _3"> </span>en: 1h <span class="ff6 ws3">40\u2019.</span> Com<span class="blank _3"> </span>pletar los datos<span class="blank _3"> </span> personales<span class="blank _3"> </span> con letra clara, m<span class="blank _3"> </span>ayúscula e imprenta. <span class="blank _3"> </span> </div><div class="t m0 xd hc y16 ff3 fs5 fc0 sc0 lse ws15">No se aceptarán respue<span class="blank _3"> </span>stas en lápiz.<span class="blank _3"> </span> </div><div class="t m0 xe hd y17 ff2 fs6 fc0 sc0 lse ws15"> </div><div class="t m0 x1 he y18 ff7 fs2 fc0 sc0 lse ws15">1. Hallar el valor de <span class="ff8 ws4">\uee91</span> para que la función <span class="ff8 ws4">\uee8c<span class="ls0 v1">\udb80\udddb</span><span class="ls1">\uee9e<span class="ls2 v1">\udb80\udddc</span><span class="ls3">\uf34c</span></span><span class="fs7 ws5 v2">\uf0dc\uf13f<span class="ls11">\uf0db\uee9e</span></span></span></div><div class="t m0 xf hf y19 ff8 fs7 fc0 sc0 ls12 ws6">\uee91\uee9e<span class="lse ws5">\uf13f\uf0de<span class="ff7 fs2 ws15 v3"> tenga una asíntota en <span class="ff8 ws7">\uee9f\ue603<span class="blank _4"> </span>\uf34c<span class="blank"> </span>\ue603<span class="blank"> </span></span></span><span class="v4">\uf0da</span></span></div><div class="t m0 x10 h10 y19 ff8 fs7 fc0 sc0 lse ws5">\uf0dd<span class="ff7 fs2 ws15 v3"> . </span></div><div class="t m0 x1 h6 y1a ff3 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x11 he y1b ff9 fs2 fc0 sc0 lse ws15">Si la recta <span class="ff8 ws8">\ued55<span class="blank _5"> </span>\uf34c<span class="blank"> </span><span class="fs7 v2">\uf135</span></span></div><div class="t m0 x12 h11 y1c ff8 fs7 fc0 sc0 lse ws5">\uf138<span class="ff9 fs2 ws15 v3"> es asíntota de la función significa<span class="blank _0"></span> que: </span></div><div class="t m0 x13 h12 y1d ff8 fs2 fc0 sc0 lse ws4">\ued48\ued45\ued49</div><div class="t m0 x14 h13 y1e ff8 fs7 fc0 sc0 lse ws9">\uf1eb\ueb5c\uf1b6<span class="blank _6"> </span><span class="fs2 ls4 v5">\ued42<span class="ls0 v1">\udb80\udddb</span><span class="ls5">\ued54<span class="ls2 v1">\udb80\udddc</span><span class="ls3">\uf34c<span class="lse v6">\ue973</span></span></span></span></div><div class="t m0 x15 h14 y1f ff8 fs2 fc0 sc0 ls6">\ue976<span class="lse wsa v7">\ue603\ue603\ue603<span class="blank"> </span>\uf43a<span class="blank"> </span>\ue603\ue603\ue603<span class="blank _4"> </span>\ued48\ued45\ued49</span></div><div class="t m0 x16 h13 y1e ff8 fs7 fc0 sc0 lse wsb">\uf1eb\ueb5c\uf1b6<span class="blank _6"> </span><span class="fs2 ws4 v5">\ue603<span class="wsc v6">\ue975<span class="blank"> </span>\uf346<span class="blank"> </span>\ue974\ued54</span></span></div><div class="t m0 x17 h15 y1f ff8 fs2 fc0 sc0 ls13 wsd">\ued47\ued54<span class="blank"> </span><span class="lse wsc">\uf346<span class="blank"> </span>\ue977<span class="blank _4"> </span><span class="ls7 v7">\uf34c</span><span class="v8">\ue973</span></span></div><div class="t m0 x18 h16 y1f ff8 fs2 fc0 sc0 ls8">\ue976<span class="ffa lse ws15 v7"> </span></div><div class="t m0 x11 h17 y20 ff9 fs2 fc0 sc0 lse ws15">Al <span class="blank _7"> </span>evaluar <span class="blank _3"> </span>numer<span class="blank _3"> </span>ador <span class="blank _7"> </span>y <span class="blank _7"> </span>denominador <span class="blank _7"> </span>nos <span class="blank _7"> </span>encontramos <span class="blank _7"> </span>que <span class="blank _7"> </span>ambos <span class="blank _7"> </span>tienden <span class="blank _7"> </span>a <span class="blank _8"> </span><span class="ff8 ws4">\ue9bb</span> <span class="blank _7"> </span>, <span class="blank _7"> </span>por <span class="blank _3"> </span>lo<span class="blank _3"> </span> <span class="blank _7"> </span>tanto <span class="blank _7"> </span>se <span class="blank _7"> </span>presenta </div><div class="t m0 x11 h17 y21 ff9 fs2 fc0 sc0 lse ws15">una indeterminación que debemos resolver; para ello dividimos numerador y<span class="blank _0"></span> denominador por <span class="blank _3"> </span><span class="ff8 ls5">\ued54</span> : </div><div class="t m0 x19 h12 y22 ff8 fs2 fc0 sc0 lse ws4">\ued48\ued45\ued49</div><div class="t m0 x1a h18 y23 ff8 fs7 fc0 sc0 lse wsb">\uf1eb\ueb5c<span class="blank"> </span>\uf1b6<span class="blank _6"> </span><span class="fs2 v5">\ue603</span></div><div class="t m0 x1b h12 y24 ff8 fs2 fc0 sc0 lse wse">\ue975<span class="blank"> </span>\uf346<span class="blank"> </span>\ue974\ued54</div><div class="t m0 x1c h12 y25 ff8 fs2 fc0 sc0 lse">\ued54</div><div class="t m0 x1b h12 y26 ff8 fs2 fc0 sc0 ls13 wsf">\ued47\ued54<span class="blank"> </span><span class="lse ws10">\uf346<span class="blank"> </span>\ue977</span></div><div class="t m0 x1c h12 y27 ff8 fs2 fc0 sc0 lse">\ued54</div><div class="t m0 x1d h12 y22 ff8 fs2 fc0 sc0 lse ws11">\ue603<span class="blank"> </span>\uf34c<span class="blank"> </span>\ue603<span class="blank _4"> </span>\ued48\ued45\ued49</div><div class="t m0 x1e h18 y23 ff8 fs7 fc0 sc0 lse wsb">\uf1eb\ueb5c\uf1b6<span class="blank _6"> </span><span class="fs2 v5">\ue603</span></div><div class="t m0 x1f h12 y24 ff8 fs2 fc0 sc0 lse">\ue975</div><div class="t m0 x1f h19 y25 ff8 fs2 fc0 sc0 ls9">\ued54<span class="lse wsc v3">\uf346<span class="blank"> </span>\ue974</span></div><div class="t m0 x1f h1a y28 ff8 fs2 fc0 sc0 lse wsc">\ued47<span class="blank _4"> </span>\uf346<span class="blank"> </span><span class="v2">\ue977</span></div><div class="t m0 xa h12 y27 ff8 fs2 fc0 sc0 lse">\ued54</div><div class="t m0 x20 h1b y22 ffa fs2 fc0 sc0 lse ws15"> </div><div class="t m0 x11 he y29 ff9 fs2 fc0 sc0 lse ws15">En esta expresión <span class="ff8 fs7 v2">\uf137</span></div><div class="t m0 x21 hf y2a ff8 fs7 fc0 sc0 lsa">\uf1eb<span class="ff9 fs2 lse ws15 v3"> y <span class="blank _3"> </span></span><span class="lse v4">\uf139</span></div><div class="t m0 x22 h11 y2a ff8 fs7 fc0 sc0 lsa">\uf1eb<span class="ff9 fs2 lse ws15 v3"> se aproximan a <span class="ff8 ws4">\ue972</span> , por lo t<span class="blank _3"> </span>anto el numerador tiende a <span class="ff8 ws4">\uf346\ue974</span> <span class="blank _3"> </span>y el denominador se </span></div><div class="t m0 x11 h17 y2b ff9 fs2 fc0 sc0 lse ws15">aproxima a <span class="ff8 ls5">\ued47</span> . Entonces: </div><div class="t m0 x23 h12 y2c ff8 fs2 fc0 sc0 lse ws4">\ued48\ued45\ued49</div><div class="t m0 x24 h13 y2d ff8 fs7 fc0 sc0 lse wsb">\uf1eb\ueb5c<span class="blank"> </span>\uf1b6<span class="blank _6"> </span><span class="fs2 ws4 v5">\ue603<span class="ws12 v6">\ue975<span class="blank"> </span>\uf346<span class="blank"> </span>\ue974\ued54</span></span></div><div class="t m0 x25 h15 y2e ff8 fs2 fc0 sc0 ls13 ws13">\ued47\ued54<span class="blank"> </span><span class="lse wsc">\uf346<span class="blank"> </span>\ue977<span class="blank _4"> </span><span class="ws14 v7">\uf34c<span class="blank _4"> </span>\uf346<span class="blank"> </span></span><span class="v8">\ue974</span></span></div><div class="t m0 x26 h16 y2e ff8 fs2 fc0 sc0 ls5">\ued47<span class="ffa lse ws15 v7"> </span></div><div class="t m0 x11 h1c y2f ff9 fs2 fc0 sc0 lse ws15">Si <span class="ff8 lsb">\uf346<span class="fs7 lse v2">\uf136</span></span></div><div class="t m0 x27 h1d y30 ff8 fs7 fc0 sc0 lsc">\uf1de<span class="fs2 ls3 v3">\uf34c</span><span class="lse v4">\uf135</span></div><div class="t m0 x28 h11 y30 ff8 fs7 fc0 sc0 lsd">\uf138<span class="fs2 lse ws7 v3">\ue603\ue603<span class="blank"> </span>\uf43a<span class="blank _4"> </span>\ue603\ue603\ued47<span class="blank _5"> </span>\uf34c<span class="blank _4"> </span>\uf346\ue97a<span class="blank _3"> </span><span class="ff9 ws15"> </span></span></div><div class="t m0 x1 h1e y31 ff5 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h1e y32 ff5 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h1e y33 ff5 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h1e y34 ff5 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h1e y35 ff5 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h1e y36 ff5 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h1e y37 ff5 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h1e y38 ff5 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h1e y39 ff5 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h1e y3a ff5 fs3 fc0 sc0 lse ws15"> <span class="blank _9"> </span> </div></div><div class="c x1 y3b w8 h1f"><div class="t m0 x29 h2 y3c ff2 fs0 fc0 sc0 lse ws15">APELLIDO: </div></div><div class="c x2a y3d w9 h20"><div class="t m0 xb h2 y3e ff2 fs0 fc0 sc0 lse ws15">CALIFICACIÓN:<span class="blank _0"></span> </div></div><div class="c x1 y3f w8 h21"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lse ws15">NOMBRE: </div></div><div class="c x1 y3d w8 h21"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lse ws15">DNI (registrado en S<span class="blank _0"></span>IU Guaraní): </div></div><div class="c x1 y40 w8 h22"><div class="t m0 xb h2 y10 ff2 fs0 fc0 sc0 lse ws15">E-MAIL: </div></div><div class="c x2a y41 w9 h23"><div class="t m0 xb h2 y42 ff2 fs0 fc0 sc0 lse ws15">DOCENTE (nombre<span class="blank _0"></span> y apellido): </div></div><div class="c x1 y43 w8 h21"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lse ws15">TEL: </div></div><div class="c x1 y41 w8 h21"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lse ws15">AULA: </div></div><div class="c x0 y44 wa h24"><div class="t m0 x29 h25 y45 ff4 fs3 fc1 sc0 lse ws15"><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 y46 wb h26" alt="" src="https://files.passeidireto.com/2744de54-7512-40cb-a3a1-ab34f88607c1/bg2.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 lse ws15">MATEMÁTICA (6<span class="lsf ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls14"> <span class="ls15"> </span></span>RECUPERATOR<span class="blank _3"> </span>IO 1° PARC<span class="blank _3"> </span>IAL </div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 lse ws15">APELLIDO Y NOMB<span class="blank _0"></span>RE: <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> DNI:<span class="ff1"> <span class="blank _a"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span>TEMA 3 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 lse ws15">Hoja 2 de 4 </div><div class="t m0 x3 h2 y47 ff2 fs0 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h4 y48 ff7 fs2 fc0 sc0 lse ws15">2. <span class="blank _3"> </span>Hallar <span class="blank _7"> </span>el <span class="blank _3"> </span>valor <span class="blank _7"> </span>de <span class="blank _7"> </span><span class="ff8 ws16">\uee89\ue603<span class="blank"> </span>\uebd0<span class="blank _4"> </span>\ueb39<span class="blank _3"> </span></span> <span class="blank _3"> </span>para <span class="blank _7"> </span>que <span class="blank _3"> </span>la <span class="blank _7"> </span>función <span class="blank _7"> </span><span class="ff8 ws4">\uee8c<span class="ls0 v1">\udb80\udddb</span><span class="ls1">\uee9e<span class="ls16 v1">\udb80\udddc</span><span class="ws17">\uf34c<span class="blank"> </span>\uf346\uee9e<span class="fs7 ls17 v9">\uf0db</span><span class="ls18 ws18">\ue603<span class="blank _b"></span>\uf345\uee9e\uf345\uee89<span class="blank _c"></span><span class="ff7 lse ws15"> <span class="blank _3"> </span>tenga <span class="blank _7"> </span>un <span class="blank _3"> </span>ú<span class="blank _3"> </span>nico <span class="blank _3"> </span>punto <span class="blank _7"> </span>de <span class="blank _3"> </span>intersección </span></span></span></span></span></div><div class="t m0 x1 h4 y49 ff7 fs2 fc0 sc0 lse ws15">con la función <span class="ff8 ws19">\uee8d\udb80\udddb\uee9e\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank _4"> </span><span class="ls1e ws1a">\uf0de\uee9e<span class="blank"> </span></span><span class="wsc">\uf345<span class="blank"> </span>\uf0db<span class="blank _3"> </span></span></span> </div><div class="t m0 x1 h17 y4a ff9 fs2 fc0 sc0 lse ws15">Para hallar los puntos en de intersección de las funciones de<span class="blank _0"></span>bemos plantear:<span class="blank _3"> </span> </div><div class="t m0 x2b h17 y4b ff8 fs2 fc0 sc0 ls4">\ued42<span class="ls19 v1">\udb80\udddb</span><span class="ls5">\ued54<span class="ls2 v1">\udb80\udddc</span><span class="lse ws1b">\uf34c<span class="blank _4"> </span>\ued43\udb80\udddb\ued54<span class="blank"> </span>\udb80\udddc<span class="blank"> </span><span class="ff9 ws15"> </span></span></span></div><div class="t m0 x1 h17 ya ff9 fs2 fc0 sc0 lse ws15">Luego, reemplazamos por las fórmulas de<span class="blank _0"></span> las funciones dadas en el enunciado y resulta que:<span class="blank _3"> </span> </div><div class="t m0 x2c h27 y4c ff8 fs2 fc0 sc0 lse ws1c">\uf346\ued54<span class="blank"> </span><span class="fs7 ls1a v9">\uf136</span><span class="wsc">\ue603<span class="blank _8"> </span>\uf345<span class="blank"> </span>\ued54<span class="blank _4"> </span>\uf345<span class="blank"> </span>\ued3f<span class="blank _5"> </span>\uf34c<span class="blank _4"> </span>\ue977\ued54<span class="blank _4"> </span>\uf345<span class="blank"> </span>\ue974<span class="ff9 ws15"> </span></span></div><div class="t m0 x1 h17 y4d ff9 fs2 fc0 sc0 lse ws15">Despejamos y obtenemos que: </div><div class="t m0 x24 h27 y4e ff8 fs2 fc0 sc0 lse ws1c">\uf346\ued54<span class="blank"> </span><span class="fs7 ls1b v9">\uf136</span><span class="wsc">\uf346<span class="blank"> </span>\ue976\ued54<span class="blank _4"> </span>\uf345<span class="blank"> </span>\ued3f<span class="blank"> </span>\uf346<span class="blank"> </span>\ue974<span class="blank _4"> </span>\uf34c<span class="blank _4"> </span>\ue972<span class="ff9 ws15"> </span></span></div><div class="t m0 x1 h17 y4f ff9 fs2 fc0 sc0 lse ws15">Aplicamos la fórmula resolvente: </div><div class="t m0 x2d h12 y50 ff8 fs2 fc0 sc0 lse">\ued54</div><div class="t m0 x2e h28 y51 ff8 fs7 fc0 sc0 lse ws1d">\uf135\ue7e1\uf136<span class="blank"> </span><span class="fs2 ls7 va">\uf34c</span><span class="fs2 wse vb">\ue976<span class="blank"> </span>\uf347<span class="blank"> </span><span class="ws4 v0">\uf3a5<span class="v0">\udb80\udddb\uf346\ue976\udb80\udddc</span></span></span><span class="ls1c vc">\uf136</span><span class="fs2 ws1e vb">\uf346<span class="blank _d"> </span>\ue976\ue7e4<span class="blank"> </span>\udb80\udddb\uf346\ue973\udb80\udddc\ue7e4<span class="blank"> </span>\udb80\udddb\ued3f<span class="blank _d"> </span>\uf346<span class="blank _d"> </span>\ue974\udb80\udddc</span></div><div class="t m0 x2f h16 y52 ff8 fs2 fc0 sc0 lse ws1f">\uf346\ue974<span class="blank"> </span><span class="ffa ws15 v7"> </span></div><div class="t m0 x1 h17 y53 ff9 fs2 fc0 sc0 lse ws15">Resolvemos y resulta: </div><div class="t m0 x30 h12 y54 ff8 fs2 fc0 sc0 lse">\ued54</div><div class="t m0 x31 h29 y55 ff8 fs7 fc0 sc0 lse ws1d">\uf135\ue7e1\uf136<span class="blank"> </span><span class="fs2 ls3 va">\uf34c</span><span class="fs2 ws10 vb">\ue976<span class="blank"> </span>\uf347<span class="blank"> </span><span class="ws4 vd">\uf3a5</span><span class="ls1f ws20">\ue973\ue978<span class="blank"> </span><span class="lse wsc">\uf345<span class="blank"> </span>\ue976\ue7e4<span class="blank _6"> </span>\udb80\udddb\ued3f<span class="blank _d"> </span>\uf346<span class="blank"> </span>\ue974\udb80\udddc</span></span></span></div><div class="t m0 x9 h16 y56 ff8 fs2 fc0 sc0 lse ws21">\uf346\ue974<span class="blank"> </span><span class="ffa ws15 v7"> </span></div><div class="t m0 x1 h17 y57 ff9 fs2 fc0 sc0 lse ws15">Como <span class="blank _7"> </span>las <span class="blank _e"> </span>funciones <span class="blank _7"> </span>deben <span class="blank _e"> </span>intersecarse <span class="blank _7"> </span>en <span class="blank _e"> </span>un <span class="blank _7"> </span>pu<span class="blank _3"> </span>nto, <span class="blank _7"> </span>la <span class="blank _e"> </span>ecuación <span class="blank _7"> </span>debe <span class="blank _e"> </span>tener <span class="blank _7"> </span>una <span class="blank _e"> </span>única <span class="blank _7"> </span>solución <span class="blank _e"> </span>por <span class="blank _7"> </span>lo <span class="blank _e"> </span>que <span class="blank _f"> </span><span class="ff8 ls1f ws20">\ue973\ue978<span class="blank"> </span><span class="lse">\uf345</span></span></div><div class="t m0 x1 h17 y58 ff8 fs2 fc0 sc0 lse ws22">\ue976\ue7e4<span class="blank"> </span>\udb80\udddb\ued3f<span class="blank _d"> </span>\uf346<span class="blank _d"> </span>\ue974\udb80\udddc<span class="ff9 ws15"> debe<span class="blank _0"></span> ser cero, es decir: </span></div><div class="t m0 x32 h17 y59 ff8 fs2 fc0 sc0 ls1f ws20">\ue973\ue978<span class="blank"> </span><span class="lse ws1e">\uf345<span class="blank _10"> </span>\ue976\ue7e4<span class="blank"> </span>\udb80\udddb\ued3f<span class="blank _d"> </span>\uf346<span class="blank _d"> </span>\ue974\udb80\udddc<span class="blank _4"> </span>\uf34c<span class="blank _4"> </span>\ue972<span class="ff9 ws15"> </span></span></div><div class="t m0 x1 h17 y5a ff9 fs2 fc0 sc0 lse ws15">Despejamos </div><div class="t m0 x8 h17 y5b ff8 fs2 fc0 sc0 lse ws1e">\ue976\ue7e4<span class="blank"> </span><span class="ls0 v1">\udb80\udddb</span><span class="wsc">\ued3f<span class="blank _d"> </span>\uf346<span class="blank"> </span>\ue974<span class="ls1d v1">\udb80\udddc</span><span class="ws8">\uf34c<span class="blank"> </span>\uf346<span class="ls1f ws23">\ue973\ue978</span><span class="ff9 ws15"> </span></span></span></div><div class="t m0 x1c h17 y5c ff8 fs2 fc0 sc0 lse wsc">\ued3f<span class="blank _d"> </span>\uf346<span class="blank"> </span>\ue974<span class="blank _4"> </span>\uf34c<span class="blank _4"> </span>\uf346<span class="blank _3"> </span>\ue976<span class="ff9 ws15"> </span></div><div class="t m0 x1 h17 y5d ff9 fs2 fc0 sc0 lse ws15">Entonces: </div><div class="t m0 x33 h17 y5e ff8 fs2 fc0 sc0 lse ws24">\ued3f<span class="blank _5"> </span>\uf34c<span class="blank"> </span>\uf346\ue974<span class="ff9 ws15"> </span></div><div class="t m0 x1 h17 y5f ff9 fs2 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h17 y60 ff9 fs2 fc0 sc0 lse ws15">Al resolver el ejercicio utilizamos los conceptos de función lineal, función cuadrática y de ecuaciones cuadráticas. </div><div class="t m0 x1 h17 y61 ff9 fs2 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h1e y62 ff5 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h1e y63 ff5 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h1e y64 ff5 fs3 fc0 sc0 lse ws15"> <span class="blank _9"> </span> </div></div><div class="c x0 y44 wa h24"><div class="t m0 x29 h25 y45 ff4 fs3 fc1 sc0 lse ws15"><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 y65 wc h2a" alt="" src="https://files.passeidireto.com/2744de54-7512-40cb-a3a1-ab34f88607c1/bg3.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2b y66 ff5 fs6 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h2 y67 ff1 fs0 fc0 sc0 lse ws15">MATEMÁTICA (6<span class="blank _0"></span><span class="lsf ws0">1)<span class="ff2 lse ws15"> Cátedra A: <span class="blank _0"></span>NUÑEZ, MYRIA<span class="blank _0"></span>M<span class="ff1"> RECUPER<span class="blank _0"></span>ATORIO 1° PARCIAL<span class="blank _0"></span> </span></span></span></div><div class="t m0 x1 h2 y68 ff2 fs0 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h2 y69 ff2 fs0 fc0 sc0 lse ws15">APELLIDO Y NOMB<span class="blank _0"></span>RE: <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="ls20"> </span><span class="ws2">D<span class="blank _0"></span>NI:<span class="ff1 ws15"> <span class="blank _a"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span>TEMA 3 </span></span></div><div class="t m0 x3 h2 y6a ff2 fs0 fc0 sc0 lse ws15">Hoja 3 de 4 </div><div class="t m0 x3 h2 y6b ff2 fs0 fc0 sc0 lse ws15"> </div><div class="t m0 x2 h2 y6c ff1 fs0 fc0 sc0 lse ws15"> </div><div class="t m0 x1 he y6d ff7 fs2 fc0 sc0 lse ws15">3. Hallar el conjunto de positividad de la función <span class="ff8 ls21">\uee8c<span class="ls0 v1">\udb80\udddb</span><span class="ls22">\uee9e<span class="ls23 v1">\udb80\udddc</span><span class="ls24">\uf34c<span class="fs7 lse ws5 v2">\uf13f\uf0db</span></span></span></span></div><div class="t m0 x34 h10 y6e ff8 fs7 fc0 sc0 ls25">\uee9e<span class="fs8 ls26 va">\uf0db</span><span class="lse ws25">\uf13e\uf0da<span class="blank"> </span><span class="fs2 wsc v3">\uf345<span class="blank"> </span>\uf0da<span class="ff7 ws15"> </span></span></span></div><div class="t m0 x35 h17 y6f ff9 fs2 fc0 sc0 lse ws15">Solución: </div><div class="t m0 x1 h17 y70 ff9 fs2 fc0 sc0 lse ws15">Para <span class="blank _7"> </span>resolver <span class="blank _e"> </span>esta <span class="blank _e"> </span>activi<span class="blank _3"> </span>dad <span class="blank _7"> </span>se <span class="blank _e"> </span>trabajarán <span class="blank _e"> </span>los <span class="blank _e"> </span>si<span class="blank _3"> </span>guientes <span class="blank _7"> </span>contenidos <span class="blank _e"> </span>abord<span class="blank _3"> </span>ados <span class="blank _7"> </span>durante <span class="blank _e"> </span>el <span class="blank _e"> </span>cuatrime<span class="blank _3"> </span>stre: <span class="blank _7"> </span>Números </div><div class="t m0 x1 h17 y71 ff9 fs2 fc0 sc0 lse ws15">Reales- <span class="blank _0"></span>Ecuaciones e <span class="blank _0"></span>inecuaciones- intervalo- <span class="blank _0"></span>Funciones- F<span class="blank _0"></span>unciones cuadráticas- <span class="blank _0"></span>Funciones <span class="blank _0"></span>polinómicas -Estudio </div><div class="t m0 x1 h17 y72 ff9 fs2 fc0 sc0 lse ws15">de una función. </div><div class="t m0 x1 h17 y73 ff9 fs2 fc0 sc0 lse ws15">Antes <span class="blank _3"> </span>de <span class="blank _7"> </span>comenzar <span class="blank _7"> </span>con <span class="blank _7"> </span>el <span class="blank _7"> </span>análisis <span class="blank _7"> </span>de <span class="blank _3"> </span>la <span class="blank _7"> </span>función <span class="blank _7"> </span>vamos <span class="blank _7"> </span>a <span class="blank _3"> </span>determinar <span class="blank _7"> </span>el <span class="blank _7"> </span>dominio <span class="blank _7"> </span>de <span class="blank _7"> </span>la <span class="blank _7"> </span>misma, <span class="blank _3"> </span>para <span class="blank _7"> </span>ello <span class="blank _7"> </span>debemos </div><div class="t m0 x1 h17 y74 ff9 fs2 fc0 sc0 lse ws15">recordar <span class="blank _0"></span>que <span class="blank _11"></span>las <span class="blank _11"></span>funciones rac<span class="blank _0"></span>ionales <span class="blank _11"></span>ti<span class="blank _3"> </span>enen <span class="blank _11"></span>como <span class="blank _0"></span>puntos <span class="blank _0"></span>restringidos <span class="blank _11"></span>aquellos valore<span class="blank _0"></span>s <span class="blank _0"></span>que <span class="blank _11"></span>anulan e<span class="blank _0"></span>l <span class="blank _0"></span>denominador, </div><div class="t m0 x1 h17 y75 ff9 fs2 fc0 sc0 lse ws15">por lo tanto: </div><div class="t m0 x36 h27 y76 ff8 fs2 fc0 sc0 ls27">\ued54<span class="fs7 ls1b v9">\uf136</span><span class="lse ws10">\uf345<span class="blank"> </span>\ue973<span class="blank _4"> </span>\uf34d<span class="blank _4"> </span>\ue972<span class="ff9 ws15"> </span></span></div><div class="t m0 x37 h27 y77 ff8 fs2 fc0 sc0 ls27">\ued54<span class="fs7 ls28 v9">\uf136</span><span class="lse ws26">\uf34d<span class="blank _4"> </span>\uf346\ue973\ue603\ue603\ue603\ue603\ued54<span class="blank _5"> </span>\uebd1<span class="blank _4"> </span>\ued34<span class="blank"> </span><span class="ff9 ws15"> </span></span></div><div class="t m0 x1 h17 y78 ff9 fs2 fc0 sc0 lse ws15">De la expresión anterior determinamos<span class="ff8 ws27">\ue7e3\ue603\ued26\ued4b\ued49<span class="blank"> </span>\ue603\ued42<span class="blank _5"> </span>\uf34c<span class="blank _4"> </span>\ue603\ued34<span class="blank _3"> </span></span> </div><div class="t m0 x1 h17 y79 ff9 fs2 fc0 sc0 lse ws15">Para determinar los c<span class="blank _0"></span>onjuntos de positividad de la función debemos analizar su comporta<span class="blank _0"></span>miento y recordar que<span class="blank _0"></span> se </div><div class="t m0 x1 h17 y7a ff9 fs2 fc0 sc0 lse ws15">denomina <span class="blank _3"> </span>conjunto <span class="blank _7"> </span>de <span class="blank _7"> </span>positividad <span class="blank _7"> </span>de <span class="blank _7"> </span>la <span class="blank _7"> </span>función <span class="blank _3"> </span>al <span class="blank _7"> </span>conjunto <span class="blank _7"> </span>de <span class="blank _7"> </span>valores <span class="blank _3"> </span>del <span class="blank _7"> </span>dominio <span class="blank _7"> </span>par<span class="blank _3"> </span>a <span class="blank _7"> </span>los <span class="blank _7"> </span>cuales <span class="blank _3"> </span>la <span class="blank _7"> </span>función <span class="blank _7"> </span>es </div><div class="t m0 x1 h17 y7b ff9 fs2 fc0 sc0 lse ws15">positiva. </div><div class="t m0 x15 he y7c ff9 fs2 fc0 sc0 lse ws15"> <span class="ff8 ls4">\ued42<span class="ls0 v1">\udb80\udddb</span><span class="ls5">\ued54<span class="ls2 v1">\udb80\udddc</span><span class="ls29">\uf34c<span class="fs7 lse ws5 v2">\uf13f\uf136</span></span></span></span></div><div class="t m0 x38 h11 y7d ff8 fs7 fc0 sc0 ls2a">\uf1eb<span class="fs8 ls2b va">\uf22e</span><span class="lse ws28">\uf13e\uf135<span class="blank"> </span><span class="fs2 wsc v3">\uf345<span class="blank"> </span>\ue973<span class="ff9 ws15"> </span></span></span></div><div class="t m0 x1 h17 y7e ff9 fs2 fc0 sc0 lse ws15">En la gráfica de la función <span class="ff8 ws29">\ued42<span class="blank"> </span>\udb80\udddb\ued54<span class="blank"> </span>\udb80\udddc<span class="blank"> </span></span> se puede observar que las dos raíces de la función son el punto </div><div class="t m0 x1 h17 y7f ff8 fs2 fc0 sc0 lse ws2a">\udb80\udddb\uf346\ue973\ue7e2<span class="blank"> </span>\ue972\udb80\udddc\ue603\ued55\ue603\udb80\udddb<span class="blank _3"> </span>\ue973\ue7e2<span class="blank"> </span>\ue972\udb80\udddc<span class="ff9 ws15">. Por lo tanto, utilizando la de<span class="blank _0"></span>finición de conjunto de positividad se deduce: </span></div><div class="t m0 x39 h12 y80 ff8 fs2 fc0 sc0 lse ws4">\uf346\ue974</div><div class="t m0 x24 h2c y81 ff8 fs2 fc0 sc0 ls27">\ued54<span class="fs7 ls1b ve">\uf136</span><span class="lse ws12">\uf345<span class="blank"> </span>\ue973<span class="blank"> </span><span class="wsc v7">\uf345<span class="blank"> </span>\ue973<span class="blank _4"> </span>\uf350<span class="blank _4"> </span>\ue972<span class="ff9 ws15"> </span></span></span></div><div class="t m0 x3a h12 y82 ff8 fs2 fc0 sc0 lse ws4">\uf346\ue974</div><div class="t m0 x30 h2d y83 ff8 fs2 fc0 sc0 ls27">\ued54<span class="fs7 ls1b ve">\uf136</span><span class="lse wsc">\uf345<span class="blank"> </span>\ue973<span class="blank"> </span><span class="ls18 v7">\uf345</span><span class="ls2c v8">\ued54</span><span class="fs7 ls1b vf">\uf136</span><span class="v8">\uf345<span class="blank"> </span>\ue973</span></span></div><div class="t m0 x3b h2c y83 ff8 fs2 fc0 sc0 ls2c">\ued54<span class="fs7 ls1b ve">\uf136</span><span class="lse wsc">\uf345<span class="blank"> </span>\ue973<span class="blank _4"> </span><span class="ws2b v7">\uf350<span class="blank"> </span>\ue972<span class="ff9 ws15"> </span></span></span></div><div class="t m0 x3a h27 y84 ff8 fs2 fc0 sc0 lse ws1c">\uf346\ue974<span class="blank _10"> </span>\uf345<span class="blank _10"> </span>\ued54<span class="blank"> </span><span class="fs7 ls2d v9">\uf136</span><span class="ws2c">\uf345<span class="blank"> </span>\ue973</span></div><div class="t m0 x36 h2c y85 ff8 fs2 fc0 sc0 ls27">\ued54<span class="fs7 ls1b ve">\uf136</span><span class="lse ws10">\uf345<span class="blank"> </span>\ue973<span class="blank _12"> </span><span class="ws2b v7">\uf350<span class="blank"> </span>\ue972<span class="ff9 ws15"> </span></span></span></div><div class="t m0 x36 h27 y86 ff8 fs2 fc0 sc0 ls27">\ued54<span class="fs7 ls1b v9">\uf136</span><span class="lse ws10">\uf346<span class="blank"> </span>\ue973</span></div><div class="t m0 x36 h2c y87 ff8 fs2 fc0 sc0 ls27">\ued54<span class="fs7 ls1b ve">\uf136</span><span class="lse ws10">\uf345<span class="blank"> </span>\ue973<span class="blank _4"> </span><span class="ws2d v7">\uf350<span class="blank"> </span>\ue972<span class="ff9 ws15"> </span></span></span></div><div class="t m0 x1 h17 y88 ff9 fs2 fc0 sc0 lse ws15">Recordemos <span class="blank _8"> </span>que <span class="blank _f"> </span>el <span class="blank _f"> </span>co<span class="blank _3"> </span>ciente <span class="blank _f"> </span>de <span class="blank _f"> </span>dos <span class="blank _f"> </span>expresiones <span class="blank _f"> </span>es <span class="blank _f"> </span>mayor <span class="blank _f"> </span>a <span class="blank _f"> </span>cero <span class="blank _f"> </span>sí <span class="blank _f"> </span>ambas <span class="blank _f"> </span>expresiones <span class="blank _f"> </span>son <span class="blank _f"> </span>positivas <span class="blank _f"> </span>o <span class="blank _f"> </span>ambas </div><div class="t m0 x1 h17 y89 ff9 fs2 fc0 sc0 lse ws15">negativas, es decir que el numerador es mayor a<span class="blank _0"></span> cero <span class="blank _3"> </span>y e<span class="blank _0"></span>l denominador es ma<span class="blank _3"> </span>y<span class="blank _0"></span>or a cero, o viceversa. <span class="blank _3"> </span> </div><div class="t m0 x1 h17 y8a ff9 fs2 fc0 sc0 lse ws15">Opción 1: +/+ </div><div class="t m0 x28 h27 y8b ff8 fs2 fc0 sc0 ls27">\ued54<span class="fs7 ls1b v9">\uf136</span><span class="lse ws1c">\uf346<span class="blank _10"> </span>\ue973<span class="blank _4"> </span>\uf350<span class="blank _4"> </span>\ue972\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank _3"> </span>\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank _10"> </span>\uebe8<span class="blank _10"> </span>\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ued54<span class="blank"> </span><span class="fs7 ls1b v9">\uf136</span>\uf345<span class="blank _d"> </span>\ue973<span class="blank _4"> </span>\uf350<span class="blank _4"> </span>\ue972\ue603<span class="blank _4"> </span>\ueb5c<span class="blank _13"> </span>\ue603<span class="blank _f"> </span>\ued54<span class="blank"> </span><span class="fs7 ls28 v9">\uf136</span><span class="ws2d">\uf350<span class="blank"> </span>\uf346\ue973<span class="ff9 ws15"> </span></span></span></div><div class="t m0 x1 h17 y8c ff8 fs2 fc0 sc0 lse ws4">\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="ls2e v1">\ue801</span><span class="ls5">\ued54<span class="ls2f v1">\ue801</span></span><span class="ws2e">\uf350<span class="blank"> </span>\ue973\ue603\ue603\ue603\ue603<span class="ff9 ws15"> El conjunto de números Reales </span></span></div><div class="t m0 x1 h17 y8d ff9 fs2 fc0 sc0 lse ws15">Pues una expresión elevada al cuadrado va dar por resultado un número positivo y este es mayor a -1. </div><div class="t m0 x1 h17 y8e ff9 fs2 fc0 sc0 lse ws15">De la expresión anterior se deduce: </div><div class="t m0 x3c h2e y8f ff8 fs2 fc0 sc0 ls2e">\ue801<span class="ls5 vd">\ued54</span><span class="ls30">\ue801<span class="lse ws2d vd">\uf350<span class="blank"> </span>\ue973\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank"> </span>\ueb5c<span class="blank"> </span>\ue603\ue603\ue603\ue603\ued54<span class="blank _5"> </span>\uf350<span class="blank"> </span>\ue973\ue603\ue603\ue603\ue603\ue603\ue603\uec80\ue603\ue603\ued54<span class="blank _5"> </span>\uf34f<span class="blank"> </span>\uf346\ue973\ue603\ue603\ued35\ued4b\ued48\ued51\ued3f\ued45\ue6d7\ued4a<span class="blank _3"> </span>\ue603\ue973<span class="blank"> </span>\uf34c<span class="blank"> </span></span><span class="ls0">\udb80\udddb<span class="lse ws2f vd">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346\ue973</span><span class="ls31">\udb80\udddc<span class="ls32 vd">\uebeb</span></span>\udb80\udddb<span class="lse ws30 vd">\ue973\ue7e2<span class="blank"> </span>\uf345\ue9bb</span>\udb80\udddc<span class="ff9 lse ws15 vd"> </span></span></span></div><div class="t m0 x1 h17 y90 ff9 fs2 fc0 sc0 lse ws15">Opción 2: -/- </div></div><div class="c x0 y91 wa h2f"><div class="t m0 x29 h25 y45 ff4 fs3 fc1 sc0 lse ws15"><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"><div class="c x0 y1 w2 h0"><div class="t m0 x28 h27 y92 ff8 fs2 fc0 sc0 ls27">\ued54<span class="fs7 ls1b v9">\uf136</span><span class="lse ws1c">\uf346<span class="blank _10"> </span>\ue973<span class="blank _4"> </span>\uf34f<span class="blank _4"> </span>\ue972\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank _3"> </span>\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank _10"> </span>\uebe8<span class="blank _10"> </span>\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ued54<span class="blank"> </span><span class="fs7 ls1b v9">\uf136</span>\uf345<span class="blank _d"> </span>\ue973<span class="blank _4"> </span>\uf34f<span class="blank _4"> </span>\ue972\ue603<span class="blank _4"> </span>\ueb5c<span class="blank _13"> </span>\ue603<span class="blank _f"> </span>\ued54<span class="blank"> </span><span class="fs7 ls28 v9">\uf136</span><span class="ws2d">\uf34f<span class="blank"> </span>\uf346\ue973<span class="ff9 ws15"> </span></span></span></div><div class="t m0 x1 h17 y93 ff8 fs2 fc0 sc0 lse ws4">\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="ls2e v1">\ue801</span><span class="ls5">\ued54<span class="ls33 v1">\ue801</span></span><span class="ws2b">\uf350<span class="blank"> </span>\ue973\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank _3"> </span>\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="ff9 ws15">(Conjunto vacío) </span></span></div><div class="t m0 x1 h17 y94 ff9 fs2 fc0 sc0 lse ws15">Pues una expresión elevada al cuadrado va dar por resultado un númer<span class="blank _0"></span>o positivo <span class="blank _3"> </span>y<span class="blank _11"></span> <span class="blank _3"> </span>este nunca es menor a -1. <span class="blank _3"> </span> </div><div class="t m0 x1 h17 y95 ff9 fs2 fc0 sc0 lse ws15">De la expresión anterior se deduce: </div><div class="t m0 x3d h2e y96 ff8 fs2 fc0 sc0 ls2e">\ue801<span class="ls5 vd">\ued54</span><span class="ls30">\ue801<span class="lse ws2d vd">\uf350<span class="blank"> </span>\ue973\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank"> </span>\ueb5c<span class="blank"> </span>\ue603\ue603\ue603\ue603\ued54<span class="blank _5"> </span>\uf350<span class="blank"> </span>\ue973\ue603\ue603\ue603\ue603\ue603\ue603\uec80\ue603\ue603\ued54<span class="blank _5"> </span>\uf34f<span class="blank"> </span>\uf346\ue973\ue603<span class="ff9 ws15"> </span></span></span></div><div class="t m0 x3e h17 y97 ff8 fs2 fc0 sc0 lse ws31">\ued35\ued4b\ued48\ued51\ued3f\ued45\ue6d7\ued4a\ue603\ue974<span class="blank _4"> </span>\uf34c<span class="blank _5"> </span><span class="ls0 v1">\udb80\udddb</span><span class="ws2f">\uf346\ue973\ue7e2<span class="blank"> </span>\ue973<span class="ls31 v1">\udb80\udddc</span><span class="ws32">\uebea<span class="blank"> </span>\uebce<span class="blank _4"> </span>\uf34c<span class="blank _4"> </span><span class="ls1 v1">\udb80\udddd</span><span class="ls1e">\uebce</span><span class="ws4 v1">\udb80\uddde</span><span class="ff9 ws15"> </span></span></span></div><div class="t m0 x1 h17 y98 ff9 fs2 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h17 y4c ff9 fs2 fc0 sc0 lse ws15">Por lo tanto, el conjunto de positividad es la solución 1 </div><div class="t m0 x3f h27 y99 ff8 fs2 fc0 sc0 ls34">\ued25<span class="fs7 ls35 v9">\uf13e</span><span class="ls7">\uf34c<span class="ls0 v1">\udb80\udddb</span><span class="lse ws2f">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346\ue973<span class="ls31 v1">\udb80\udddc</span><span class="ls32">\uebeb<span class="ls0 v1">\udb80\udddb</span></span><span class="ws30">\ue973\ue7e2<span class="blank"> </span>\uf345\ue9bb<span class="ws4 v1">\udb80\udddc</span><span class="ff9 ws15"> </span></span></span></span></div><div class="t m0 x1 h6 y9a ff3 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x33 h6 y9b ff3 fs3 fc0 sc0 lse ws15"> <span class="blank _9"> </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="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y9c wb h30" alt="" src="https://files.passeidireto.com/2744de54-7512-40cb-a3a1-ab34f88607c1/bg5.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 lse ws15">MATEMÁTICA (6<span class="lsf ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls14"> <span class="ls15"> </span></span>RECUPERATOR<span class="blank _3"> </span>IO 1° PARC<span class="blank _3"> </span>IAL </div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 lse ws15">APELLIDO Y NOMBR<span class="blank _0"></span>E: <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> DNI:<span class="ff1"> <span class="blank _a"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span>TEMA 3 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 lse ws15">Hoja 4 de 4 </div><div class="t m0 x3 h2 y47 ff2 fs0 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h25 y9d ff4 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x1 he y9e ff7 fs2 fc0 sc0 lse ws15">4. Hallar <span class="ff8 ws4">\uee8c<span class="fs7 ws33 v9">\uf13f\uf0da<span class="blank"> </span></span><span class="ls0 v1">\udb80\udddb</span><span class="ls1">\uee9e</span><span class="v1">\udb80\udddc</span></span> , <span class="ff8 ws8">\uee88<span class="blank"> </span>\uebd0<span class="blank"> </span>\ueb39</span>; tal que <span class="ff8 ws4">\uee8c<span class="ls0 v1">\udb80\udddb</span><span class="ls1">\uee9e<span class="ls2 v1">\udb80\udddc</span><span class="ls3">\uf34c<span class="fs7 ls11 ws34 v2">\uf0db\uee88<span class="lse ws5">\uf13f\uee9e</span></span></span></span></span></div><div class="t m0 x40 h10 y9f ff8 fs7 fc0 sc0 lse ws35">\uf13f\uf0dc<span class="blank"> </span><span class="ff7 fs2 ws15 v3"> , si: <span class="ff8 ws4">\uee8c<span class="ls0 v1">\udb80\udddb</span>\uf346\uee88<span class="ls23 v1">\udb80\udddc</span><span class="ws24">\uf34c<span class="blank"> </span>\uee8c</span></span></span><span class="ws36 v10">\uf13f\uf0da<span class="blank"> </span></span><span class="fs2 ls0 v11">\udb80\udddb<span class="ls18 ws18 vd">\uee88\uf346\uf0da<span class="blank _c"></span><span class="lse ws4 v1">\udb80\udddc<span class="ff7 ws15 vd"> </span></span></span></span></div><div class="t m0 x1 h17 ya0 ff9 fs2 fc0 sc0 lse ws15">Para la realización de este ejercicio, recomenda<span class="blank _0"></span>mos ver <span class="blank _3"> </span>apuntes de: Función inversa </div><div class="t m0 x1 h27 ya1 ff9 fs2 fc0 sc0 lse ws15">Para <span class="blank _7"> </span>hallar <span class="blank _e"> </span>la <span class="blank _e"> </span>función <span class="blank _7"> </span>in<span class="blank _3"> </span>versa <span class="blank _7"> </span>de <span class="blank _8"> </span><span class="ff8 ws1b">\ued42<span class="blank"> </span>\udb80\udddb<span class="blank"> </span>\ued54<span class="blank"> </span>\udb80\udddc</span>, <span class="blank _7"> </span>como <span class="blank _e"> </span>nos <span class="blank _e"> </span>dan <span class="blank _7"> </span>de <span class="blank _e"> </span>dato <span class="blank _e"> </span>que <span class="blank _e"> </span><span class="ff8 ls4">\ued42<span class="ls0 v1">\udb80\udddb</span><span class="lse ws37">\uf346\ued3e<span class="blank"> </span><span class="ls23 v1">\udb80\udddc</span><span class="ws38">\uf34c<span class="blank _5"> </span>\ued42<span class="blank"> </span><span class="fs7 ws39 v9">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v1">\udb80\udddb</span><span class="wsc">\ued3e<span class="blank"> </span>\uf346<span class="blank"> </span>\ue973<span class="ls0 v1">\udb80\udddc</span></span></span></span></span>, <span class="blank _e"> </span>basta <span class="blank _e"> </span>con <span class="blank _e"> </span>encontrar <span class="blank _7"> </span>l<span class="blank _3"> </span>a </div><div class="t m0 x1 h27 ya2 ff9 fs2 fc0 sc0 lse ws15">imagen de <span class="ff8 ws3a">\ued42<span class="blank"> </span>\udb80\udddb\ued54<span class="blank"> </span>\udb80\udddc<span class="blank"> </span></span>, ya que la misma será el dominio de <span class="ff8 ls36">\ued42<span class="fs7 lse ws3b v9">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v1">\udb80\udddb</span><span class="ls5">\ued54<span class="ls0 v1">\udb80\udddc</span><span class="lse ws4">\ue7e4</span></span></span> </div><div class="t m0 x1 h17 ya3 ff9 fs2 fc0 sc0 lse ws15">Al <span class="blank _3"> </span>despejar <span class="blank _3"> </span>l<span class="blank _3"> </span>a <span class="blank _7"> </span><span class="ff8 ws4">\ue7f2\ued54\ue7f3</span> <span class="blank _3"> </span>de <span class="blank _7"> </span>la <span class="blank _3"> </span>función <span class="blank _7"> </span><span class="ff8 ls4">\ued42</span>, <span class="blank _7"> </span>y <span class="blank _3"> </span>realizando <span class="blank _7"> </span>un <span class="blank _3"> </span>ca<span class="blank _3"> </span>mbio <span class="blank _7"> </span><span class="ffb">de <span class="blank _3"> </span>variables <span class="blank _7"> </span>(intercambiamos <span class="blank _3"> </span>a <span class="blank _3"> </span>cada <span class="blank _7"> </span>\u201cy\u201d <span class="blank _3"> </span>po<span class="blank _3"> </span>r <span class="blank _3"> </span>\u201cx\u201d <span class="blank _7"> </span>y <span class="blank _3"> </span>la </span></div><div class="t m0 x1 h17 ya4 ffb fs2 fc0 sc0 lse ws15">\u201cx\u201d por \u201cy\u201d), lograremos encontrar dicha función inversa<span class="blank _0"></span>:<span class="blank _3"> </span><span class="ff9"> </span></div><div class="t m0 x41 h31 ya5 ff8 fs2 fc0 sc0 lse ws3c">\ued55<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="wsc v6">\ue974\ued3e<span class="blank"> </span>\uf346<span class="blank"> </span>\ued54</span></div><div class="t m0 x42 h2c ya6 ff8 fs2 fc0 sc0 lse ws3d">\uf346\ue975<span class="blank"> </span><span class="ff9 ws15 v7"> </span></div><div class="t m0 x39 h17 ya7 ff8 fs2 fc0 sc0 lse ws3e">\uf346\ue975\ued55<span class="blank _4"> </span>\uf34c<span class="blank _5"> </span>\ue974\ued3e<span class="blank _10"> </span>\uf346<span class="blank _d"> </span>\ued54<span class="blank"> </span><span class="ff9 ws15"> </span></div><div class="t m0 x43 h17 ya8 ff8 fs2 fc0 sc0 lse ws1b">\uf346\ue975\ued55<span class="blank _d"> </span>\uf346<span class="blank _10"> </span>\ue974\ued3e<span class="blank _5"> </span>\uf34c<span class="blank _4"> </span>\uf346\ued54<span class="blank"> </span><span class="ff9 ws15"> </span></div><div class="t m0 x1b h17 ya9 ff8 fs2 fc0 sc0 lse ws37">\ued54<span class="blank _5"> </span>\uf34c<span class="blank _4"> </span>\ue975\ued55<span class="blank _d"> </span>\uf345<span class="blank _10"> </span>\ue974\ued3e<span class="blank"> </span><span class="ff9 ws15"> </span></div><div class="t m0 x1 h17 yaa ff9 fs2 fc0 sc0 lse ws15">Realizando el cambio de variables que mencionamos anteriormente, nos quedará<span class="blank _0"></span>:<span class="blank _3"> </span> </div><div class="t m0 x1b h17 yab ff8 fs2 fc0 sc0 lse ws37">\ued55<span class="blank _4"> </span>\uf34c<span class="blank _5"> </span>\ue975\ued54<span class="blank _d"> </span>\uf345<span class="blank _10"> </span>\ue974\ued3e<span class="blank"> </span><span class="ff9 ws15"> </span></div><div class="t m0 x1 h17 yac ff9 fs2 fc0 sc0 lse ws15">Es decir que, la función inversa es: </div><div class="t m0 x2c h27 yad ff8 fs2 fc0 sc0 ls36">\ued42<span class="fs7 lse ws3f v9">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v1">\udb80\udddb</span><span class="ls5">\ued54<span class="ls37 v1">\udb80\udddc</span><span class="lse ws40">\uf34c<span class="blank _4"> </span>\ue975\ued54<span class="blank _d"> </span>\uf345<span class="blank _d"> </span>\ue974\ued3e<span class="blank"> </span><span class="ff9 ws15"> </span></span></span></div><div class="t m0 x1 h27 yae ff9 fs2 fc0 sc0 lse ws15">Como <span class="blank _8"> </span>sabemos <span class="blank _8"> </span>que <span class="blank _f"> </span><span class="ff8 ls4">\ued42<span class="ls0 v1">\udb80\udddb</span><span class="lse ws37">\uf346\ued3e<span class="blank"> </span><span class="ls2 v1">\udb80\udddc</span><span class="ws38">\uf34c<span class="blank _4"> </span>\ued42<span class="blank"> </span><span class="fs7 ws3f v9">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v1">\udb80\udddb</span><span class="wsc">\ued3e<span class="blank _d"> </span>\uf346<span class="blank"> </span>\ue973<span class="ws4 v1">\udb80\udddc</span></span></span></span></span>, <span class="blank _8"> </span>si <span class="blank _f"> </span>evaluamos <span class="blank _8"> </span>en<span class="blank _3"> </span> <span class="blank _8"> </span>cada <span class="blank _8"> </span>miembro <span class="blank _f"> </span>de <span class="blank _8"> </span>la <span class="blank _f"> </span>igualdad <span class="blank _8"> </span>y <span class="blank _8"> </span>l<span class="blank _3"> </span>uego <span class="blank _8"> </span>despejamos, </div><div class="t m0 x1 h17 yaf ffb fs2 fc0 sc0 lse ws15">podremos obtener \u201c<span class="ff8 ls38">\ued3e</span>\u201d y por lo tanto la función inversa pedida:<span class="ff9"> </span></div><div class="t m0 x2e h27 yb0 ff8 fs2 fc0 sc0 ls36">\ued42<span class="fs7 lse ws3f v9">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v1">\udb80\udddb</span><span class="lse wsc">\ued3e<span class="blank"> </span>\uf346<span class="blank"> </span>\ue973<span class="ls1d v1">\udb80\udddc</span><span class="ws1e">\uf34c<span class="blank _4"> </span>\ue603\ue975\ue7e4<span class="blank"> </span><span class="ls0 v1">\udb80\udddb</span></span>\ued3e<span class="blank _d"> </span>\uf346<span class="blank"> </span>\ue973<span class="ls31 v1">\udb80\udddc</span><span class="ws37">\uf345<span class="blank _10"> </span>\ue974\ued3e<span class="blank"> </span><span class="ff9 ws15"> </span></span></span></div><div class="t m0 x40 h27 yb1 ff8 fs2 fc0 sc0 ls36">\ued42<span class="fs7 lse ws3f v9">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v1">\udb80\udddb</span><span class="lse wsc">\ued3e<span class="blank _d"> </span>\uf346<span class="blank"> </span>\ue973<span class="ls37 v1">\udb80\udddc</span>\uf34c<span class="blank _4"> </span>\ue975\ued3e<span class="blank"> </span>\uf346<span class="blank"> </span>\ue975<span class="blank _d"> </span>\uf345<span class="blank"> </span>\ue974\ued3e<span class="blank _3"> </span><span class="ff9 ws15"> </span></span></div><div class="t m0 x31 h27 yb2 ff8 fs2 fc0 sc0 ls36">\ued42<span class="fs7 lse ws3f v9">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v1">\udb80\udddb</span><span class="lse ws10">\ued3e<span class="blank"> </span>\uf346<span class="blank"> </span>\ue973<span class="ls2 v1">\udb80\udddc</span><span class="wsc">\uf34c<span class="blank _5"> </span>\ue977\ued3e<span class="blank _d"> </span>\uf346<span class="blank"> </span>\ue975<span class="ff9 ws15"> </span></span></span></div></div><div class="c x0 y44 wa h24"><div class="t m0 x29 h25 y45 ff4 fs3 fc1 sc0 lse ws15"><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="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x3a yb3 wd h32" alt="" src="https://files.passeidireto.com/2744de54-7512-40cb-a3a1-ab34f88607c1/bg6.png"><div class="c x0 y1 w2 h0"><div class="t m0 x44 h17 yb4 ff9 fs2 fc0 sc0 lse ws15"> </div><div class="t m0 x3a h31 yb5 ff8 fs2 fc0 sc0 ls4">\ued42<span class="ls0 v1">\udb80\udddb</span><span class="lse ws37">\uf346\ued3e<span class="blank"> </span><span class="ls23 v1">\udb80\udddc</span><span class="ls39">\uf34c</span><span class="wsc v6">\ue974\ued3e<span class="blank _d"> </span>\uf346<span class="blank"> </span>\udb80\udddb\uf346\ued3e<span class="blank _3"> </span>\udb80\udddc</span></span></div><div class="t m0 x45 h33 yb6 ff8 fs2 fc0 sc0 lse ws41">\uf346\ue975<span class="blank"> </span><span class="ff9 ws15 v7"> </span></div><div class="t m0 x8 h31 yb7 ff8 fs2 fc0 sc0 ls4">\ued42<span class="ls0 v1">\udb80\udddb</span><span class="lse ws42">\uf346\ued3e<span class="blank"> </span><span class="ls2 v1">\udb80\udddc</span><span class="ls3a">\uf34c</span><span class="ws4 v6">\ue975\ued3e</span></span></div><div class="t m0 x45 h2c yb8 ff8 fs2 fc0 sc0 lse ws4">\uf346\ue975<span class="ff9 ws15 v7"> </span></div><div class="t m0 x8 h17 yb9 ff8 fs2 fc0 sc0 ls4">\ued42<span class="ls0 v1">\udb80\udddb</span><span class="lse ws42">\uf346\ued3e<span class="blank"> </span><span class="ls23 v1">\udb80\udddc</span><span class="ws37">\uf34c<span class="blank _4"> </span>\uf346\ued3e<span class="blank"> </span><span class="ff9 ws15"> </span></span></span></div><div class="t m0 x44 h17 yba ff9 fs2 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h17 ybb ff9 fs2 fc0 sc0 lse ws15">Es decir que: </div><div class="t m0 x46 h27 ybc ff8 fs2 fc0 sc0 ls36">\ued42<span class="fs7 lse ws3f v9">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v1">\udb80\udddb</span><span class="lse wsc">\ued3e<span class="blank _d"> </span>\uf346<span class="blank"> </span>\ue973<span class="ls2 v1">\udb80\udddc</span><span class="ws43">\uf34c<span class="blank _4"> </span>\ued42<span class="blank"> </span>\udb80\udddb\ued3e<span class="blank"> </span>\udb80\udddc<span class="ff9 ws15">, entonces </span><span class="ws37">\ue977\ued3e<span class="blank _d"> </span>\uf346<span class="blank _10"> </span>\ue975<span class="blank _4"> </span>\uf34c<span class="blank _4"> </span>\uf346\ued3e<span class="blank"> </span><span class="ff9 ws15"> </span></span></span></span></div><div class="t m0 x41 h17 ybd ff8 fs2 fc0 sc0 lse ws10">\ue977\ued3e<span class="blank _d"> </span>\uf345<span class="blank"> </span>\ued3e<span class="blank _5"> </span>\uf34c<span class="blank _4"> </span>\ue975<span class="ff9 ws15"> </span></div><div class="t m0 x1c h17 ybe ff8 fs2 fc0 sc0 lse ws8">\ue978\ued3e<span class="blank _5"> </span>\uf34c<span class="blank"> </span>\ue975<span class="ff9 ws15"> </span></div><div class="t m0 x47 h34 ybf ff8 fs2 fc0 sc0 lse ws24">\ued3e<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="v6">\ue973</span></div><div class="t m0 x48 h2c yc0 ff8 fs2 fc0 sc0 lse ws4">\ue974<span class="ff9 ws15 v7"> </span></div><div class="t m0 x1 h27 yc1 ff9 fs2 fc0 sc0 lse ws15">Reemplazando en <span class="ff8 ls36">\ued42<span class="fs7 lse ws3f v9">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v1">\udb80\udddb</span><span class="ls5">\ued54<span class="ls23 v1">\udb80\udddc</span><span class="lse ws40">\uf34c<span class="blank _4"> </span>\ue975\ued54<span class="blank _4"> </span>\uf345<span class="blank _10"> </span>\ue974\ued3e<span class="blank"> </span></span></span></span>, resultará: </div><div class="t m0 x31 h31 yc2 ff8 fs2 fc0 sc0 ls36">\ued42<span class="fs7 lse ws3f v9">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v1">\udb80\udddb</span><span class="ls5">\ued54<span class="ls2 v1">\udb80\udddc</span><span class="lse ws44">\uf34c<span class="blank _4"> </span>\ue975\ued54<span class="blank _d"> </span>\uf345<span class="blank _d"> </span>\ue974\ue603\ue7e4\ue603\ue603<span class="blank"> </span><span class="v6">\ue973</span></span></span></div><div class="t m0 x49 h2c yc3 ff8 fs2 fc0 sc0 lse ws4">\ue974<span class="ff9 ws15 v7"> </span></div><div class="t m0 x3a h27 yc4 ff8 fs2 fc0 sc0 ls36">\ued42<span class="fs7 lse ws3f v9">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v1">\udb80\udddb</span><span class="ls5">\ued54<span class="ls2 v1">\udb80\udddc</span><span class="lse wsc">\uf34c<span class="blank _4"> </span>\ue975\ued54<span class="blank _d"> </span>\uf345<span class="blank"> </span>\ue973<span class="ff9 ws15"> </span></span></span></div><div class="t m0 x1 h17 yc5 ff9 fs2 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h6 yc6 ff3 fs3 fc0 sc0 lse ws15"> </div><div class="t m0 x1 h35 yc7 ffc fs3 fc0 sc0 lse ws15"> </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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