<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/8396748b-aa44-4725-8f34-77061a97f2e7/bg1.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 lsb ws15">MATEMÁTICA (6<span class="lsc ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM </span></div><div class="t m0 x1 h2 y3 ff1 fs0 fc0 sc0 lsb ws15">RECUPERATORI<span class="blank _0"></span>O 1° PARCIAL </div><div class="t m0 x2 h2 y4 ff1 fs0 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h2 y5 ff2 fs0 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h3 y6 ff2 fs1 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h2 y7 ff2 fs0 fc0 sc0 lsd ws1">21<span class="lsb 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 2 </span></span></div><div class="t m0 x3 h2 y8 ff2 fs0 fc0 sc0 lsb ws15"> Hoja 1 de 4 </div><div class="t m0 x3 h2 y9 ff2 fs0 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h3 ya ff2 fs1 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h3 yb ff2 fs1 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h4 yc ff3 fs2 fc0 sc0 lsb 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 lsb ws15"> </div></div><div class="c x6 yd w4 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lsb ws15">1 </div></div><div class="c x8 yd w5 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lsb ws15">2 </div></div><div class="c x9 yd w6 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lsb ws15">3 </div></div><div class="c xa yd w7 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lsb ws15">4 </div></div><div class="c x4 yf w3 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsb ws15"> </div></div><div class="c x6 yf w4 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsb ws15"> </div></div><div class="c x8 yf w5 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsb ws15"> </div></div><div class="c x9 yf w6 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsb ws15"> </div></div><div class="c xa yf w7 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsb ws15"> </div></div><div class="c x4 y11 w5 h9"><div class="t m0 xb ha y12 ff4 fs4 fc0 sc0 lsb ws15">Puntaje de cada </div><div class="t m0 xb ha y13 ff4 fs4 fc0 sc0 lsb ws15">ejercicio </div></div><div class="c x6 y11 w4 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lsb ws15">2,50 </div></div><div class="c x8 y11 w5 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lsb ws15">2,50 </div></div><div class="c x9 y11 w6 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lsb ws15">2,50 </div></div><div class="c xa y11 w7 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lsb ws15">2,50 </div></div><div class="c x0 y1 w2 h0"><div class="t m0 x1 hb y15 ff5 fs5 fc0 sc0 lsb 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 lsb 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 lsb ws15"> </div><div class="t m0 x1 he y18 ff7 fs2 fc0 sc0 lsb ws15">1. Hallar <span class="ff8 ws4">\uee8c<span class="fs7 ws5 v1">\uf13f\uf0da<span class="blank"> </span></span><span class="ls0 v2">\udb80\udddb</span><span class="ls1">\uee9e</span><span class="v2">\udb80\udddc</span></span> , <span class="ff8 ws6">\uee87<span class="blank"> </span>\uebd0<span class="blank"> </span>\ueb39</span>; s<span class="ff9 lse">i <span class="ff8 ls2">\ued42<span class="ls0 v2">\udb80\udddb</span><span class="ls3">\ued54<span class="ls4 v2">\udb80\udddc</span><span class="ls5">\uf34c<span class="fs7 lsb ws7 v3">\uf13a\uf1d4\uf13f\uf1eb</span></span></span></span></span></div><div class="t m0 xd hf y19 ff8 fs7 fc0 sc0 lsb ws8">\uf13f\uf136<span class="blank"> </span><span class="ff9 fs2 ws15 v4"> , se cumple: <span class="ff8 ls6">\ued42<span class="ls0 v2">\udb80\udddb</span><span class="lsb ws9">\ue974\ued3d<span class="ls7 v2">\udb80\udddc</span><span class="wsa">\uf34c<span class="blank _4"> </span>\ued42<span class="blank"> </span></span></span></span></span><span class="wsb v5">\uf13f\uf135<span class="blank"> </span></span><span class="fs2 ls0 v6">\udb80\udddb</span><span class="fs2 wsc v4">\ued3d<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ue976<span class="ws4 v2">\udb80\udddc</span><span class="ff9 ws15"> </span></span></div><div class="t m0 x1 h10 y1a ff9 fs2 fc0 sc0 lsb ws15">Para la realización de este ejercicio, recomendamos ver apuntes de: Función inversa </div><div class="t m0 x1 h11 y1b ff9 fs2 fc0 sc0 lsb ws15">Para <span class="blank _6"> </span>hallar <span class="blank _6"> </span>la <span class="blank _6"> </span>función <span class="blank _6"> </span>in<span class="blank _3"> </span>versa <span class="blank _6"> </span>de <span class="blank _7"> </span><span class="ff8 wsd">\ued42<span class="blank"> </span>\udb80\udddb\ued54<span class="blank"> </span>\udb80\udddc</span>, <span class="blank _6"> </span>como <span class="blank _6"> </span>nos <span class="blank _7"> </span>dan <span class="blank _6"> </span>de <span class="blank _6"> </span>dato <span class="blank _6"> </span>que <span class="blank _7"> </span><span class="ff8 ls8">\ued42<span class="ls0 v2">\udb80\udddb</span><span class="lsb ws9">\ue974\ued3d<span class="blank"> </span><span class="ls4 v2">\udb80\udddc</span><span class="wsa">\uf34c<span class="blank _4"> </span>\ued42<span class="blank"> </span><span class="fs7 wse v1">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v2">\udb80\udddb</span><span class="wsc">\ued3d<span class="blank"> </span>\uf345<span class="blank"> </span>\ue976<span class="ls0 v2">\udb80\udddc</span></span></span></span></span>, <span class="blank _6"> </span>basta <span class="blank _7"> </span>con <span class="blank _6"> </span>encontrar <span class="blank _6"> </span>la </div><div class="t m0 x1 h11 y1c ff9 fs2 fc0 sc0 lsb ws15">imagen de <span class="ff8 wsf">\ued42<span class="blank"> </span>\udb80\udddb\ued54<span class="blank"> </span>\udb80\udddc</span>, ya que la misma será el dominio de <span class="ff8 ls9">\ued42<span class="fs7 lsb ws10 v1">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v2">\udb80\udddb</span><span class="ls3">\ued54<span class="ls0 v2">\udb80\udddc</span><span class="lsb ws4">\ue7e4</span></span></span> </div><div class="t m0 x1 h12 y1d ff9 fs2 fc0 sc0 lsb ws15">Al <span class="blank _3"> </span>despejar <span class="blank _3"> </span>l<span class="blank _3"> </span>a <span class="blank _6"> </span><span class="ff8 ws4">\ue7f2\ued54\ue7f3<span class="blank _0"></span><span class="ff9 ws15"> <span class="blank _3"> </span>de <span class="blank _6"> </span>la fun<span class="blank _3"> </span>ción <span class="blank _3"> </span><span class="ff8 ls8">\ued42</span><span class="ffa">, <span class="blank _6"> </span>y<span class="blank _0"></span> <span class="blank _6"> </span>realizando <span class="blank _3"> </span>un <span class="blank _3"> </span>cambio <span class="blank _6"> </span>de<span class="blank _0"></span> <span class="blank _3"> </span>variables <span class="blank _6"> </span>(intercambiamos <span class="blank _3"> </span>a <span class="blank _3"> </span>cada <span class="blank _3"> </span>\u201c<span class="blank _3"> </span>y\u201d <span class="blank _3"> </span>por <span class="blank _8"> </span>\u201cx\u201d <span class="blank _8"> </span>y l<span class="blank _3"> </span>a </span></span></span></div><div class="t m0 x1 h10 y1e ffa fs2 fc0 sc0 lsb 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 xf h13 y1f ff8 fs2 fc0 sc0 lsb ws11">\ued55<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="wsc v7">\ue978\ued3d<span class="blank _5"> </span>\uf346<span class="blank"> </span>\ued54</span></div><div class="t m0 x10 h14 y20 ff8 fs2 fc0 sc0 lsb ws12">\uf346\ue974<span class="blank"> </span><span class="ff9 ws15 v8"> </span></div><div class="t m0 x11 h12 y21 ff8 fs2 fc0 sc0 lsb ws13">\uf346\ue974\ued55<span class="blank _4"> </span>\uf34c<span class="blank _4"> </span>\ue978\ued3d<span class="blank _5"> </span>\uf346<span class="blank _9"> </span>\ued54<span class="blank"> </span><span class="ff9 ws15"> </span></div><div class="t m0 x12 h12 y22 ff8 fs2 fc0 sc0 lsb wsd">\uf346\ue974\ued55<span class="blank _5"> </span>\uf346<span class="blank _9"> </span>\ue978\ued3d<span class="blank _a"> </span>\uf34c<span class="blank _4"> </span>\uf346\ued54<span class="ff9 ws15"> </span></div><div class="t m0 x8 h12 y23 ff8 fs2 fc0 sc0 lsb ws9">\ued54<span class="blank _4"> </span>\uf34c<span class="blank _4"> </span>\ue974\ued55<span class="blank _5"> </span>\uf345<span class="blank _9"> </span>\ue978\ued3d<span class="blank"> </span><span class="ff9 ws15"> </span></div><div class="t m0 x1 h10 y24 ff9 fs2 fc0 sc0 lsb 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 x13 h12 y25 ff8 fs2 fc0 sc0 lsb ws9">\ued55<span class="blank _4"> </span>\uf34c<span class="blank _4"> </span>\ue974\ued54<span class="blank _5"> </span>\uf345<span class="blank _9"> </span>\ue978\ued3d<span class="blank"> </span><span class="ff9 ws15"> </span></div><div class="t m0 x1 h10 y26 ff9 fs2 fc0 sc0 lsb ws15">Es decir que, la función inversa es: </div><div class="t m0 x14 h11 y27 ff8 fs2 fc0 sc0 ls9">\ued42<span class="fs7 lsb wsb v1">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v2">\udb80\udddb</span><span class="ls3">\ued54<span class="lsa v2">\udb80\udddc</span><span class="lsb ws14">\uf34c<span class="blank _4"> </span>\ue974\ued54<span class="blank _5"> </span>\uf345<span class="blank _9"> </span>\ue978\ued3d<span class="blank"> </span><span class="ff9 ws15"> </span></span></span></div></div><div class="c x1 y28 w8 h15"><div class="t m0 x15 h2 y29 ff2 fs0 fc0 sc0 lsb ws15">APELLIDO: </div></div><div class="c x16 y2a w9 h16"><div class="t m0 xb h2 y2b ff2 fs0 fc0 sc0 lsb ws15">CALIFICACIÓN:<span class="blank _0"></span> </div></div><div class="c x1 y2c w8 h17"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lsb ws15">NOMBRE: </div></div><div class="c x1 y2a w8 h17"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lsb ws15">DNI (registrado en S<span class="blank _0"></span>IU Guaraní): </div></div><div class="c x1 y2d w8 h18"><div class="t m0 xb h2 y10 ff2 fs0 fc0 sc0 lsb ws15">E-MAIL: </div></div><div class="c x16 y2e w9 h19"><div class="t m0 xb h2 y2f ff2 fs0 fc0 sc0 lsb ws15">DOCENTE (nombre<span class="blank _0"></span> y apellido): </div></div><div class="c x1 y30 w8 h17"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lsb ws15">TEL: </div></div><div class="c x1 y2e w8 h17"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lsb ws15">AULA: </div></div><div class="c x0 y31 wa h1a"><div class="t m0 x15 h1b y32 ff4 fs3 fc1 sc0 lsb 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 x14 y33 wb h1c" alt="" src="https://files.passeidireto.com/8396748b-aa44-4725-8f34-77061a97f2e7/bg2.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h11 y34 ff9 fs2 fc0 sc0 lsb ws15">Como <span class="blank _b"> </span>sabemos <span class="blank _b"> </span>que <span class="blank _b"> </span><span class="ff8 ls8">\ued42<span class="ls0 v2">\udb80\udddb</span><span class="lsb ws9">\ue974\ued3d<span class="blank"> </span><span class="ls4 v2">\udb80\udddc</span><span class="wsa">\uf34c<span class="blank _4"> </span>\ued42<span class="blank"> </span><span class="fs7 wsb v1">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v2">\udb80\udddb</span><span class="wsc">\ued3d<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ue976<span class="ws4 v2">\udb80\udddc</span></span></span></span></span>, <span class="blank _7"> </span>si <span class="blank _b"> </span>evaluamos <span class="blank _b"> </span>en <span class="blank _b"> </span>cada <span class="blank _b"> </span>miembro <span class="blank _b"> </span>de <span class="blank _b"> </span>la <span class="blank _b"> </span>igualdad <span class="blank _b"> </span>y<span class="blank _0"></span> <span class="blank _c"> </span>luego <span class="blank _7"> </span>despejamos, </div><div class="t m0 x1 h12 y35 ff9 fs2 fc0 sc0 lsb ws16">podremo<span class="ffa ws15">s obtener \u201c<span class="ff8 lsf">\ued3d</span>\u201d y por lo tanto la función inversa pedida:<span class="ff9"> </span></span></div><div class="t m0 x17 h11 y36 ff8 fs2 fc0 sc0 ls9">\ued42<span class="fs7 lsb wsb v1">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v2">\udb80\udddb</span><span class="lsb wsc">\ued3d<span class="blank"> </span>\uf345<span class="blank"> </span>\ue976<span class="ls7 v2">\udb80\udddc</span><span class="ws17">\uf34c<span class="blank _4"> </span>\ue603\ue974\ue7e4<span class="blank"> </span><span class="ls0 v2">\udb80\udddb</span></span>\ued3d<span class="blank"> </span>\uf345<span class="blank"> </span>\ue976<span class="ls10 v2">\udb80\udddc</span><span class="ws14">\uf345<span class="blank _5"> </span>\ue978\ued3d<span class="blank"> </span><span class="ff9 ws15"> </span></span></span></div><div class="t m0 x18 h11 y37 ff8 fs2 fc0 sc0 ls9">\ued42<span class="fs7 lsb wsb v1">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v2">\udb80\udddb</span><span class="lsb ws18">\ued3d<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ue976<span class="ls11 v2">\udb80\udddc</span><span class="wsc">\uf34c<span class="blank _4"> </span>\ue974\ued3d<span class="blank"> </span>\uf345<span class="blank"> </span>\ue97a<span class="blank"> </span>\uf345<span class="blank"> </span>\ue978\ued3d<span class="blank _3"> </span><span class="ff9 ws15"> </span></span></span></div><div class="t m0 x19 h11 y38 ff8 fs2 fc0 sc0 ls9">\ued42<span class="fs7 lsb wsb v1">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v2">\udb80\udddb</span><span class="lsb ws19">\ued3d<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ue976<span class="ls4 v2">\udb80\udddc</span><span class="wsc">\uf34c<span class="blank _4"> </span>\ue97a\ued3d<span class="blank"> </span>\uf345<span class="blank"> </span>\ue97a<span class="ff9 ws15"> </span></span></span></div><div class="t m0 x1a h10 y39 ff9 fs2 fc0 sc0 lsb ws15"> </div><div class="t m0 x11 h13 y3a ff8 fs2 fc0 sc0 ls8">\ued42<span class="ls0 v2">\udb80\udddb</span><span class="ls3">\ued54<span class="lsa v2">\udb80\udddc</span><span class="ls12">\uf34c<span class="lsb wsc v7">\ue978\ued3d<span class="blank _5"> </span>\uf346<span class="blank"> </span>\ued54</span></span></span></div><div class="t m0 x1b h14 y3b ff8 fs2 fc0 sc0 lsb ws1a">\uf346\ue974<span class="blank"> </span><span class="ff9 ws15 v8"> </span></div><div class="t m0 x1c h13 y3c ff8 fs2 fc0 sc0 ls8">\ued42<span class="ls0 v2">\udb80\udddb</span><span class="lsb ws9">\ue974\ued3d<span class="lsa v2">\udb80\udddc</span><span class="ls12">\uf34c</span><span class="wsc v7">\ue978\ued3d<span class="blank _d"> </span>\uf346<span class="blank"> </span>\ue974\ued3d</span></span></div><div class="t m0 x1d h14 y3d ff8 fs2 fc0 sc0 lsb ws1b">\uf346\ue974<span class="blank"> </span><span class="ff9 ws15 v8"> </span></div><div class="t m0 x1e h13 y3e ff8 fs2 fc0 sc0 ls8">\ued42<span class="ls0 v2">\udb80\udddb</span><span class="lsb ws1c">\ue974\ued3d<span class="ls4 v2">\udb80\udddc</span><span class="ls13">\uf34c</span><span class="ws4 v7">\ue976\ued3d</span></span></div><div class="t m0 x1d h14 y3f ff8 fs2 fc0 sc0 lsb ws4">\uf346\ue974<span class="ff9 ws15 v8"> </span></div><div class="t m0 x1f h11 y40 ff8 fs2 fc0 sc0 ls8">\ued42<span class="ls0 v2">\udb80\udddb</span><span class="lsb ws1c">\ue974\ued3d<span class="ls4 v2">\udb80\udddc</span><span class="ws14">\uf34c<span class="blank _4"> </span>\uf346\ue974\ued3d<span class="blank"> </span><span class="ff9 ws15"> </span></span></span></div><div class="t m0 x1a h10 y41 ff9 fs2 fc0 sc0 lsb ws15">Es decir que: </div><div class="t m0 x20 h11 y42 ff8 fs2 fc0 sc0 ls9">\ued42<span class="fs7 lsb wsb v1">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v2">\udb80\udddb</span><span class="lsb wsc">\ued3d<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ue976<span class="ls4 v2">\udb80\udddc</span><span class="ws1c">\uf34c<span class="blank _d"> </span>\ued42<span class="blank"> </span>\udb80\udddb<span class="blank"> </span>\ue974\ued3d\udb80\udddc<span class="ff9 ws15">, entonces </span><span class="ws14">\ue97a\ued3d<span class="blank _5"> </span>\uf345<span class="blank _5"> </span>\ue97a<span class="blank _d"> </span>\uf34c<span class="blank _d"> </span>\uf346\ue974\ued3d<span class="blank"> </span><span class="ff9 ws15"> </span></span></span></span></div><div class="t m0 x11 h12 y43 ff8 fs2 fc0 sc0 lsb ws19">\ue97a\ued3d<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ue974\ued3d<span class="blank _4"> </span>\uf34c<span class="blank _d"> </span>\uf346\ue97a<span class="blank _3"> </span><span class="ff9 ws15"> </span></div><div class="t m0 x21 h12 y44 ff8 fs2 fc0 sc0 ls17 ws1d">\ue973\ue972<span class="lsb ws1e">\ued3d<span class="blank _4"> </span>\uf34c<span class="blank"> </span>\uf346\ue97a<span class="ff9 ws15"> </span></span></div><div class="t m0 x22 h13 y45 ff8 fs2 fc0 sc0 lsb ws1f">\ued3d<span class="blank _4"> </span>\uf34c<span class="blank"> </span>\uf346<span class="blank _e"> </span><span class="v7">\ue97a</span></div><div class="t m0 x23 h1d y46 ff8 fs2 fc0 sc0 ls17 ws1d">\ue973\ue972<span class="ff9 lsb ws15 v8"> </span></div><div class="t m0 x24 h13 y47 ff8 fs2 fc0 sc0 lsb ws20">\ued3d<span class="blank _4"> </span>\uf34c<span class="blank _d"> </span>\uf346<span class="blank"> </span><span class="v7">\ue976</span></div><div class="t m0 x25 h14 y48 ff8 fs2 fc0 sc0 ls14">\ue977<span class="ff9 lsb ws15 v8"> </span></div><div class="t m0 x1 h11 y49 ff9 fs2 fc0 sc0 lsb ws15">Reemplazando en <span class="ff8 ls9">\ued42<span class="fs7 lsb wsb v1">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v2">\udb80\udddb</span><span class="ls3">\ued54<span class="ls15 v2">\udb80\udddc</span><span class="lsb ws14">\uf34c<span class="blank _4"> </span>\ue974\ued54<span class="blank _5"> </span>\uf345<span class="blank _5"> </span>\ue978\ued3d</span></span></span>, resultará: </div><div class="t m0 x26 h13 y4a ff8 fs2 fc0 sc0 ls9">\ued42<span class="fs7 lsb wsb v1">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v2">\udb80\udddb</span><span class="ls3">\ued54<span class="ls4 v2">\udb80\udddc</span><span class="lsb ws20">\uf34c<span class="blank _d"> </span>\ue974\ued54<span class="blank _5"> </span>\uf345<span class="blank _5"> </span>\ue978\ue7e4<span class="blank"> </span>\uf36c\uf346<span class="blank"> </span><span class="v7">\ue976</span></span></span></div><div class="t m0 x27 h1e y4b ff8 fs2 fc0 sc0 ls14">\ue977<span class="lsb ws4 v8">\uf370<span class="ff9 ws15"> </span></span></div><div class="t m0 x14 h13 y4c ff8 fs2 fc0 sc0 ls9">\ued42<span class="fs7 lsb wsb v1">\uf13f\uf135<span class="blank"> </span></span><span class="ls0 v2">\udb80\udddb</span><span class="ls3">\ued54<span class="lsa v2">\udb80\udddc</span><span class="lsb wsc">\uf34c<span class="blank _d"> </span>\ue974\ued54<span class="blank _5"> </span>\uf346<span class="blank"> </span><span class="ls17 v7">\ue974\ue976</span></span></span></div><div class="t m0 x28 h14 y4d ff8 fs2 fc0 sc0 ls16">\ue977<span class="ff9 lsb ws15 v8"> </span></div><div class="t m0 x1 h6 y4e ff3 fs3 fc0 sc0 lsb ws15"> </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 y4f wc h1f" alt="" src="https://files.passeidireto.com/8396748b-aa44-4725-8f34-77061a97f2e7/bg3.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h20 y2 ff1 fs0 fc0 sc0 lsb ws15">MATEMÁTICA (6<span class="lsc ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls18"> <span class="ls19"> </span></span>RECUPERATOR<span class="blank _3"> </span>IO 1° PARC<span class="blank _3"> </span>IAL<span class="ff5 fs3"> </span></div><div class="t m0 x1 h2 y50 ff2 fs0 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h2 y51 ff2 fs0 fc0 sc0 lsb 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 _f"> </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 2 </span></div><div class="t m0 x3 h2 y52 ff2 fs0 fc0 sc0 lsb ws15">Hoja 2 de 4 </div><div class="t m0 x3 h2 y53 ff2 fs0 fc0 sc0 lsb ws15"> </div><div class="t m0 x2 h2 y54 ff1 fs0 fc0 sc0 ls1a ws15"> <span class="ff7 fs2 lsb v9">2. Determinar los conjuntos <span class="ff8 ls1b">\uee6f<span class="fs7 ls1c v1">\uf13e</span></span> y <span class="ff8 ls1">\uee6f<span class="fs7 ls1c v1">\uf13f</span></span> de la función <span class="ff8 ls1d">\uee8c<span class="ls1e v2">\udb80\udddb</span><span class="ls1">\uee9e<span class="ls15 v2">\udb80\udddc</span><span class="lsb wsc">\uf34c<span class="blank _d"> </span>\udb80\udddb\uee9e<span class="blank"> </span>\uf345<span class="blank"> </span>\uf0da\udb80\udddc<span class="fs7 ls1f v1">\uf0dc</span><span class="ws17">\ue7e4<span class="blank"> </span>\udb80\udddb\uee9e<span class="blank _3"> </span><span class="fs7 ls20 v1">\uf0db</span><span class="ls21">\uf346<span class="lse ws21">\uf0db\uee9e<span class="blank"> </span></span></span></span>\uf345<span class="blank"> </span>\uf0dc\udb80\udddc</span></span></span>. </span></div><div class="t m0 x1 h20 y55 ff5 fs3 fc0 sc0 lsb ws15"> </div><div class="t m0 x29 h10 y56 ff9 fs2 fc0 sc0 lsb ws15">Solución: </div><div class="t m0 x1 h10 y57 ff9 fs2 fc0 sc0 lsb ws15">Para <span class="blank _8"> </span>resolver <span class="blank _6"> </span>esta <span class="blank _6"> </span>activi<span class="blank _3"> </span>dad <span class="blank _8"> </span>se <span class="blank _6"> </span>trabajarán <span class="blank _6"> </span>los <span class="blank _6"> </span>si<span class="blank _3"> </span>guientes <span class="blank _8"> </span>contenidos <span class="blank _7"> </span>abordados <span class="blank _8"> </span>durante <span class="blank _6"> </span>el <span class="blank _6"> </span>cuatrime<span class="blank _3"> </span>stre: <span class="blank _8"> </span>Números </div><div class="t m0 x1 h10 y58 ff9 fs2 fc0 sc0 lsb 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 h10 y59 ff9 fs2 fc0 sc0 lsb ws15">de una función. </div><div class="t m0 x1 h10 y5a ff9 fs2 fc0 sc0 lsb ws15">Se <span class="blank _3"> </span>denomina <span class="blank _3"> </span>conj<span class="blank _3"> </span>unto <span class="blank _3"> </span>de <span class="blank _3"> </span>positividad <span class="blank _8"> </span>de <span class="blank _3"> </span>la <span class="blank _8"> </span>función <span class="blank _3"> </span>al <span class="blank _8"> </span>conjunto <span class="blank _3"> </span>de <span class="blank _3"> </span>valores <span class="blank _8"> </span>del <span class="blank _3"> </span>dominio <span class="blank _8"> </span>para <span class="blank _3"> </span>los <span class="blank _8"> </span>cuales <span class="blank _3"> </span>la <span class="blank _3"> </span>función </div><div class="t m0 x1 h10 y5b ff9 fs2 fc0 sc0 lsb ws15">es positiva, lo mismo sucede con el conjunto de neg<span class="blank _0"></span>atividad cuando la función es negativa. <span class="blank _3"> </span> </div><div class="t m0 x1 h10 y5c ff9 fs2 fc0 sc0 lsb ws15">Para determinar los conjuntos de positividad y negatividad de la función debemos analizar su comportamiento. </div><div class="t m0 x2a h11 y5d ff8 fs2 fc0 sc0 ls8">\ued42<span class="ls0 v2">\udb80\udddb</span><span class="ls3">\ued54<span class="ls4 v2">\udb80\udddc</span><span class="lsb ws18">\uf34c<span class="blank _d"> </span>\udb80\udddb<span class="blank _3"> </span>\ued54<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ue973\udb80\udddc<span class="fs7 ls22 v1">\uf137</span><span class="ws22">\ue7e4<span class="blank _c"> </span>\udb80\udddb\ued54<span class="blank"> </span><span class="fs7 ls23 v1">\uf136</span><span class="wsc">\uf346<span class="blank"> </span>\ue974\ued54<span class="blank _d"> </span>\uf345<span class="blank"> </span>\ue975\udb80\udddc<span class="ff9 ws15"> </span></span></span></span></span></div><div class="t m0 x2b h10 y5e ff9 fs2 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h12 y5f ff9 fs2 fc0 sc0 lsb ws15">Utilizando la gráfica de la función, se puede observar que la única raíz de la misma es el punto <span class="ff8 ws23">\udb80\udddb\uf346\ue973\ue7e2<span class="blank"> </span>\ue972\udb80\udddc</span>, este </div><div class="t m0 x1 h10 y60 ff9 fs2 fc0 sc0 lsb ws15">valor se puede obtener de: </div><div class="t m0 x2c h21 y61 ff8 fs2 fc0 sc0 lsb wsc">\ue972<span class="blank _d"> </span>\uf34c<span class="blank _4"> </span>\udb80\udddb\ued54<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ue973\udb80\udddc<span class="fs7 ls22 v1">\uf137</span><span class="ws22">\ue7e4<span class="blank _c"> </span>\udb80\udddb\ued54<span class="blank"> </span><span class="fs7 ls23 v1">\uf136</span></span>\uf346<span class="blank"> </span>\ue974\ued54<span class="blank _d"> </span>\uf345<span class="blank"> </span>\ue975\udb80\udddc<span class="ff9 ws15"> </span></div><div class="t m0 x1 h10 y62 ff9 fs2 fc0 sc0 lsb ws15">Debemos <span class="blank _0"></span>recordar <span class="blank _0"></span>que e<span class="blank _0"></span>l producto <span class="blank _0"></span>de <span class="blank _0"></span>dos expresiones <span class="blank _0"></span>sólo <span class="blank _0"></span>nos da<span class="blank _0"></span> ce<span class="blank _0"></span>ro c<span class="blank _0"></span>uando alguna <span class="blank _0"></span>de <span class="blank _0"></span>las e<span class="blank _0"></span>xpresiones lo <span class="blank _0"></span>es, por </div><div class="t m0 x1 h10 y63 ff9 fs2 fc0 sc0 lsb ws15">lo tanto: </div><div class="t m0 x1 h21 y64 ff8 fs2 fc0 sc0 lsb ws24">\udb80\udddb\ued54<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ue973\udb80\udddc<span class="fs7 ls24 v1">\uf137</span><span class="ws25">\uf34c<span class="blank _d"> </span>\ue972\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank _5"> </span>\uebe9<span class="blank"> </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<span class="blank"> </span>\ued54<span class="blank _8"> </span><span class="fs7 ls25 v1">\uf136</span><span class="wsc">\uf346<span class="blank"> </span>\ue974\ued54<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ue975<span class="blank _d"> </span>\uf34c<span class="blank _4"> </span>\ue972\ue603\udb80\udddb\ued3d\ued4c\ued48\ued45\ued3f\ued3d\ued49\ued4b\ued4f<span class="blank _3"> </span>\ue603<span class="ls2b ws26">\ued48\ued3d</span><span class="ws27">\ue603\ued42\ue6d7\ued4e<span class="blank"> </span>\ued49\ued51\ued48\ued3d\ue603\ued40\ued41<span class="blank"> </span>\ue603<span class="ls2b ws28">\ued48\ued3d<span class="blank"> </span></span><span class="ws4">\ue603\ued4e\ued41\ued3f\ued4b\ued48\ued52\ued41\ued4a\ued50\ued41<span class="blank _3"> </span>\udb80\udddc<span class="ff9 ws15"> </span></span></span></span></span></div><div class="t m0 x1 h12 y65 ff8 fs2 fc0 sc0 lsb wsc">\ued54<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ue973<span class="blank _4"> </span>\uf34c<span class="blank _10"> </span><span class="ls1 v0">\ue9be</span>\ue972</div><div class="t m0 x2d h22 y66 ff8 fs8 fc0 sc0 ls26">\uf22f<span class="fs2 lsb ws29 va">\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\ued54<span class="blank _a"> </span>\uf34c<span class="blank"> </span><span class="ws2a v7">\uf346\udb80\udddb\uf346\ue974\udb80\udddc<span class="blank"> </span>\uf347<span class="blank"> </span><span class="ls1d v0">\uf3a5</span><span class="ws4">\udb80\udddb<span class="blank _3"> </span>\uf346\ue974\udb80\udddc<span class="fs7 ls27 vb">\uf136</span><span class="wsc">\uf346<span class="blank"> </span>\ue976\ue7e4\ue973\ue7e4\ue975</span></span></span></span></div><div class="t m0 x11 h14 y67 ff8 fs2 fc0 sc0 lsb ws2b">\ue974\ue7e4\ue973<span class="blank"> </span><span class="ff9 ws15 v8"> </span></div><div class="t m0 x1 h13 y68 ff8 fs2 fc0 sc0 lsb ws2c">\ued54<span class="blank"> </span>\uf34c<span class="blank _d"> </span>\uf346\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<span class="blank _3"> </span>\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ued54<span class="blank"> </span>\uf34c<span class="blank _d"> </span><span class="wsc v7">\ue974<span class="blank"> </span>\uf347<span class="blank"> </span></span><span class="ls1 vc">\ue9be</span><span class="ws2d v7">\ue976<span class="blank"> </span>\uf346<span class="blank"> </span><span class="ls17 ws2e">\ue973\ue974<span class="blank"> </span><span class="lsb ws11">\uf34c<span class="blank"> </span>\uf346\ue97a</span></span></span></div><div class="t m0 x1c h23 y69 ff8 fs2 fc0 sc0 ls28">\ue974<span class="ls12 v8">\uf34c</span><span class="lsb wsc vd">\ue974<span class="blank"> </span>\uf347<span class="blank"> </span></span><span class="ls1 ve">\ue9be</span><span class="lsb ws4 vd">\uf346\ue97a</span></div><div class="t m0 x2e h1e y69 ff8 fs2 fc0 sc0 ls29">\ue974<span class="ls5 v8">\uf34c<span class="ls2c ws2f">\ued30\ued4b<span class="lsb ws4">\ue603<span class="blank _3"> </span>\ued50\ued45\ued41\ued4a\ued41\ue603<span class="ls2b ws26">\ued4e\ued3d</span><span class="ws14">\ue6c0\ued3f\ued41<span class="blank"> </span>\ued4f\ue603\ued34<span class="blank"> </span><span class="ff9 ws15"> </span></span></span></span></span></div><div class="t m0 x1 h10 y6a ff9 fs2 fc0 sc0 lsb ws15">Ahora bien, para determinar el conjunto de positividad la única expresión con raíz real debe ser mayor a cero. </div><div class="t m0 x2f h21 y6b ff8 fs2 fc0 sc0 lsb wsc">\udb80\udddb\ued54<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ue973\udb80\udddc<span class="fs7 ls24 v1">\uf137</span><span class="ws30">\uf350<span class="blank"> </span>\ue972\ue603\ue603\ue603\ue603<span class="blank"> </span>\ueb5c<span class="blank"> </span>\ue603\ue603\ue603\ue603\ued54<span class="blank _4"> </span>\uf350<span class="blank"> </span>\uf346<span class="blank _3"> </span>\ue973\ue603\ue603\ue603\ue603<span class="blank"> </span>\ueb5c<span class="blank _b"> </span>\ue603<span class="blank _c"> </span>\ued25<span class="blank _3"> </span><span class="fs7 ls2a v1">\uf13e</span><span class="ws31">\uf34c<span class="blank _4"> </span>\udb80\udddb\uf346\ue973\ue7e2<span class="blank"> </span>\uf345\ue9bb\udb80\udddc<span class="ff9 ws15"> </span></span></span></div><div class="t m0 x1 h10 y6c ff9 fs2 fc0 sc0 lsb ws15">Lo mismo sucede con el conjunto de negatividad la expresión debe ser menor a cero </div><div class="t m0 x2f h21 y6d ff8 fs2 fc0 sc0 lsb wsc">\udb80\udddb\ued54<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ue973\udb80\udddc<span class="fs7 ls24 v1">\uf137</span><span class="ws30">\uf34f<span class="blank"> </span>\ue972\ue603\ue603\ue603\ue603<span class="blank"> </span>\ueb5c<span class="blank"> </span>\ue603\ue603\ue603\ue603\ued54<span class="blank _4"> </span>\uf34f<span class="blank"> </span>\uf346<span class="blank _3"> </span>\ue973\ue603\ue603\ue603\ue603<span class="blank"> </span>\ueb5c<span class="blank _b"> </span>\ue603<span class="blank _c"> </span>\ued25<span class="blank _3"> </span><span class="fs7 ls2a v1">\uf13f</span><span class="ws23">\uf34c<span class="blank _4"> </span>\udb80\udddb\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346\ue973\udb80\udddc<span class="ff9 ws15"> </span></span></span></div><div class="t m0 x1 h10 y6e ff9 fs2 fc0 sc0 lsb ws15"> </div><div class="t m0 x29 h1b y6f ff4 fs3 fc0 sc0 lsb ws15"> <span class="blank _11"> </span> </div></div><div class="c x0 y31 wa h1a"><div class="t m0 x15 h1b y32 ff4 fs3 fc1 sc0 lsb 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"><img fetchpriority="low" loading="lazy" class="bi x0 y70 wd h24" alt="" src="https://files.passeidireto.com/8396748b-aa44-4725-8f34-77061a97f2e7/bg4.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 lsb ws15">MATEMÁTICA (6<span class="lsc ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls18"> <span class="ls19"> </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 lsb ws15"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 lsb 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 _f"> </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 2 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 lsb ws15">Hoja 3 de 4 </div><div class="t m0 x3 h2 y71 ff2 fs0 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h1b y72 ff4 fs3 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h21 y73 ff7 fs2 fc0 sc0 lsb ws15">3. Hallar los valores de <span class="ff8 ws6">\uee89\ue603<span class="blank"> </span>\uebd0<span class="blank"> </span>\ueb39</span> para que la función <span class="ff8 ws32">\uee8c\udb80\udddb<span class="blank _3"> </span>\uee9e\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank"> </span>\uf346<span class="blank _3"> </span>\uee9e<span class="fs7 ls2d v1">\uf0db</span><span class="ls21 ws33">\ue603<span class="blank _12"></span>\uf345\uee9e\uf345\uee89<span class="blank _13"></span><span class="ff7 lsb ws15"> se interseque con la función </span></span></span></div><div class="t m0 x1 h21 y74 ff8 fs2 fc0 sc0 lsb ws34">\uee8d\udb80\udddb\uee9e\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank _4"> </span>\uee9e<span class="fs7 ls2d v1">\uf0db</span><span class="wsc">\ue603<span class="blank _7"> </span>\uf345<span class="blank"> </span>\uee9e<span class="blank"> </span>\uf345<span class="blank"> </span>\uf0dc<span class="ff7 ws15">. </span></span></div><div class="t m0 x1 h20 y75 ff5 fs3 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h10 y76 ff9 fs2 fc0 sc0 lsb 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 x24 h11 y77 ff8 fs2 fc0 sc0 ls8">\ued42<span class="ls1e v2">\udb80\udddb</span><span class="ls3">\ued54<span class="ls4 v2">\udb80\udddc</span><span class="lsb wsd">\uf34c<span class="blank _d"> </span>\ued43<span class="blank"> </span>\udb80\udddb\ued54<span class="blank"> </span>\udb80\udddc<span class="ff9 ws15"> </span></span></span></div><div class="t m0 x1 h10 y78 ff9 fs2 fc0 sc0 lsb 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 x30 h21 y79 ff8 fs2 fc0 sc0 lsb ws22">\uf346\ued54<span class="blank"> </span><span class="fs7 ls2e v1">\uf136</span><span class="wsc">\ue603<span class="blank _b"> </span>\uf345<span class="blank"> </span>\ued54<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ued3f<span class="blank _a"> </span>\uf34c<span class="blank _d"> </span>\ued54<span class="blank _8"> </span><span class="fs7 ls2f v1">\uf136</span>\ue603<span class="blank _7"> </span>\uf345<span class="blank"> </span>\ued54<span class="blank _d"> </span>\uf345<span class="blank"> </span>\ue975<span class="ff9 ws15"> </span></span></div><div class="t m0 x1 h10 y7a ff9 fs2 fc0 sc0 lsb ws15">Despejamos y obtenemos que: <span class="blank _14"> </span><span class="ff8 ws22 vf">\ue974\ued54<span class="blank"> </span><span class="fs7 ls2f v1">\uf136</span><span class="ws35">\ue603<span class="blank"> </span>\uf345<span class="blank _9"> </span>\ue975<span class="blank _9"> </span>\uf346<span class="blank _5"> </span>\ued3f<span class="blank _4"> </span>\uf34c<span class="blank _d"> </span>\ue972<span class="blank _3"> </span></span></span><span class="vf"> </span></div><div class="t m0 x1 h10 y7b ff9 fs2 fc0 sc0 lsb ws15">Aplicamos la fórmula resolvente: </div><div class="t m0 x31 h12 y7c ff8 fs2 fc0 sc0 lsb">\ued54</div><div class="t m0 x32 h25 y7d ff8 fs7 fc0 sc0 lsb ws36">\uf135\ue7e1\uf136<span class="blank"> </span><span class="fs2 ls5 v10">\uf34c</span><span class="fs2 ws2d v11">\ue972<span class="blank"> </span>\uf347<span class="blank"> </span><span class="ws4 v0">\uf3a5<span class="v0">\ue972</span></span></span><span class="ls25 v12">\uf136</span><span class="fs2 wsc v11">\uf346<span class="blank"> </span>\ue976\ue7e4\ue974\ue7e4<span class="blank _c"> </span>\udb80\udddb\ue975<span class="blank"> </span>\uf346<span class="blank"> </span>\ued3f<span class="blank _3"> </span>\udb80\udddc</span></div><div class="t m0 x33 h26 y7e ff8 fs2 fc0 sc0 ls30">\ue976<span class="ffb lsb ws15 v8"> </span></div><div class="t m0 x1 h10 y7f ff9 fs2 fc0 sc0 lsb ws15">Como <span class="blank _9"> </span>las <span class="blank _9"> </span>funciones <span class="blank _9"> </span>debe<span class="blank _0"></span>n <span class="blank _9"> </span>intersecarse <span class="blank _9"> </span>en <span class="blank _9"> </span>un <span class="blank _9"> </span>punto, <span class="blank _9"> </span>la <span class="blank _9"> </span>ec<span class="blank _0"></span>uación <span class="blank _9"> </span>debe <span class="blank _9"> </span>tener <span class="blank _9"> </span>una <span class="blank _9"> </span>única <span class="blank _9"> </span>solución <span class="blank _9"> </span>por <span class="blank _15"> </span>lo <span class="blank _9"> </span>que </div><div class="t m0 x1 h12 y80 ff8 fs2 fc0 sc0 lsb wsf">\uf346\ue976\ue7e4\ue974\ue7e4<span class="blank _c"> </span>\udb80\udddb\ue975<span class="blank _9"> </span>\uf346<span class="blank _5"> </span>\ued3f<span class="blank"> </span>\udb80\udddc<span class="ff9 ws15"> debe ser cero, es decir: <span class="blank _16"> </span></span><span class="ws17 vf">\uf346\ue976\ue7e4\ue974\ue7e4<span class="blank"> </span></span><span class="ls0 v13">\udb80\udddb</span><span class="vf">\ue975<span class="blank _9"> </span>\uf346<span class="blank _5"> </span>\ued3f</span><span class="ls7 v13">\udb80\udddc</span><span class="ws29 vf">\uf34c<span class="blank"> </span>\ue972<span class="ff9 ws15"> </span></span></div><div class="t m0 x1 h12 y81 ff9 fs2 fc0 sc0 lsb ws15">Por lo tanto, para que este producto sea nulo <span class="ff8 ws37">\ue975<span class="blank _9"> </span>\uf346<span class="blank _9"> </span>\ued3f<span class="blank"> </span></span> debe ser cero, entonces: </div><div class="t m0 x11 h12 y82 ff8 fs2 fc0 sc0 lsb ws29">\ue975<span class="blank _9"> </span>\uf346<span class="blank _5"> </span>\ued3f<span class="blank _4"> </span>\uf34c<span class="blank"> </span>\ue972<span class="blank"> </span>\ueb5e<span class="blank _4"> </span>\ued3f<span class="blank _a"> </span>\uf34c<span class="blank"> </span>\ue975<span class="ff9 ws15"> </span></div><div class="t m0 x1 h10 y83 ff9 fs2 fc0 sc0 lsb ws15">Al resolver el ejercicio utilizamos los conceptos de func<span class="blank _0"></span>ión cuadrática y de ecuaciones cuadráticas. </div><div class="t m0 x29 h10 y84 ff9 fs2 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h20 y85 ff5 fs3 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h20 y86 ff5 fs3 fc0 sc0 lsb ws15"> <span class="blank _17"> </span> </div></div><div class="c x0 y31 wa h1a"><div class="t m0 x15 h1b y32 ff4 fs3 fc1 sc0 lsb 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="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y87 wd h27" alt="" src="https://files.passeidireto.com/8396748b-aa44-4725-8f34-77061a97f2e7/bg5.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h20 y88 ff5 fs3 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h2 y89 ff1 fs0 fc0 sc0 lsb ws15">MATEMÁTICA (6<span class="blank _0"></span><span class="lsc ws0">1)<span class="ff2 lsb ws15"> Cátedra A: <span class="blank _0"></span>NUÑEZ, MYRIA<span class="blank _0"></span>M<span class="ff1"> RECUPE<span class="blank _0"></span>RATORIO 1° PARCIAL<span class="blank _0"></span> </span></span></span></div><div class="t m0 x1 h2 y8a ff2 fs0 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h2 y8b ff2 fs0 fc0 sc0 lsb 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 _f"> </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 2 </span></div><div class="t m0 x3 h2 y8c ff2 fs0 fc0 sc0 lsb ws15">Hoja 4 de 4 </div><div class="t m0 x3 h2 y8d ff2 fs0 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 he y8e ff7 fs2 fc0 sc0 lsb ws15">4. Hallar el valor de <span class="ff8 ws4">\uee89</span> para que la función <span class="ff8 ls1d">\uee8c<span class="ls0 v2">\udb80\udddb</span><span class="ls1">\uee9e<span class="ls15 v2">\udb80\udddc</span><span class="ls31">\uf34c<span class="fs7 lsb v3">\uf0dd</span></span></span></span></div><div class="t m0 x34 h28 y8f ff8 fs7 fc0 sc0 ls32">\uee9e<span class="fs8 ls33 v10">\uf0db</span><span class="ls34">\uf13f<span class="ls37 ws38">\uf0da\uf0db\uee9e</span><span class="lsb ws39">\uf13e\uee89</span></span></div><div class="t m0 x9 h12 y8e ff7 fs2 fc0 sc0 lsb ws15"> tenga una asíntota en <span class="ff8 ws29">\uee9e\ue603<span class="blank"> </span>\uf34c<span class="blank"> </span>\ue603\uf0e1</span>. </div><div class="t m0 x29 h12 y90 ff9 fs2 fc0 sc0 lsb ws15">Si la recta <span class="ff8 ws1e">\ued54<span class="blank _4"> </span>\uf34c<span class="blank"> </span>\ue97a</span> es asíntota de la función significa que: </div><div class="t m0 x35 h12 y91 ff8 fs2 fc0 sc0 lsb ws4">\ued48\ued45\ued49</div><div class="t m0 x35 h29 y92 ff8 fs7 fc0 sc0 lsb ws3a">\uf1eb\ueb5c\uf13c<span class="blank _9"> </span><span class="fs2 ls8 v14">\ued42<span class="ls0 v2">\udb80\udddb</span><span class="ls3">\ued54<span class="ls4 v2">\udb80\udddc</span><span class="lsb ws3b">\uf34c<span class="blank _d"> </span>\ue9bb\ue603\ue603\ue603<span class="blank _4"> </span>\uf43a<span class="blank"> </span>\ue603\ue603\ue603<span class="blank"> </span>\ued48\ued45\ued49</span></span></span></div><div class="t m0 x36 h2a y92 ff8 fs7 fc0 sc0 lsb ws3c">\uf1eb<span class="blank"> </span>\ueb5c\uf13c<span class="blank _15"> </span><span class="fs2 ls35 v14">\ue603</span><span class="fs2 ve">\ue976</span></div><div class="t m0 x23 h1e y93 ff8 fs2 fc0 sc0 ls36">\ued54<span class="fs7 ls25 vb">\uf136</span><span class="ls21">\uf346<span class="ls17 ws1d">\ue973\ue974</span><span class="lsb wsc">\ued54<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ued3f<span class="blank _a"> </span><span class="ws29 v8">\uf34c<span class="blank"> </span>\ue9bb<span class="ffb ws15"> </span></span></span></span></div><div class="t m0 x29 h12 y94 ff9 fs2 fc0 sc0 lsb ws15">Como <span class="blank _7"> </span>el <span class="blank _7"> </span>numerador <span class="blank _7"> </span>es <span class="blank _7"> </span><span class="ff8 ws4">\ue976</span>, <span class="blank _7"> </span>para <span class="blank _7"> </span>que <span class="blank _7"> </span>esto <span class="blank _7"> </span>sea <span class="blank _7"> </span>posible <span class="blank _7"> </span>el <span class="blank _7"> </span>denominador <span class="blank _7"> </span>debe <span class="blank _7"> </span>aproximarse <span class="blank _7"> </span>a <span class="blank _b"> </span><span class="ff8 ws4">\ue972</span> <span class="blank _7"> </span>cuando <span class="blank _7"> </span><span class="ff8 ls3">\ued54</span> <span class="blank _7"> </span>se </div><div class="t m0 x29 h12 y95 ff9 fs2 fc0 sc0 lsb ws15">aproxima a <span class="ff8 ws4">\ue97a</span>. </div><div class="t m0 x29 h21 y96 ff9 fs2 fc0 sc0 lsb ws15">Por lo tanto resolvemos la ecuación <span class="ff8 ls36">\ued54<span class="fs7 ls25 v1">\uf136</span><span class="ls21">\uf346<span class="ls17 ws1d">\ue973\ue974<span class="lsb ws19">\ued54<span class="blank _5"> </span>\uf345<span class="blank"> </span>\ued3f<span class="blank _a"> </span>\uf34c<span class="blank _4"> </span>\ue972</span></span></span></span> cuando <span class="ff8 ws29">\ued54<span class="blank _4"> </span>\uf34c<span class="blank"> </span>\ue97a<span class="blank _3"> </span></span>. </div><div class="t m0 x37 h21 y97 ff8 fs2 fc0 sc0 lsb ws4">\ue97a<span class="fs7 ls25 v1">\uf136</span><span class="ls21">\uf346<span class="ls17 ws1d">\ue973\ue974</span></span><span class="ws2d">\ue7e4\ue97a<span class="blank"> </span>\uf345<span class="blank"> </span>\ued3f<span class="blank _a"> </span>\uf34c<span class="blank _d"> </span>\ue972\ue603<span class="blank _4"> </span>\uf43a<span class="blank _d"> </span><span class="ls17 ws3d">\ue978\ue976<span class="blank"> </span><span class="ls21">\uf346</span><span class="ws3e">\ue97b\ue978<span class="blank"> </span></span></span><span class="wsc">\uf345<span class="blank"> </span>\ued3f<span class="blank _a"> </span>\uf34c<span class="blank _d"> </span>\ue972<span class="blank _3"> </span>\ue603<span class="blank _5"> </span>\uf43a<span class="blank _4"> </span>\uf346<span class="ls17 ws3d">\ue975\ue974<span class="blank"> </span></span><span class="ws3f">\uf345<span class="blank _5"> </span>\ued3f<span class="blank"> </span>\uf34c<span class="blank _5"> </span>\ue972\ue603<span class="blank"> </span>\uf43a<span class="blank _5"> </span>\ued3f<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="ls17 ws1d">\ue975\ue974</span><span class="ff9 ws15"> </span></span></span></span></div><div class="t m0 x1 h10 y98 ff9 fs2 fc0 sc0 lsb ws15">En este ejercicio trabajamos con la definición de Asíntota Vertical. </div><div class="t m0 x1 h6 y99 ff3 fs3 fc0 sc0 lsb ws15"> </div><div class="t m0 x1 h20 y9a ff5 fs3 fc0 sc0 lsb ws15"> </div></div><div class="c x0 y9b wa h2b"><div class="t m0 x15 h1b y32 ff4 fs3 fc1 sc0 lsb 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>
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