<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/21fa5c2b-4f9f-4ca0-bf5f-d7a54443d9fd/bg1.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls10 ws22">MATEMÁTICA (<span class="ls11 ws0">61</span><span class="ws1">)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM </span></div><div class="t m0 x1 h2 y3 ff1 fs0 fc0 sc0 ls10 ws22">2° PARCIAL </div><div class="t m0 x2 h2 y4 ff1 fs0 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h2 y5 ff2 fs0 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h3 y6 ff2 fs1 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h2 y7 ff2 fs0 fc0 sc0 ls12 ws2">14<span class="ls10 ws3">/06/2023<span class="ff1 ws22"> <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 4 </span></span></div><div class="t m0 x3 h2 y8 ff2 fs0 fc0 sc0 ls10 ws22"> Hoja 1 de 4 </div><div class="t m0 x3 h2 y9 ff2 fs0 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h3 ya ff2 fs1 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h3 yb ff2 fs1 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h4 yc ff3 fs2 fc0 sc0 ls10 ws22">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 ls10 ws22"> </div></div><div class="c x6 yd w4 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls10 ws22">1 </div></div><div class="c x8 yd w5 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls10 ws22">2 </div></div><div class="c x9 yd w6 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls10 ws22">3 </div></div><div class="c xa yd w7 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls10 ws22">4 </div></div><div class="c x4 yf w3 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls10 ws22"> </div></div><div class="c x6 yf w4 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls10 ws22"> </div></div><div class="c x8 yf w5 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls10 ws22"> </div></div><div class="c x9 yf w6 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls10 ws22"> </div></div><div class="c xa yf w7 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls10 ws22"> </div></div><div class="c x4 y11 w5 h9"><div class="t m0 xb ha y12 ff4 fs4 fc0 sc0 ls10 ws22">Puntaje de cada </div><div class="t m0 xb ha y13 ff4 fs4 fc0 sc0 ls10 ws22">ejercicio </div></div><div class="c x6 y11 w4 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls10 ws22">2,50 </div></div><div class="c x8 y11 w5 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls10 ws22">2,50 </div></div><div class="c x9 y11 w6 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls10 ws22">2,50 </div></div><div class="c xa y11 w7 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls10 ws22">2,50 </div></div><div class="c x0 y1 w2 h0"><div class="t m0 x1 hb y15 ff5 fs5 fc0 sc0 ls10 ws22">Duración del exam<span class="blank _3"> </span>en: 1h <span class="ff6 ws4">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 ls10 ws22">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 ls10 ws22"> </div><div class="t m0 x1 h4 y18 ff3 fs3 fc0 sc0 ls10 ws22">1. <span class="fs2">Dado el siguiente sistema: </span></div><div class="t m0 xf he y19 ff7 fs2 fc0 sc0 ls10 ws5">\uee6d<span class="blank"> </span>\uf349<span class="blank"> </span>\udb80\udde7<span class="v1">\uee9e</span></div><div class="t m0 x10 hf y1a ff7 fs2 fc0 sc0 ls10">\uee9f</div><div class="t m0 x10 h10 y1b ff7 fs2 fc0 sc0 ls0">\ueea0<span class="ls10 ws6 v2">\udb80\udde8<span class="blank _4"> </span>\uf34c<span class="blank _4"> </span>\uf36d<span class="blank"> </span></span><span class="ls10 ws7 v3">\ue603\ue603\uf0d9</span></div><div class="t m0 x11 hf y1c ff7 fs2 fc0 sc0 ls10 ws7">\ue603\ue603\uf0dc</div><div class="t m0 x12 h11 y1d ff7 fs2 fc0 sc0 ls10 ws7">\uf346\uf0da<span class="v1">\uf371<span class="ff3 ls1 ws22"> <span class="ls10">siendo </span></span>\uee6d<span class="fs7 ls2 v4">\uee9a</span><span class="ws8">\uf34c<span class="blank"> </span>\uf36d<span class="ws9 v2">\uf0da<span class="blank"> </span>\uf0dc<span class="blank"> </span>\uf0d9</span></span></span></div><div class="t m0 x13 hf y1c ff7 fs2 fc0 sc0 ls10 wsa">\uf0db<span class="blank"> </span>\uf346\uf0da<span class="blank"> </span>\uf0e0</div><div class="t m0 x13 h12 y1d ff7 fs2 fc0 sc0 ls10 wsb">\uf0da<span class="blank"> </span>\uee91<span class="blank"> </span>\uf0da<span class="ws7 v1">\uf371<span class="ff3 ws22"> </span></span></div><div class="t m0 x1 hf y1e ff3 fs2 fc0 sc0 ls10 ws22">Determinar el o los valor<span class="ls13 wsc">es</span> de <span class="ff7 wsd">\uee91<span class="blank"> </span>\uebd0<span class="blank"> </span>\ueb39</span> para que el sistema sea compatible determinado.<span class="fc1"> </span></div><div class="t m0 x1 h13 y1f ff4 fs3 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h6 y20 ff3 fs3 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h14 y21 ff5 fs3 fc0 sc0 ls10 ws22">Para resolv<span class="blank _0"></span>er el sistema pl<span class="blank _0"></span>anteado necesitamos<span class="blank _0"></span> deter<span class="blank _0"></span>minar la matriz<span class="blank _0"></span> <span class="ff7 ls3">\uee6d</span><span class="ff3 wse">.</span> </div><div class="t m0 x14 h15 y22 ff7 fs3 fc0 sc0 ls3">\uee6d<span class="fs0 ls4 v5">\uee9a</span><span class="ls10 wsf">\uf34c<span class="blank"> </span>\uf36d<span class="ws10 v6">\uf0da<span class="blank"> </span>\uf0dc<span class="blank"> </span>\uf0d9</span></span></div><div class="t m0 x15 h14 y23 ff7 fs3 fc0 sc0 ls10 ws11">\uf0db<span class="blank"> </span>\uf346\uf0da<span class="blank"> </span>\uf0e0</div><div class="t m0 x15 h16 y24 ff7 fs3 fc0 sc0 ls10 ws12">\uf0da<span class="blank"> </span>\uee91<span class="blank"> </span>\uf0da<span class="ws13 v2">\uf371<span class="blank"> </span>\uf43a<span class="blank"> </span>\uee6d<span class="blank"> </span>\uf34c<span class="blank"> </span>\uf36d</span><span class="ws10 v7">\uf0da<span class="blank"> </span>\uf0db<span class="blank _5"> </span>\uf0da</span></div><div class="t m0 x16 h14 y23 ff7 fs3 fc0 sc0 ls10 ws11">\uf0dc<span class="blank"> </span>\uf346\uf0da<span class="blank"> </span>\uee91</div><div class="t m0 x16 h17 y24 ff7 fs3 fc0 sc0 ls10 ws10">\uf0d9<span class="blank"> </span>\uf0e0<span class="blank"> </span>\uf0da<span class="ws14 v2">\uf371<span class="ff5 ws22"> </span></span></div><div class="t m0 x1 h18 y25 ff5 fs3 fc0 sc0 ls10 ws22">La matriz ampli<span class="blank _0"></span>ada del sistema<span class="blank _0"></span> es: </div><div class="t m0 x11 h15 y26 ff7 fs3 fc0 sc0 ls3">\uee6d<span class="fs0 ls5 v5">\uebdb</span><span class="ls10 wsf">\uf34c<span class="blank"> </span>\uf36d<span class="ws15 v6">\uf0da<span class="blank"> </span>\uf0db<span class="blank"> </span>\uf0da</span></span></div><div class="t m0 x17 h14 y27 ff7 fs3 fc0 sc0 ls10 ws11">\uf0dc<span class="blank"> </span>\uf346\uf0da<span class="blank"> </span>\uee91</div><div class="t m0 x17 h19 y28 ff7 fs3 fc0 sc0 ls10 ws16">\uf0d9<span class="blank _6"> </span>\uf0e0<span class="blank _6"> </span>\uf0da<span class="blank"> </span><span class="ls6 v2">\uf42d</span><span class="v7">\uf0d9</span></div><div class="t m0 x18 h14 y29 ff7 fs3 fc0 sc0 ls10">\uf0dc</div><div class="t m0 x19 h1a y28 ff7 fs3 fc0 sc0 ls10 ws14">\uf346\uf0da<span class="v2">\uf371<span class="ff3 ws22"> </span></span></div><div class="t m0 x1 h18 y2a ff5 fs3 fc0 sc0 ls10 ws22">El paso siguiente e<span class="blank _0"></span>s buscar la for<span class="blank _0"></span>ma escalonad<span class="blank _0"></span>a de la matriz<span class="blank _0"></span> ampliada. </div><div class="t m0 x1 h14 y2b ff5 fs3 fc0 sc0 ls10 ws22">Buscamos <span class="ls14">un </span>cero en<span class="blank _0"></span> <span class="ls14 ws17">el</span> lugar <span class="ff7 ws14">\uee87<span class="fs0 ls15 ws18 v8">\uf0db\uf0da</span></span>. <span class="blank _3"> </span>Hacemos <span class="blank _0"></span> <span class="ff7 ws19">\uf0dc\ue7e4<span class="blank"> </span>\uee72<span class="fs0 ls7 v8">\uf0da</span><span class="ws1a">\uf346<span class="blank"> </span>\uee72<span class="fs0 ls8 v8">\uf0db</span><span class="ws1b">\uf437<span class="blank"> </span>\uee72<span class="fs0 ls9 v8">\uf0db</span></span></span></span><span class="ff3"> </span></div><div class="t m0 x1a h1b y2c ff7 fs3 fc0 sc0 ls3">\uee6d<span class="fs0 lsa v4">\uebdb</span><span class="lsb">\uf34c<span class="fs2 lsc">\uf36d</span><span class="ls10 ws1c v2">\uf0da<span class="blank"> </span>\uf0db<span class="blank _7"> </span>\uf0da</span></span></div><div class="t m0 x1b h14 y2d ff7 fs3 fc0 sc0 ls10 ws1d">\uf0d9<span class="blank _8"> </span>\uf0e0<span class="blank _8"> </span>\uf0dc<span class="blank"> </span>\uf346<span class="blank"> </span>\uee91</div><div class="t m0 x1b h1c y2e ff7 fs3 fc0 sc0 ls10 ws1c">\uf0d9<span class="blank"> </span>\uf0e0<span class="blank _7"> </span>\uf0da<span class="blank"> </span><span class="fs2 lsd v1">\uf42d</span><span class="v9">\uf0d9</span></div><div class="t m0 x1c h14 y2d ff7 fs3 fc0 sc0 ls10 ws14">\uf346\uf0dc</div><div class="t m0 x1c h1d y2f ff7 fs3 fc0 sc0 ls10 ws14">\uf346\uf0da<span class="fs2 lsc v1">\uf371</span><span class="ff3 ws22 v1"> </span></div><div class="t m0 x1 h14 y30 ff5 fs3 fc0 sc0 ls10 ws22">Buscamos un ce<span class="blank _0"></span>ro en el l<span class="blank _0"></span>ugar <span class="ff7 ws14">\uee87<span class="fs0 ls15 ws18 v8">\uf0dc\uf0db<span class="blank"> </span></span></span>. Hacemos <span class="ff7 lse">\uee72<span class="fs0 ls7 v8">\uf0db</span><span class="ls10 ws1a">\uf346<span class="blank"> </span>\uee72<span class="fs0 ls8 v8">\uf0dc</span><span class="ws1e">\uf437<span class="blank"> </span>\uee72<span class="fs0 ls9 v8">\uf0dc</span></span></span></span><span class="ff3"> </span></div><div class="t m0 x1a h1b y31 ff7 fs3 fc0 sc0 ls3">\uee6d<span class="fs0 lsa v4">\uebdb</span><span class="lsb">\uf34c<span class="fs2 lsc">\uf36d</span><span class="ls10 ws1c v2">\uf0da<span class="blank"> </span>\uf0db<span class="blank _7"> </span>\uf0da</span></span></div><div class="t m0 x1b h14 y32 ff7 fs3 fc0 sc0 ls10 ws1d">\uf0d9<span class="blank _8"> </span>\uf0e0<span class="blank _8"> </span>\uf0dc<span class="blank"> </span>\uf346<span class="blank"> </span>\uee91</div><div class="t m0 x1b h1c y33 ff7 fs3 fc0 sc0 ls10 ws1f">\uf0d9<span class="blank _8"> </span>\uf0d9<span class="blank _8"> </span>\uf0db<span class="blank _9"> </span>\uf346<span class="blank _9"> </span>\uee91<span class="blank"> </span><span class="fs2 lsd v1">\uf42d</span><span class="v9">\uf0d9</span></div><div class="t m0 x1c h14 y32 ff7 fs3 fc0 sc0 ls10 ws14">\uf346\uf0dc</div><div class="t m0 x1c h1d y34 ff7 fs3 fc0 sc0 ls10 ws14">\uf346\uf0db<span class="fs2 lsc v1">\uf371</span><span class="ff3 ws22 v1"> </span></div><div class="t m0 x1 h18 y35 ff5 fs3 fc0 sc0 ls10 ws22">La matriz y<span class="blank _0"></span>a está en su <span class="blank _0"></span>forma escalonada.<span class="blank _0"></span> </div><div class="t m0 x1 h18 y36 ff5 fs3 fc0 sc0 ls10 ws22">Para <span class="blank _a"> </span>que <span class="blank _a"> </span>el <span class="blank _a"> </span>sistema <span class="blank _a"> </span>sea <span class="blank _a"> </span>compatibl<span class="blank _0"></span>e <span class="blank _b"> </span>determina<span class="blank _0"></span>do, <span class="blank _a"> </span>el <span class="blank _a"> </span>rango <span class="blank _a"> </span>de <span class="blank _a"> </span>la <span class="blank _a"> </span>matri<span class="blank _0"></span>z <span class="blank _a"> </span>debe <span class="blank _a"> </span>ser <span class="blank _a"> </span>igual <span class="blank _a"> </span>al <span class="blank _a"> </span>rango <span class="blank _a"> </span>de <span class="blank _a"> </span>la <span class="blank _a"> </span>matriz </div><div class="t m0 x1 h14 y37 ff5 fs3 fc0 sc0 ls10 ws22">ampliada <span class="blank _c"> </span>e <span class="blank _c"> </span>igual <span class="blank _c"> </span>al <span class="blank _a"> </span>nú<span class="blank _0"></span>mero <span class="blank _c"> </span>de <span class="blank _c"> </span>incógnitas. <span class="blank _c"> </span>En <span class="blank _c"> </span>este <span class="blank _c"> </span>caso <span class="blank _c"> </span>el <span class="blank _c"> </span>número <span class="blank _c"> </span>de <span class="blank _a"> </span>in<span class="blank _0"></span>cógnitas <span class="blank _c"> </span>es <span class="blank _a"> </span><span class="ff7 ws14">\uf0dc</span> <span class="blank _c"> </span>y <span class="blank _c"> </span>el <span class="blank _c"> </span>rango <span class="blank _c"> </span>de <span class="blank _c"> </span>la <span class="blank _c"> </span>m<span class="blank _3"> </span>atriz<span class="blank _0"></span> </div><div class="t m0 x1 h14 y38 ff5 fs3 fc0 sc0 ls10 ws22">ampliada es <span class="ff7 ws14">\uf0dc</span>. Anali<span class="blank _0"></span>zamos que ocu<span class="blank _0"></span>rre con <span class="ff7 ws14">\uee91<span class="ff3 lsf">.</span></span> </div><div class="t m0 x1 h14 y39 ff5 fs3 fc0 sc0 ls16 ws22">Si <span class="ff7 ls10 ws20">\uee91<span class="blank"> </span>\uf34c<span class="blank"> </span>\uf0db</span><span class="ls10"> <span class="blank _3"> </span>entonces el <span class="blank _0"></span>rango de l<span class="blank _0"></span>a matriz es <span class="ff7 ws14">\uf0db</span> y por lo <span class="blank _0"></span>tanto el sistema <span class="blank _0"></span>sería compa<span class="blank _0"></span>tible indeter<span class="blank _0"></span>minado. </span></div><div class="t m0 x1 h14 y3a ff5 fs3 fc0 sc0 ls10 ws22">Por lo tanto el siste<span class="blank _0"></span>ma es co<span class="blank _0"></span>mpatible dete<span class="blank _0"></span>rminado para<span class="blank _0"></span> todo val<span class="blank _0"></span>or real <span class="ff7 ws21">\uee91<span class="blank"> </span>\uf34d<span class="blank"> </span>\uf0db<span class="ff3 wse">.</span></span> </div><div class="t m0 x1 h6 y3b ff3 fs3 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h6 y3c ff3 fs3 fc0 sc0 ls10 ws22"> <span class="blank _d"> </span> </div></div><div class="c x1 y3d w8 h1e"><div class="t m0 x1d h2 y3e ff2 fs0 fc0 sc0 ls10 ws22">APELLIDO: </div></div><div class="c x1e y3f w9 h1f"><div class="t m0 xb h2 y40 ff2 fs0 fc0 sc0 ls10 ws22">CALIFICACIÓN:<span class="blank _0"></span> </div></div><div class="c x1 y41 w8 h20"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls10 ws22">NOMBRE: </div></div><div class="c x1 y3f w8 h20"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls10 ws22">DNI (registrado en S<span class="blank _0"></span>IU Guaran<span class="blank _0"></span>í): </div></div><div class="c x1 y42 w8 h21"><div class="t m0 xb h2 y10 ff2 fs0 fc0 sc0 ls10 ws22">E-MAIL: </div></div><div class="c x1e y43 w9 h22"><div class="t m0 xb h2 y44 ff2 fs0 fc0 sc0 ls10 ws22">DOCENTE (nombre<span class="blank _0"></span> y apelli<span class="blank _0"></span>do): </div></div><div class="c x1 y45 w8 h20"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls10 ws22">TEL: </div></div><div class="c x1 y43 w8 h20"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls10 ws22">AULA: </div></div><div class="c x0 y46 wa h23"><div class="t m0 x1d h13 y47 ff4 fs3 fc2 sc0 ls10 ws22"><span class="fc3 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 y48 wb h24" alt="" src="https://files.passeidireto.com/21fa5c2b-4f9f-4ca0-bf5f-d7a54443d9fd/bg2.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls10 ws22">MATEMÁTICA (<span class="ls11 ws0">61</span><span class="ws1">)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls17"> <span class="ls18"> </span></span>2° PARC<span class="blank _3"> </span>IAL </div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 ls10 ws22">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> <span class="blank _0"></span> DNI:<span class="blank _0"></span><span class="ff1"> <span class="blank _e"> </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 4 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 ls10 ws22">Hoja 2 de 4 </div><div class="t m0 x3 h2 y49 ff2 fs0 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 hf y4a ff3 fs2 fc0 sc0 ls10 ws22">2. <span class="blank _b"> </span>Dados <span class="blank _b"> </span>los <span class="blank _a"> </span>vectores <span class="blank _b"> </span><span class="ff7">\uee9b</span></div></div><div class="c x0 y1 wc h0"><div class="t m0 x1f hf y4b ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x20 y1 wd h0"><div class="t m0 x21 hf y4b ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x22 y1 we h0"><div class="t m0 x23 hf y4b ff7 fs2 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x24 h25 y4a ff7 fs2 fc0 sc0 ls19">\uf34c<span class="ls1a va">\udb80\udddb</span><span class="ls10 ws23">\uf346\uf0da\ue7e2<span class="blank"> </span>\uf0db\ue7e2<span class="blank"> </span>\uf0de<span class="ls1a va">\udb80\udddc</span><span class="ws24">\ue603\ue7e1<span class="blank"> </span>\uee9c</span></span></div></div><div class="c x0 y1 wf h0"><div class="t m0 x25 hf y4b ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x11 y1 w10 h0"><div class="t m0 x21 hf y4b ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x26 y1 w11 h0"><div class="t m0 x21 hf y4b ff7 fs2 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x27 h25 y4a ff7 fs2 fc0 sc0 ls1b">\uf34c<span class="ls1a va">\udb80\udddb</span><span class="ls10 ws23">\uf0da\ue7e2<span class="blank"> </span>\uf346\uf0da\ue7e2<span class="blank"> </span>\uf0da<span class="ls1a va">\udb80\udddc</span><span class="ws25">\ue7e1<span class="blank"> </span>\uee9d</span></span></div></div><div class="c x0 y1 w12 h0"><div class="t m0 x28 hf y4a ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x9 y1 w13 h0"><div class="t m0 x21 hf y4a ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x29 y1 w13 h0"><div class="t m0 x21 hf y4a ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x2a y1 w14 h0"><div class="t m0 x23 hf y4a ff7 fs2 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x2b hf y4a ff7 fs2 fc0 sc0 ls10 ws23">\uf34c<span class="blank _4"> </span>\udb80\udddb\uf346\uf0dc\ue7e2<span class="blank"> </span>\uf0da\ue7e2<span class="blank"> </span>\uf346<span class="blank _3"></span>\uf0da\udb80\udddc<span class="ff3 ws22"> <span class="blank _a"> </span>halla<span class="blank _3"> </span>r <span class="blank _b"> </span>el <span class="blank _a"> </span>valor <span class="blank _b"> </span>del <span class="blank _b"> </span>producto </span></div><div class="t m0 x1 hf y4c ff3 fs2 fc0 sc0 ls10 ws22">mixto <span class="ff7">\uee9c</span></div></div><div class="c x0 y1 w15 h0"><div class="t m0 x2c hf y4d ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x2d y1 w10 h0"><div class="t m0 x21 hf y4d ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x2d y1 w16 h0"><div class="t m0 x21 hf y4d ff7 fs2 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x2e h25 y4c ff7 fs2 fc0 sc0 ls1c">\ue7e4<span class="ls1a va">\udb80\udddb</span><span class="ls10">\uee9b</span></div></div><div class="c x0 y1 w17 h0"><div class="t m0 x2f hf y4d ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x30 y1 wd h0"><div class="t m0 x21 hf y4d ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x31 y1 w18 h0"><div class="t m0 x23 hf y4d ff7 fs2 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x32 hf y4c ff7 fs2 fc0 sc0 ls10 ws7">\uee9e\uee9d</div></div><div class="c x0 y1 w19 h0"><div class="t m0 x33 hf y4c ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x34 y1 w13 h0"><div class="t m0 x21 hf y4c ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x35 y1 w13 h0"><div class="t m0 x21 hf y4c ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x36 y1 w1a h0"><div class="t m0 x23 hf y4c ff7 fs2 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x37 hf y4e ff7 fs2 fc0 sc0 ls1a">\udb80\udddc<span class="ls10 ws7 vb">\ue7e4<span class="ff3 ws22"> </span></span></div><div class="t m0 x1 h4 y4f ff3 fs2 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h14 y50 ff5 fs3 fc0 sc0 ls10 ws22">Para de<span class="blank _0"></span>terminar <span class="blank _0"></span>el p<span class="blank _0"></span>roducto<span class="blank _0"></span> mixto <span class="blank _0"></span>lo <span class="blank _0"></span>primero<span class="blank _0"></span> que<span class="blank _0"></span> debe<span class="blank _0"></span>mos hal<span class="blank _0"></span>lar es<span class="blank _0"></span> el<span class="blank _0"></span> producto<span class="blank _0"></span> vectori<span class="blank _0"></span>al <span class="ff7">\uee9b</span></div></div><div class="c x0 y1 w1b h0"><div class="t m0 x38 h14 y51 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x39 y1 wd h0"><div class="t m0 x21 h14 y51 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x3a y1 w1c h0"><div class="t m0 x23 h14 y51 ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x3b h14 y50 ff7 fs3 fc0 sc0 ls10 ws14">\uee9e\uee9d</div></div><div class="c x0 y1 w1d h0"><div class="t m0 x3c h14 y52 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x3d y1 w1e h0"><div class="t m0 x21 h14 y52 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x3e y1 w1e h0"><div class="t m0 x21 h14 y52 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x3f y1 w1f h0"><div class="t m0 x23 h14 y52 ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x40 h6 y50 ff3 fs3 fc0 sc0 ls10 ws22"> <span class="ff5"> <span class="blank _0"></span>(el esta<span class="blank _0"></span>r <span class="blank _0"></span>indicad<span class="blank _0"></span>o </span></div><div class="t m0 x1 h18 y53 ff5 fs3 fc0 sc0 ls10 ws22">entre paréntesis si<span class="blank _0"></span>gnifica que lo debe<span class="blank _0"></span>mos resolv<span class="blank _0"></span>er antes del p<span class="blank _0"></span>roducto escal<span class="blank _0"></span>ar). </div><div class="t m0 x41 h14 y54 ff7 fs3 fc0 sc0 ls10">\uee9b</div></div><div class="c x0 y1 w20 h0"><div class="t m0 x41 h14 y55 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x42 y1 wd h0"><div class="t m0 x21 h14 y55 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x43 y1 w21 h0"><div class="t m0 x23 h14 y55 ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x44 h14 y54 ff7 fs3 fc0 sc0 ls10 ws14">\uee9e\uee9d</div></div><div class="c x0 y1 w22 h0"><div class="t m0 x45 h14 y56 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x25 y1 w1e h0"><div class="t m0 x21 h14 y56 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x12 y1 w1e h0"><div class="t m0 x21 h14 y56 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x11 y1 w23 h0"><div class="t m0 x23 h14 y56 ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x46 h26 y54 ff7 fs3 fc0 sc0 ls1d">\uf34c<span class="ls10 ws14 va">\udb80\udddb</span><span class="ls10 ws26">\uf346\uf0da\ue7e2<span class="blank"> </span>\uf0db\ue7e2<span class="blank"> </span>\uf0de<span class="ws14 va">\udb80\udddc<span class="vb">\ue603\uee9e\ue603</span>\udb80\udddb</span>\uf346\uf0dc\ue7e2<span class="blank"> </span>\uf0da\ue7e2<span class="blank"> </span>\uf346\uf0da<span class="ws14 va">\udb80\udddc</span><span class="ff3 ws22"> </span></span></div><div class="t m0 x47 h14 y57 ff7 fs3 fc0 sc0 ls10">\uee9b</div></div><div class="c x0 y1 w24 h0"><div class="t m0 x47 h14 y58 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x48 y1 wd h0"><div class="t m0 x21 h14 y58 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x49 y1 w25 h0"><div class="t m0 x23 h14 y58 ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x4a h14 y57 ff7 fs3 fc0 sc0 ls10 ws14">\uee9e\uee9d</div></div><div class="c x0 y1 w26 h0"><div class="t m0 x4b h14 y59 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x22 y1 w1e h0"><div class="t m0 x21 h14 y59 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x4c y1 w1e h0"><div class="t m0 x21 h14 y59 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x4d y1 w27 h0"><div class="t m0 x23 h14 y59 ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x4e h26 y57 ff7 fs3 fc0 sc0 ls1e">\uf34c<span class="ls10 ws14 v0">\uf36b</span><span class="ls10 ws27">\uf0db\ue7e4<span class="blank"> </span><span class="ws14 va">\udb80\udddb<span class="vb">\uf346\uf0da</span><span class="ls1f">\udb80\udddc</span></span><span class="ws19">\uf346<span class="blank _f"> </span>\uf0de\ue7e4<span class="blank"> </span>\uf0da\ue7e2<span class="blank"> </span>\uf0de\ue7e4<span class="blank"> </span><span class="ws14 va">\udb80\udddb<span class="vb">\uf346\uf0dc</span><span class="ls20">\udb80\udddc</span></span><span class="ls21">\uf346</span><span class="ws14 va">\udb80\udddb<span class="vb">\uf346\uf0da</span>\udb80\udddc</span><span class="ls22">\ue7e4</span><span class="ws14 va">\udb80\udddb<span class="vb">\uf346\uf0da</span>\udb80\udddc</span><span class="ls23">\ue7e2</span><span class="ws14 va">\udb80\udddb<span class="vb">\uf346\uf0da</span>\udb80\udddc</span>\ue7e4<span class="blank"> </span>\uf0da<span class="blank _f"> </span>\uf346<span class="blank _f"> </span>\uf0db\ue7e4<span class="blank"> </span><span class="ws14 va">\udb80\udddb<span class="vb">\uf346\uf0dc</span>\udb80\udddc<span class="vb">\uf36f</span></span><span class="ff3 ws22"> </span></span></span></div><div class="t m0 x46 h14 y5a ff7 fs3 fc0 sc0 ls10">\uee9c</div></div><div class="c x0 y1 w28 h0"><div class="t m0 x46 hf y5a ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x4f y1 w29 h0"><div class="t m0 x23 hf y5a ff7 fs2 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x50 h14 y5a ff7 fs3 fc0 sc0 ls10 ws14">\uee9e\uee9d</div></div><div class="c x0 y1 w2a h0"><div class="t m0 x51 hf y5a ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x52 y1 w2b h0"><div class="t m0 x21 hf y5a ff7 fs2 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x53 y1 w2c h0"><div class="t m0 x23 hf y5a ff7 fs2 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x54 h25 y5a ff7 fs3 fc0 sc0 ls24">\uf34c<span class="fs2 ls1a va">\udb80\udddb</span><span class="ls10 ws28">\uf346\uf0e0\ue7e2<span class="blank"> </span>\uf346</span><span class="ls2a ws29">\uf0da\uf0df</span><span class="ls10 ws28">\ue7e2<span class="blank"> </span>\uf0de<span class="fs2 ws7 va">\udb80\udddc</span><span class="ff3 ws22"> </span></span></div><div class="t m0 x1 h18 y5b ff5 fs3 fc0 sc0 ls10 ws22">A continuación calculam<span class="blank _0"></span>os el producto<span class="blank _0"></span> escalar: </div><div class="t m0 x55 h14 y5c ff7 fs3 fc0 sc0 ls10">\uee9c</div></div><div class="c x0 y1 w2d h0"><div class="t m0 x55 h14 y5d ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x56 y1 w10 h0"><div class="t m0 x21 h14 y5d ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x56 y1 w2e h0"><div class="t m0 x21 h14 y5d ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x57 h26 y5c ff7 fs3 fc0 sc0 ls25">\ue7e4<span class="ls10 ws14 va">\udb80\udddb</span><span class="ls2b ws2a">\uee9b\uee9e<span class="ls10">\uee9d</span></span></div></div><div class="c x0 y1 w2f h0"><div class="t m0 x58 h14 y5e ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x59 y1 w1e h0"><div class="t m0 x21 h14 y5e ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x5a y1 w1e h0"><div class="t m0 x21 h14 y5e ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x5b y1 w30 h0"><div class="t m0 x23 h14 y5e ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x5c h14 y5f ff7 fs3 fc0 sc0 ls26">\udb80\udddc<span class="ls1d vb">\uf34c</span><span class="ls10 ws14">\udb80\udddb<span class="ws26 vb">\uf0da\ue7e2<span class="blank"> </span>\uf346\uf0da\ue7e2<span class="blank"> </span>\uf0da</span>\udb80\udddc<span class="ls25 vb">\ue7e4</span>\udb80\udddb<span class="ws26 vb">\uf346\uf0e0\ue7e2<span class="blank"> </span>\uf346</span></span><span class="ls2a ws29 vb">\uf0da\uf0df</span><span class="ls10 ws2b vb">\ue7e2<span class="blank"> </span>\uf0de</span>\udb80\udddc<span class="ls10 ws1e vb">\uf43a<span class="blank"> </span>\uee9b</span></div></div><div class="c x0 y1 w31 h0"><div class="t m0 x5d h14 y5d ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x5e y1 wd h0"><div class="t m0 x21 h14 y5d ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x5f y1 w32 h0"><div class="t m0 x23 h14 y5d ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x60 h26 y5c ff7 fs3 fc0 sc0 ls25">\ue7e4<span class="ls10 ws14 va">\udb80\udddb</span><span class="ls10">\uee9c</span></div></div><div class="c x0 y1 w33 h0"><div class="t m0 x61 h14 y5d ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x62 y1 w10 h0"><div class="t m0 x21 h14 y5d ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x62 y1 w34 h0"><div class="t m0 x21 h14 y5d ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x63 h14 y5c ff7 fs3 fc0 sc0 ls10 ws14">\uee9e\uee9d</div></div><div class="c x0 y1 w35 h0"><div class="t m0 x9 h14 y5e ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x29 y1 w1e h0"><div class="t m0 x21 h14 y5e ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x2a y1 w1e h0"><div class="t m0 x21 h14 y5e ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x64 y1 w36 h0"><div class="t m0 x23 h14 y5e ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x65 h14 y5f ff7 fs3 fc0 sc0 ls26">\udb80\udddc<span class="ls10 ws19 vb">\uf34c<span class="blank _10"> </span>\uf0da\ue7e4<span class="blank"> </span></span><span class="ls10 ws14">\udb80\udddb<span class="vb">\uf346\uf0e0</span><span class="ls27">\udb80\udddc<span class="ls28 vb">\uf345</span></span>\udb80\udddb<span class="vb">\uf346\uf0da</span>\udb80\udddc<span class="ls25 vb">\ue7e4</span>\udb80\udddb<span class="ls29 vb">\uf346</span></span><span class="ls2a ws29 vb">\uf0da\uf0df</span><span class="ls1f">\udb80\udddc<span class="ls10 ws19 vb">\uf345<span class="blank _f"> </span>\uf0da\ue7e4<span class="blank"> </span>\uf0de<span class="ff3 ws22"> </span></span></span></div><div class="t m0 x66 h14 y60 ff7 fs3 fc0 sc0 ls10">\uee9b</div></div><div class="c x0 y1 w37 h0"><div class="t m0 x66 h14 y61 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x67 y1 wd h0"><div class="t m0 x21 h14 y61 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x68 y1 w38 h0"><div class="t m0 x23 h14 y61 ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x14 h26 y60 ff7 fs3 fc0 sc0 ls25">\ue7e4<span class="ls10 ws14 va">\udb80\udddb</span><span class="ls10">\uee9c</span></div></div><div class="c x0 y1 w39 h0"><div class="t m0 xd h14 y61 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x69 y1 w10 h0"><div class="t m0 x21 h14 y61 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x69 y1 w3a h0"><div class="t m0 x21 h14 y61 ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x6a h14 y60 ff7 fs3 fc0 sc0 ls10 ws14">\uee9e\uee9d</div></div><div class="c x0 y1 w3b h0"><div class="t m0 x41 h14 y62 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x42 y1 w1e h0"><div class="t m0 x21 h14 y62 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x43 y1 w1e h0"><div class="t m0 x21 h14 y62 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x6b y1 w3c h0"><div class="t m0 x23 h14 y62 ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x15 h14 y63 ff7 fs3 fc0 sc0 ls26">\udb80\udddc<span class="ls10 ws2c vb">\uf34c<span class="blank _10"> </span>\uf346\uf0e0<span class="blank"> </span>\uf345<span class="blank"> </span></span><span class="ls2a ws2d vb">\uf0da\uf0df<span class="blank"> </span></span><span class="ls10 ws1a vb">\uf345<span class="blank"> </span>\uf0de<span class="blank _10"> </span>\uf43a<span class="blank _10"> </span>\uee9b</span></div></div><div class="c x0 y1 w3d h0"><div class="t m0 x19 h14 y61 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x2b y1 wd h0"><div class="t m0 x21 h14 y61 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x18 y1 w3e h0"><div class="t m0 x23 h14 y61 ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x16 h26 y60 ff7 fs3 fc0 sc0 ls25">\ue7e4<span class="ls10 ws14 va">\udb80\udddb</span><span class="ls10">\uee9c</span></div></div><div class="c x0 y1 w3f h0"><div class="t m0 x6c h14 y61 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x6d y1 w10 h0"><div class="t m0 x21 h14 y61 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x6d y1 w40 h0"><div class="t m0 x21 h14 y61 ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x13 h14 y60 ff7 fs3 fc0 sc0 ls10 ws14">\uee9e\uee9d</div></div><div class="c x0 y1 w41 h0"><div class="t m0 x6e h14 y62 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x6f y1 w1e h0"><div class="t m0 x21 h14 y62 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x70 y1 w1e h0"><div class="t m0 x21 h14 y62 ff7 fs3 fc0 sc0 ls10">\udb80\uddcd</div></div><div class="c x71 y1 w42 h0"><div class="t m0 x23 h14 y62 ff7 fs3 fc0 sc0 ls10">\ueb26</div></div><div class="c x0 y1 w2 h0"><div class="t m0 x72 h14 y63 ff7 fs3 fc0 sc0 ls26">\udb80\udddc<span class="ls1d vb">\uf34c<span class="ls2a ws29">\uf0da\uf0dd<span class="ff5 ls10 ws22"> </span></span></span></div><div class="t m0 x1 h18 y64 ff5 fs3 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h4 y65 ff3 fs2 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h18 y66 ff5 fs3 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h18 y67 ff5 fs3 fc0 sc0 ls10 ws22"> <span class="blank _d"> </span> </div></div><div class="c x0 y46 wa h23"><div class="t m0 x1d h13 y47 ff4 fs3 fc2 sc0 ls10 ws22"><span class="fc3 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 y68 wb h27" alt="" src="https://files.passeidireto.com/21fa5c2b-4f9f-4ca0-bf5f-d7a54443d9fd/bg3.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h28 y69 ff5 fs6 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h2 y6a ff1 fs0 fc0 sc0 ls10 ws22">MATEMÁTICA (<span class="ls40 ws2e">61</span><span class="ws1">)</span><span class="ff2"> Cátedra<span class="blank _0"></span> A: NUÑEZ, <span class="blank _0"></span>MYRIAM<span class="ff1"> <span class="blank _0"></span> 2° PARC<span class="blank _0"></span>IAL </span></span></div><div class="t m0 x1 h2 y6b ff2 fs0 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h2 y6c ff2 fs0 fc0 sc0 ls10 ws22">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> <span class="blank _0"></span> DNI<span class="blank _0"></span>:<span class="ff1"> <span class="blank _e"> </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 4 </span></div><div class="t m0 x3 h2 y6d ff2 fs0 fc0 sc0 ls10 ws22">Hoja 3 de 4 </div><div class="t m0 x3 h2 y6e ff2 fs0 fc0 sc0 ls10 ws22"> </div><div class="t m0 x2 h29 y6f ff1 fs0 fc0 sc0 ls2c ws22"> <span class="ff3 fs2 ls10 vc">3. Calcular el área de la región comprendida entre el gráfico de <span class="ff7 ls2d">\uee8c<span class="ls1a va">\udb80\udddb</span><span class="ls2e">\uee9e<span class="ls2f va">\udb80\udddc</span><span class="ls10 ws2f">\uf34c<span class="blank"> </span>\uee9e<span class="fs7 ls30 v4">\uf0dc</span><span class="ws30">\uf346<span class="blank"> </span>\uf0da</span></span></span></span> <span class="ls1">, </span><span class="ff7 ws8">\uee9e<span class="blank"> </span>\uf34c<span class="blank"> </span>\uf346\uf0da</span><span class="ls1"> <span class="ls41">y <span class="blank _c"> </span></span></span><span class="ff7 ws31">\uee9e<span class="blank"> </span>\uf34c<span class="blank"> </span>\uf0db</span><span class="ls1">. </span> </span></div><div class="t m0 x24 h4 y70 ff3 fs2 fc0 sc0 ls10 ws22"> </div><div class="t m0 x24 h18 y71 ff5 fs3 fc0 sc0 ls10 ws22"> </div><div class="t m0 x24 h18 y72 ff5 fs3 fc0 sc0 ls10 ws22">Como <span class="blank _0"></span>el<span class="blank _0"></span> <span class="blank _11"></span>área <span class="blank _11"></span>a <span class="blank _11"></span>calcular <span class="blank _11"></span>está<span class="blank _0"></span> <span class="blank _11"></span>formada <span class="blank _11"></span>por <span class="blank _11"></span>una <span class="blank _11"></span>región <span class="blank _11"></span>por <span class="blank _11"></span>debajo<span class="blank _0"></span> <span class="blank _11"></span>del <span class="blank _11"></span>eje <span class="blank _0"></span>de <span class="blank _11"></span>abscisas </div><div class="t m0 x24 h14 y73 ff5 fs3 fc0 sc0 ls10 ws22">y <span class="blank _c"> </span>otra <span class="blank _c"> </span>por <span class="blank _c"> </span>enci<span class="blank _0"></span>ma <span class="blank _c"> </span>del <span class="blank _3"> </span>m<span class="blank _3"> </span>ismo, <span class="blank _c"> </span>debe<span class="blank _0"></span>mos <span class="blank _c"> </span>dete<span class="blank _0"></span>rminar <span class="blank _c"> </span>el <span class="blank _c"> </span>val<span class="blank _0"></span>or <span class="blank _c"> </span>de <span class="blank _c"> </span><span class="ff7 ws14">\uee9e</span> <span class="blank _c"> </span>donde <span class="blank _c"> </span>la <span class="blank _12"> </span>gráfica </div><div class="t m0 x24 h14 y74 ff5 fs3 fc0 sc0 ls10 ws22">corta dicho eje.<span class="blank _0"></span> Es decir, dete<span class="blank _0"></span>rminar el val<span class="blank _0"></span>or de <span class="ff7 ws14">\uee9e</span> para el cual <span class="ff7 ws32">\uee8c\udb80\udddb\uee9e\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank"> </span>\uf0d9</span>. </div><div class="t m0 x24 h14 y75 ff5 fs3 fc0 sc0 ls10 ws22">Verificamos <span class="blank _13"> </span>que <span class="blank _13"> </span><span class="ff7 ws33">\uee9e<span class="blank"> </span>\uf34c<span class="blank _10"> </span>\uf0da</span> <span class="blank _f"> </span>es <span class="blank _13"> </span>el <span class="blank _f"> </span>punto <span class="blank _13"> </span>de <span class="blank _f"> </span>i<span class="blank _0"></span>ntersección<span class="blank _11"></span> <span class="blank _f"> </span>de <span class="blank _13"> </span>la <span class="blank _f"> </span>grá<span class="blank _0"></span>fica <span class="blank _13"> </span>con <span class="blank _f"> </span>el <span class="blank _13"> </span>eje <span class="blank _13"> </span>de </div><div class="t m0 x24 h26 y76 ff5 fs3 fc0 sc0 ls10 ws22">abscisas, ya que <span class="blank _0"></span><span class="ff7 ls31">\uee8c<span class="ls10 ws14 va">\udb80\udddb<span class="vb">\uf0da</span><span class="ls26">\udb80\udddc</span></span><span class="ls10 wsf">\uf34c<span class="blank"> </span>\uf0da<span class="fs0 ls7 v5">\uf0dc</span><span class="ws1a">\uf346<span class="blank"> </span>\uf0da<span class="blank _10"> </span>\uf34c<span class="blank _10"> </span>\uf0d9<span class="ff5 ws22"> </span></span></span></span></div><div class="t m0 x24 h18 y77 ff5 fs3 fc0 sc0 ls10 ws22">Entonces el área<span class="blank _0"></span> a calcular es: </div><div class="t m0 x5f h14 y78 ff7 fs3 fc0 sc0 ls10 ws34">\uee6d<span class="blank _10"> </span>\uf34c<span class="blank _10"> </span>\uf346<span class="blank _14"> </span>\uf3b1<span class="blank"> </span>\uee8c\udb80\udddb\uee9e\udb80\udddc<span class="ls42">\uee8a\uee9e</span></div><div class="t m0 x16 h2a y79 ff7 fs0 fc0 sc0 ls10">\uf0da</div><div class="t m0 x19 h2b y7a ff7 fs0 fc0 sc0 ls10 ws35">\uf13f\uf0da<span class="blank"> </span><span class="fs3 ws34 vd">\uf345<span class="blank _f"> </span>\uf3b1<span class="blank"> </span>\uee8c\udb80\udddb\uee9e\udb80\udddc</span></div><div class="t m0 x73 h2a y79 ff7 fs0 fc0 sc0 ls10">\uf0db</div><div class="t m0 x74 h2b y7a ff7 fs0 fc0 sc0 ls32">\uf0da<span class="fs3 ls42 ws36 vd">\uee8a\uee9e<span class="ff3 ls10 ws22"> </span></span></div><div class="t m0 x24 h18 y7b ff5 fs3 fc0 sc0 ls10 ws22">Por otra parte,<span class="blank _0"></span> </div><div class="t m0 x1f h26 y7c ff7 fs3 fc0 sc0 ls10 ws34">\uf3b1<span class="blank"> </span>\uee8c<span class="ws14 va">\udb80\udddb<span class="vb">\uee9e</span>\udb80\udddc</span><span class="ls42 ws37">\uee8a\uee9e<span class="blank"> </span></span><span class="ws38">\ue603<span class="blank"> </span>\uf34c<span class="blank _10"> </span>\uf3b1<span class="ws14 v0">\uf36b<span class="v0">\uee9e<span class="fs0 ls7 v5">\uf0dc</span><span class="ws1a">\uf346<span class="blank"> </span>\uf0da</span></span>\uf36f</span><span class="ls42 ws39">\uee8a\uee9e<span class="blank"> </span></span></span>\uf43a<span class="blank"> </span>\uf3b1<span class="blank"> </span>\uee8c<span class="ws14 va">\udb80\udddb<span class="vb">\uee9e</span>\udb80\udddc</span><span class="ls42 ws37">\uee8a\uee9e<span class="blank"> </span></span><span class="ws38">\ue603<span class="blank"> </span>\uf34c<span class="blank _10"> </span>\uf3b1<span class="blank"> </span>\uee9e<span class="fs0 ls33 v5">\uf0dc</span><span class="ls42 ws3a">\uee8a\uee9e<span class="blank"> </span></span><span class="ws3b">\uf346<span class="blank _f"> </span>\uf3b1<span class="blank"> </span><span class="ls42 ws36">\uee8a\uee9e</span><span class="ff3 ws22"> </span></span></span></div><div class="t m0 x75 h2c y7d ff7 fs3 fc0 sc0 ls10 ws34">\uf3b1<span class="blank"> </span>\uee8c<span class="ws14 va">\udb80\udddb<span class="vb">\uee9e</span>\udb80\udddc</span><span class="ls42 ws39">\uee8a\uee9e<span class="blank"> </span><span class="ls34">\uf34c</span></span><span class="ve">\uf0da</span></div><div class="t m0 x5e h2d y7e ff7 fs3 fc0 sc0 ls35">\uf0dd<span class="ls10 ws14 vf">\uee9e</span><span class="fs0 ls7 v10">\uf0dd</span><span class="ls10 ws1a vf">\uf346<span class="blank"> </span>\uee9e<span class="blank"> </span>\uf345<span class="blank"> </span>\uee6f<span class="ff3 ws22"> </span></span></div><div class="t m0 x1 h18 y7f ff5 fs3 fc0 sc0 ls10 ws22">Entonces: </div><div class="t m0 x69 h2c y80 ff7 fs3 fc0 sc0 ls10 ws3c">\uee6d<span class="blank _10"> </span>\uf34c<span class="blank _10"> </span>\uf346<span class="blank"> </span>\uf36c<span class="ve">\uf0da</span></div><div class="t m0 x27 h2d y81 ff7 fs3 fc0 sc0 ls35">\uf0dd<span class="ls10 ws14 vf">\uee9e</span><span class="fs0 ls7 v10">\uf0dd</span><span class="ls10 ws1a vf">\uf346<span class="blank"> </span>\uee9e\uf370</span><span class="ls36 vf">\uf42c</span><span class="fs0 ls10 ws3d v8">\uf13f\uf0da</span></div><div class="t m0 x5e h2e y82 ff7 fs0 fc0 sc0 ls37">\uf0da<span class="fs3 ls10 ws1a vc">\uf345<span class="blank"> </span>\uf36c<span class="ve">\uf0da</span></span></div><div class="t m0 x64 h2d y81 ff7 fs3 fc0 sc0 ls35">\uf0dd<span class="ls10 ws14 vf">\uee9e</span><span class="fs0 ls7 v10">\uf0dd</span><span class="ls10 ws1a vf">\uf346<span class="blank"> </span>\uee9e\uf370</span><span class="ls36 vf">\uf42c</span><span class="fs0 ls10 v8">\uf0da</span></div><div class="t m0 x76 h2a y82 ff7 fs0 fc0 sc0 ls33">\uf0db<span class="ff3 fs3 ls10 ws22 vc"> </span></div><div class="t m0 x77 h2c y83 ff7 fs3 fc0 sc0 ls10 ws3e">\uee6d<span class="blank _10"> </span>\uf34c<span class="blank _10"> </span>\uf346<span class="blank"> </span>\uf36d<span class="ve">\uf0da</span></div><div class="t m0 x4e h2f y84 ff7 fs3 fc0 sc0 ls38">\uf0dd<span class="ls10 ws19 vf">\ue7e4<span class="blank"> </span>\uf0da</span><span class="fs0 ls7 v10">\uf0dd</span><span class="ls28 ws3f vf">\uf346\uf0da\uf346</span><span class="ls39 vf">\udb80\udde7</span><span class="ls10 v11">\uf0da</span></div><div class="t m0 x15 h2f y84 ff7 fs3 fc0 sc0 ls35">\uf0dd<span class="ls25 vf">\ue7e4</span><span class="ls10 ws14 v12">\udb80\udddb<span class="vb">\uf346\uf0da</span>\udb80\udddc<span class="fs0 ls7 v13">\uf0dd</span><span class="ls21 vb">\uf346</span>\udb80\udddb<span class="vb">\uf346\uf0da</span>\udb80\udddc<span class="ls39 vb">\udb80\udde8</span><span class="ws40 vb">\uf371<span class="blank"> </span>\uf345<span class="blank"> </span></span><span class="ls39 vb">\udb80\udde7</span><span class="v12">\uf0da</span></span></div><div class="t m0 x78 h2f y84 ff7 fs3 fc0 sc0 ls3a">\uf0dd<span class="ls10 ws19 vf">\ue7e4<span class="blank"> </span>\uf0db</span><span class="fs0 ls7 v10">\uf0dd</span><span class="ls10 ws1a vf">\uf346<span class="blank"> </span>\uf0db<span class="blank"> </span>\uf346<span class="blank"> </span>\uf36c<span class="ve">\uf0da</span></span></div><div class="t m0 x79 h2d y84 ff7 fs3 fc0 sc0 ls3b">\uf0dd<span class="ls10 ws19 vf">\ue7e4<span class="blank"> </span>\uf0da</span><span class="fs0 ls7 v10">\uf0dd</span><span class="ls10 ws41 vf">\uf346<span class="blank"> </span>\uf0da\uf370</span><span class="ls10 ws14 vf">\udb80\udde8</span><span class="ff3 ls10 ws22 vf"> </span></div><div class="t m0 x4 h2c y85 ff7 fs3 fc0 sc0 ls10 ws3e">\uee6d<span class="blank _10"> </span>\uf34c<span class="blank _10"> </span>\uf346<span class="blank"> </span>\uf36c\uf346<span class="blank"> </span><span class="ve">\uf0dc</span></div><div class="t m0 x7a h2f y86 ff7 fs3 fc0 sc0 ls3c">\uf0dd<span class="ls21 vf">\uf346</span><span class="ls10 v11">\uf0de</span></div><div class="t m0 x1a h2f y86 ff7 fs3 fc0 sc0 ls10 ws14">\uf0dd<span class="ws41 vf">\uf370<span class="blank"> </span>\uf345<span class="blank"> </span>\uf36c\uf0db<span class="blank _f"> </span>\uf345<span class="blank _f"> </span></span><span class="v11">\uf0dc</span></div><div class="t m0 x7b h2f y86 ff7 fs3 fc0 sc0 ls10 ws14">\uf0dd<span class="ws2c vf">\uf370<span class="blank _10"> </span>\uf43a<span class="blank _10"> </span>\uee6d<span class="blank _10"> </span>\uf34c<span class="blank _10"> </span>\uf0db<span class="blank"> </span>\uf345<span class="blank"> </span></span><span class="ls2a v11">\uf0da\uf0da</span></div><div class="t m0 x7c h2f y86 ff7 fs3 fc0 sc0 ls3d">\uf0dd<span class="ls10 ws38 vf">\ue603<span class="blank"> </span>\uf43a<span class="blank _10"> </span>\uee6d<span class="blank _10"> </span>\uf34c<span class="blank _10"> </span></span><span class="ls2a v11">\uf0da\uf0e2</span></div><div class="t m0 x7d h14 y86 ff7 fs3 fc0 sc0 ls3e">\uf0dd<span class="ff3 ls10 ws22 vf"> </span></div><div class="t m0 x1 h18 y87 ff5 fs3 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h4 y88 ff3 fs2 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h4 y89 ff3 fs2 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h4 y8a ff3 fs2 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h4 y8b ff3 fs2 fc0 sc0 ls3f ws22"> <span class="ff4 fs3 ls10 v14"> </span></div><div class="t m0 x1 h6 y8c ff3 fs3 fc0 sc0 ls10 ws22"> <span class="blank _d"> </span> </div></div><div class="c x0 y8d wa h30"><div class="t m0 x1d h13 y47 ff4 fs3 fc2 sc0 ls10 ws22"><span class="fc3 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 y8e wb h31" alt="" src="https://files.passeidireto.com/21fa5c2b-4f9f-4ca0-bf5f-d7a54443d9fd/bg4.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls10 ws22">MATEMÁTICA (<span class="ls11 ws0">61</span><span class="ws1">)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls17"> <span class="ls18"> </span></span>2° PARC<span class="blank _3"> </span>IAL </div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 ls10 ws22">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> <span class="blank _0"></span> DNI<span class="blank _0"></span>:<span class="ff1"> <span class="blank _e"> </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 4 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 ls10 ws22">Hoja 4 de 4 </div><div class="t m0 x3 h2 y49 ff2 fs0 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h13 y8f ff4 fs3 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h32 y90 ff3 fs2 fc0 sc0 ls13">4<span class="ls1 ws22">. <span class="fs3 ls10">Hallar los in<span class="blank _0"></span>tervalos de<span class="blank _0"></span> crecimiento d<span class="blank _0"></span>e la func<span class="blank _0"></span>ión <span class="ff7 ws32">\uee8c\udb80\udddb\uee9e\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="fs0 v15">\uf0da</span></span></span></span></div><div class="t m0 x65 h33 y4d ff7 fs0 fc0 sc0 ls43">\uf0dc<span class="fs3 ls10 ws14 v16">\uee9e</span><span class="ls7 v17">\uf0dc</span><span class="fs3 ls10 ws1a v16">\uf345<span class="blank"> </span>\uee9e</span><span class="ls44 v17">\uf0db</span><span class="fs3 ls10 ws42 v16">\ue603<span class="blank"> </span>\uf346<span class="blank _f"> </span>\ue603<span class="ls2a ws29">\uf0dc\uee9e<span class="ff3 fs2 ls10 ws22"> </span></span></span></div><div class="t m0 x1 h4 y91 ff3 fs2 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h18 y92 ff5 fs3 fc0 sc0 ls10 ws22">Para <span class="blank _c"> </span>analiz<span class="blank _0"></span>ar <span class="blank _c"> </span>el <span class="blank _12"> </span>crecimiento<span class="blank _0"></span> <span class="blank _c"> </span>de <span class="blank _12"> </span>una <span class="blank _12"> </span>f<span class="blank _3"> </span>unción<span class="blank _0"></span> <span class="blank _c"> </span>es <span class="blank _12"> </span>necesario <span class="blank _c"> </span>dete<span class="blank _0"></span>rminar <span class="blank _12"> </span>previamente <span class="blank _12"> </span>su <span class="blank _12"> </span>dominio. <span class="blank _12"> </span>En <span class="blank _c"> </span>este <span class="blank _12"> </span>caso <span class="blank _c"> </span>la </div><div class="t m0 x1 h26 y93 ff5 fs3 fc0 sc0 ls10 ws22">función es una <span class="blank _0"></span>función poli<span class="blank _0"></span>nómica por lo tan<span class="blank _0"></span>to: <span class="ff7 ws14">\uee70\uee95\uee93<span class="va">\udb80\udddb</span><span class="ls31">\uee8c<span class="ls45 va">\udb80\udddc</span></span><span class="wsf">\uf34c<span class="blank"> </span>\ueb39</span></span> . </div><div class="t m0 x1 h18 y94 ff5 fs3 fc0 sc0 ls10 ws22">Teniendo <span class="blank _12"> </span>en <span class="blank _c"> </span>cuenta <span class="blank _c"> </span>que <span class="blank _12"> </span>en <span class="blank _c"> </span>los <span class="blank _c"> </span>intervalos <span class="blank _c"> </span>de <span class="blank _c"> </span>crecimiento <span class="blank _12"> </span>de <span class="blank _c"> </span>una <span class="blank _12"> </span>f<span class="blank _3"> </span>unción, <span class="blank _12"> </span>su <span class="blank _c"> </span>derivada <span class="blank _12"> </span>es <span class="blank _c"> </span>positiva, <span class="blank _c"> </span>hallamos <span class="blank _12"> </span>la </div><div class="t m0 x1 h14 y95 ff5 fs3 fc0 sc0 ls10 ws22">derivada de la <span class="blank _0"></span>función <span class="ff7 ls31">\uee8c</span> y deter<span class="blank _0"></span>minamos el con<span class="blank _0"></span>junto de positiv<span class="blank _0"></span>idad de <span class="ff7 ws14">\uee8c\ue7b2</span> . </div><div class="t m0 x7e h2c y96 ff7 fs3 fc0 sc0 ls31">\uee8c<span class="ls10 ws14 va">\udb80\udddb<span class="vb">\uee9e</span><span class="ls26">\udb80\udddc</span></span><span class="ls1d">\uf34c<span class="ls10 ve">\uf0da</span></span></div><div class="t m0 x6a h34 y97 ff7 fs3 fc0 sc0 ls35">\uf0dc<span class="ls10 ws14 vf">\uee9e</span><span class="fs0 ls7 v10">\uf0dc</span><span class="ls10 ws41 vf">\uf345<span class="blank"> </span>\uee9e</span><span class="fs0 ls44 v10">\uf0db</span><span class="ls10 ws43 vf">\ue603<span class="blank"> </span>\uf346<span class="blank _f"> </span>\ue603</span><span class="ls2a ws29 vf">\uf0dc\uee9e</span><span class="ls10 ws44 vf">\ue603<span class="blank"> </span>\uf43a<span class="blank"> </span>\uee8c\ue7b2</span><span class="ls10 ws14 v12">\udb80\udddb<span class="vb">\uee9e</span><span class="ls26">\udb80\udddc</span></span><span class="ls10 wsf vf">\uf34c<span class="blank"> </span>\uee9e</span><span class="fs0 ls7 v10">\uf0db</span><span class="ls28 vf">\uf345<span class="ls2a ws45">\uf0db\uee9e<span class="blank"> </span><span class="ls10 ws1a">\uf346<span class="blank"> </span>\uf0dc\ue603<span class="ff3 ws22"> </span></span></span></span></div><div class="t m0 x1 h14 y98 ff5 fs3 fc0 sc0 ls10 ws22">Para determinar los<span class="blank _11"></span> <span class="blank _3"> </span>puntos crí<span class="blank _0"></span>ticos hallamos l<span class="blank _0"></span>os ceros de <span class="ff7 ws14">\uee8c\ue7b2</span>. </div><div class="t m0 x7f h14 y99 ff7 fs3 fc0 sc0 ls10 ws14">\uee9e<span class="fs0 ls7 v5">\uf0db</span><span class="ls21">\uf345<span class="ls2a ws46">\uf0db\uee9e<span class="blank"> </span></span></span><span class="ws1a">\uf346<span class="blank"> </span>\uf0dc<span class="blank _10"> </span>\uf34c<span class="blank _10"> </span>\uf0d9<span class="ff3 ws22"> </span></span></div><div class="t m0 x80 h35 y9a ff7 fs3 fc0 sc0 ls10 ws14">\uee9e<span class="fs0 ws47 v8">\uf0da\ue7e1\uf0db<span class="blank"> </span></span><span class="ls1d">\uf34c</span><span class="ws48 ve">\uf346\uf0db<span class="blank"> </span>\uf347<span class="blank"> </span></span><span class="ve">\uf3a5<span class="vb">\uf0db</span></span><span class="fs0 ls7 v10">\uf0db</span><span class="ws19 ve">\uf346<span class="blank _f"> </span>\uf0dd\ue7e4<span class="blank"> </span>\uf0da\ue7e4<span class="blank"> </span></span><span class="v18">\udb80\udddb<span class="vb">\uf346\uf0dc</span>\udb80\udddc</span></div><div class="t m0 x10 h2f y9b ff7 fs3 fc0 sc0 ls10 ws19">\uf0db\ue7e4<span class="blank"> </span>\uf0da<span class="blank _15"> </span><span class="ws1b vf">\uf43a<span class="blank"> </span>\uee9e</span><span class="fs0 ws49 v19">\uf0da\ue7e1\uf0db<span class="blank"> </span></span><span class="ls1d vf">\uf34c</span><span class="ws4a v11">\uf346\uf0db<span class="blank"> </span>\uf347<span class="blank"> </span></span><span class="ws14 vd">\ue9be</span><span class="ls2a v11">\uf0da\uf0df</span></div><div class="t m0 x81 h2d y9b ff7 fs3 fc0 sc0 ls46">\uf0db<span class="ls10 ws1b vf">\uf43a<span class="blank"> </span>\uee9e</span><span class="fs0 ls47 v19">\uf0da</span><span class="ls10 ws4b vf">\uf34c<span class="blank _10"> </span>\uf0da\ue603<span class="blank"> </span>\uebe8<span class="blank"> </span>\uee9e</span><span class="fs0 ls47 v19">\uf0db</span><span class="ls10 wsf vf">\uf34c<span class="blank"> </span>\uf346\uf0dc<span class="ff3 ws22"> </span></span></div><div class="t m0 x1 h26 y9c ff5 fs3 fc0 sc0 ls10 ws22">Los puntos crí<span class="blank _11"></span>t<span class="blank _3"> </span>icos de la función<span class="blank _0"></span> son: <span class="ff7 ws14">\uee9e<span class="fs0 ls47 v8">\uf0da</span><span class="ws4c">\uf34c<span class="blank _10"> </span>\uf0da\ue603<span class="blank"> </span>\uebe8<span class="blank"> </span>\uee9e<span class="fs0 ls47 v8">\uf0db</span><span class="ws4d">\uf34c<span class="blank"> </span>\uf346\uf0dc</span></span></span><span class="ls49"> <span class="ls4a">y <span class="blank _3"> </span><span class="ls4b"> </span></span></span><span class="ff7 ws14">\uee8c\ue7b2<span class="va">\udb80\udddb</span>\uee9e<span class="ls26 va">\udb80\udddc</span><span class="ls1d">\uf34c</span><span class="va">\udb80\udddb</span><span class="ws4e">\uee9e<span class="blank"> </span>\uf346<span class="blank"> </span>\uf0da</span><span class="va">\udb80\udddc\udb80\udddb</span><span class="ws4e">\uee9e<span class="blank"> </span>\uf345<span class="blank"> </span>\uf0dc</span><span class="va">\udb80\udddc</span></span> </div><div class="t m0 x1 h18 y9d ff5 fs3 fc0 sc0 ls10 ws22">Analizamos los inte<span class="blank _11"></span>r<span class="blank _3"> </span>valos dete<span class="blank _0"></span>rminados<span class="blank _0"></span> en su domini<span class="blank _0"></span>o: </div></div><div class="c x31 y9e w43 h36"><div class="t m0 x82 h14 y9f ff7 fs3 fc0 sc0 ls10 ws14">\udb80\udddb<span class="ws26 vb">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346\uf0dc</span>\udb80\udddc<span class="ff3 ws22 vb"> </span></div></div><div class="c x42 y9e w43 h36"><div class="t m0 x83 h14 y9f ff7 fs3 fc0 sc0 ls10 ws14">\udb80\udddb<span class="ws26 vb">\uf346\uf0dc\ue7e2<span class="blank"> </span>\uf0da</span>\udb80\udddc<span class="ff3 ws22 vb"> </span></div></div><div class="c x84 y9e w44 h36"><div class="t m0 x85 h14 y9f ff7 fs3 fc0 sc0 ls10 ws14">\udb80\udddb<span class="ws26 vb">\uf0da\ue7e2<span class="blank"> </span>\uf345\ue9bb</span>\udb80\udddc<span class="ff3 ws22 vb"> </span></div></div><div class="c x31 ya0 w43 h37"><div class="t m0 x83 h14 ya1 ff7 fs3 fc0 sc0 ls10 wsf">\uee9e<span class="blank"> </span>\uf34c<span class="blank"> </span>\uf346\uf0dd<span class="ff3 ws22"> </span></div><div class="t m0 x86 h26 ya2 ff7 fs3 fc0 sc0 ls10 ws14">\uee8c\ue7b2<span class="va">\udb80\udddb</span>\uf346\uf0dd<span class="ls26 va">\udb80\udddc</span><span class="ws4f">\uf350<span class="blank"> </span>\uf0d9<span class="ff3 ws22"> </span></span></div><div class="t m0 x87 h38 ya3 ff8 fs3 fc0 sc0 ls10 ws22">La función es<span class="blank _0"></span> creciente </div></div><div class="c x42 ya0 w43 h37"><div class="t m0 x88 h14 ya4 ff7 fs3 fc0 sc0 ls10 ws50">\uee9e<span class="blank"> </span>\uf34c<span class="ff3 ws22"> </span></div><div class="t m0 x82 h26 ya5 ff7 fs3 fc0 sc0 ls10 ws14">\uee8c\ue7b2<span class="va">\udb80\udddb</span><span class="ls48">\uf0d9<span class="ls26 va">\udb80\udddc</span></span><span class="ws51">\uf34f<span class="blank"> </span>\uf0d9<span class="ff3 ws22"> </span></span></div><div class="t m0 x1 h38 ya6 ff8 fs3 fc0 sc0 ls10 ws22">La función es<span class="blank _0"></span> </div><div class="t m0 x89 h38 ya7 ff8 fs3 fc0 sc0 ls10 ws22">decreciente </div></div><div class="c x84 ya0 w44 h37"><div class="t m0 x8a h14 ya1 ff7 fs3 fc0 sc0 ls10 ws33">\uee9e<span class="blank"> </span>\uf34c<span class="blank"> </span>\uf0db<span class="ff3 ws22"> </span></div><div class="t m0 x82 h26 ya2 ff7 fs3 fc0 sc0 ls10 ws14">\uee8c\ue7b2<span class="va">\udb80\udddb</span>\uf0db<span class="ls26 va">\udb80\udddc</span><span class="ws51">\uf350<span class="blank"> </span>\uf0d9<span class="ff3 ws22"> </span></span></div><div class="t m0 x87 h38 ya3 ff8 fs3 fc0 sc0 ls10 ws22">La función es<span class="blank _0"></span> creciente </div></div><div class="c x0 y1 w2 h0"><div class="t m0 x1 h18 ya8 ff5 fs3 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h18 ya9 ff5 fs3 fc0 sc0 ls10 ws22">Por lo tanto: </div><div class="t m0 x31 h26 yaa ff3 fs3 fc0 sc0 ls10 ws22">La función <span class="ff7 ws14">\uee8c\ue603</span>es crec<span class="blank _11"></span>i<span class="blank _3"> </span>ente en los <span class="blank _0"></span>intervalos: <span class="ff7 ws14 va">\udb80\udddb</span><span class="ff7 ws26">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346\uf0dc<span class="ws14 va">\udb80\udddc<span class="blank _0"></span><span class="ff3 lsf ws22 vb"> <span class="ls4c">y <span class="blank _3"> </span><span class="ff7 ls10 ws14 va">\udb80\udddb<span class="ws28 vb">\uf0da\ue7e2<span class="blank"> </span>\uf345\ue9bb</span>\udb80\udddc</span><span class="ls10"> </span></span></span></span></span></div><div class="t m0 x1 h18 yab ff5 fs3 fc0 sc0 ls10 ws22"> </div><div class="t m0 x1 h39 yac ff9 fs3 fc0 sc0 ls10 ws22"> </div></div><div class="c x0 y46 wa h23"><div class="t m0 x1d h13 y47 ff4 fs3 fc2 sc0 ls10 ws22"><span class="fc3 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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