<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/c2f1404f-661b-45c9-8d0f-90de15593d63/bg1.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls18 ws17">MATEMÁTICA (6<span class="ls19 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM </span></div><div class="t m0 x1 h2 y3 ff1 fs0 fc0 sc0 ls18 ws17">RECUPERATORI<span class="blank _0"></span>O 2° PARCIAL </div><div class="t m0 x2 h2 y4 ff1 fs0 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h2 y5 ff2 fs0 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h3 y6 ff2 fs1 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h2 y7 ff2 fs0 fc0 sc0 ls1a ws1">21<span class="ls18 ws2">/06/2023<span class="ff1 ws17"> <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 1 </span></span></div><div class="t m0 x3 h2 y8 ff2 fs0 fc0 sc0 ls18 ws17"> Hoja 1 de 4 </div><div class="t m0 x3 h2 y9 ff2 fs0 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h3 ya ff2 fs1 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h3 yb ff2 fs1 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h4 yc ff3 fs2 fc0 sc0 ls18 ws17">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 ls18 ws17"> </div></div><div class="c x6 yd w4 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls18 ws17">1 </div></div><div class="c x8 yd w5 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls18 ws17">2 </div></div><div class="c x9 yd w6 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls18 ws17">3 </div></div><div class="c xa yd w7 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls18 ws17">4 </div></div><div class="c x4 yf w3 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls18 ws17"> </div></div><div class="c x6 yf w4 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls18 ws17"> </div></div><div class="c x8 yf w5 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls18 ws17"> </div></div><div class="c x9 yf w6 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls18 ws17"> </div></div><div class="c xa yf w7 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls18 ws17"> </div></div><div class="c x4 y11 w5 h9"><div class="t m0 xb ha y12 ff4 fs4 fc0 sc0 ls18 ws17">Puntaje de cada </div><div class="t m0 xb ha y13 ff4 fs4 fc0 sc0 ls18 ws17">ejercicio </div></div><div class="c x6 y11 w4 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls18 ws17">2,50 </div></div><div class="c x8 y11 w5 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls18 ws17">2,50 </div></div><div class="c x9 y11 w6 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls18 ws17">2,50 </div></div><div class="c xa y11 w7 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls18 ws17">2,50 </div></div><div class="c x0 y1 w2 h0"><div class="t m0 x1 hb y15 ff5 fs5 fc0 sc0 ls18 ws17">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 ls18 ws17">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 ls18 ws17"> </div><div class="t m0 x1 he y18 ff7 fs2 fc0 sc0 ls18 ws17">1. Encontrar los intervalos de crecimiento y decrecimiento de<span class="blank _0"></span> la función <span class="blank _3"> </span><span class="ff8 ws4">\uee8c\udb80\udddb\uee9e<span class="blank _3"></span>\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank _4"> </span><span class="fs7 ls0 v1">\uee9e</span><span class="fs8 v2">\uf0db</span></span></div><div class="t m0 xf hf y19 ff8 fs7 fc0 sc0 ls18 ws5">\uee9e\ue603\uf13f\ue603\uf0da<span class="ff7 fs2 ws17 v3"> </span></div><div class="t m0 x1 h6 y1a ff3 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h10 y1b ff5 fs3 fc0 sc0 ls18 ws17">Sea <span class="ff8 ws6">\ued42<span class="blank _3"></span>\udb80\udddb\ued54\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank _5"> </span><span class="fs0 ls1 v4">\uf1eb</span><span class="fs9 v5">\uf22e</span></span></div><div class="t m0 x10 h11 y1c ff8 fs0 fc0 sc0 ls18 ws7">\uf1eb\ue603\uf13f\ue603<span class="blank _3"> </span>\uf135<span class="ff5 fs3 ws17 v6"> </span></div><div class="t m0 x1 h12 y1d ff5 fs3 fc0 sc0 ls18 ws17">Como no se puede<span class="blank _0"></span> dividir por ce<span class="blank _0"></span>ro, el dominio de <span class="blank _0"></span>la función f es <span class="ff8 ws8">\ueb39<span class="blank"> </span>\uf346<span class="blank"> </span><span class="ls2 v7">\udb80\udddd</span><span class="ls3">\ue973</span><span class="ws9 v7">\udb80\uddde</span></span>. </div><div class="t m0 x1 h13 y1e ff5 fs3 fc0 sc0 ls18 ws17">Buscamos la deriv<span class="blank _0"></span>ada y su dominio: </div><div class="t m0 x11 h14 y1f ff8 fs3 fc0 sc0 ls4">\ued42<span class="fs0 ls5 v8">\udb80\udd92</span><span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls6">\ued54<span class="ls7 v7">\udb80\udddc</span><span class="ls8">\uf34c<span class="ls18 wsa v9">\ue974\ued54<span class="blank"> </span>\ue603\ue7e4<span class="blank _6"> </span></span><span class="ls18 ws9 va">\udb80\udddb</span><span class="ls18 wsb v9">\ued54<span class="blank _7"> </span>\uf346<span class="blank"> </span>\ue973</span><span class="ls9 va">\udb80\udddc</span><span class="ls18 wsc v9">\uf346<span class="blank _8"> </span>\ued54<span class="blank"> </span><span class="fs0 v8">\uf136</span></span></span></span></div><div class="t m0 x12 h15 y20 ff8 fs3 fc0 sc0 ls18 ws9">\udb80\udddb<span class="wsb vb">\ued54<span class="blank _7"> </span>\uf346<span class="blank"> </span>\ue973</span>\udb80\udddc<span class="fs0 lsa vc">\uf136</span><span class="ff5 ws17 v1"> </span></div><div class="t m0 x13 h16 y21 ff8 fs3 fc0 sc0 ls4">\ued42<span class="fs0 ls5 v8">\udb80\udd92</span><span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls6">\ued54<span class="lsb v7">\udb80\udddc</span><span class="lsc">\uf34c<span class="ls18 wsd v9">\ue974\ued54<span class="blank"> </span></span><span class="fs0 lsd vd">\uf136</span><span class="ls18 wsc v9">\uf346<span class="blank _8"> </span>\ue974\ued54<span class="blank _8"> </span>\uf346<span class="blank _8"> </span>\ued54<span class="blank"> </span><span class="fs0 v8">\uf136</span></span></span></span></div><div class="t m0 x12 h15 y22 ff8 fs3 fc0 sc0 ls18 ws9">\udb80\udddb<span class="wsb vb">\ued54<span class="blank _7"> </span>\uf346<span class="blank"> </span>\ue973</span>\udb80\udddc<span class="fs0 lse vc">\uf136</span><span class="ff5 ws17 v1"> </span></div><div class="t m0 x14 h16 y23 ff8 fs3 fc0 sc0 ls4">\ued42<span class="fs0 ls5 v8">\udb80\udd92</span><span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls6">\ued54<span class="lsb v7">\udb80\udddc</span><span class="lsf">\uf34c<span class="ls10 v9">\ued54</span><span class="fs0 lsd vd">\uf136</span><span class="ls18 wsb v9">\uf346<span class="blank"> </span>\ue974\ued54</span></span></span></div><div class="t m0 x12 h15 y24 ff8 fs3 fc0 sc0 ls18 ws9">\udb80\udddb<span class="wsb vb">\ued54<span class="blank _7"> </span>\uf346<span class="blank"> </span>\ue973</span>\udb80\udddc<span class="fs0 ls11 vc">\uf136</span><span class="ff5 ws17 v1"> </span></div><div class="t m0 x15 h17 y25 ff8 fs3 fc0 sc0 ls18 ws9">\ued26\ued4b\ued49<span class="v7">\udb80\udddb</span><span class="ls4">\ued42<span class="fs0 ls12 v8">\udb80\udd92</span><span class="ls13 v7">\udb80\udddc</span></span><span class="wsb">\uf34c<span class="blank _9"> </span>\ueb39<span class="blank"> </span>\uf346<span class="blank"> </span>\udb80\udddd\ue973\udb80\uddde<span class="ff5 ws17"> </span></span></div><div class="t m0 x1 h13 y26 ff5 fs3 fc0 sc0 ls18 ws17">Hallamos los punto<span class="blank _0"></span>s críticos, buscando l<span class="blank _0"></span>os ceros de la deri<span class="blank _0"></span>vada: </div><div class="t m0 x16 h17 y27 ff8 fs3 fc0 sc0 ls4">\ued42<span class="fs0 ls12 v8">\udb80\udd92</span><span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls14">\ued54<span class="ls7 v7">\udb80\udddc</span><span class="ls18 wse">\uf34c<span class="blank"> </span>\ue972<span class="ff5 ws17"> </span></span></span></div><div class="t m0 x17 h15 y28 ff8 fs3 fc0 sc0 ls10">\ued54<span class="fs0 lsd v8">\uf136</span><span class="ls18 ws8">\uf346<span class="blank"> </span>\ue974\ued54</span></div><div class="t m0 x18 h18 y29 ff8 fs3 fc0 sc0 ls18 ws9">\udb80\udddb<span class="wsb vb">\ued54<span class="blank _7"> </span>\uf346<span class="blank"> </span>\ue973</span>\udb80\udddc<span class="fs0 ls15 vc">\uf136</span><span class="wse v1">\uf34c<span class="blank"> </span>\ue972<span class="ff5 ws17"> </span></span></div><div class="t m0 x17 h15 y2a ff8 fs3 fc0 sc0 ls10">\ued54<span class="fs0 lsd v8">\uf136</span><span class="ls18 ws8">\uf346<span class="blank"> </span>\ue974\ued54<span class="blank _9"> </span>\uf34c<span class="blank _9"> </span>\ue972<span class="ff5 ws17"> </span></span></div><div class="t m0 x18 h17 y2b ff8 fs3 fc0 sc0 ls6">\ued54<span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls18 wsf">\ued54<span class="blank _7"> </span>\uf346<span class="blank"> </span>\ue974<span class="ls7 v7">\udb80\udddc</span><span class="wse">\uf34c<span class="blank"> </span>\ue972<span class="ff5 ws17"> </span></span></span></div><div class="t m0 x1 h13 y2c ff5 fs3 fc0 sc0 ls18 ws17">Por lo tanto, los<span class="blank _0"></span> puntos crí<span class="blank _0"></span>ticos son: <span class="blank _a"> </span><span class="ff8 wse ve">\ued54<span class="blank _9"> </span>\uf34c<span class="blank"> </span>\ue972\ue603\ued55<span class="blank _3"></span>\ue603\ued54<span class="blank _b"> </span>\uf34c<span class="blank"> </span>\ue974</span><span class="ve"> </span></div><div class="t m0 x1 h15 y2d ff5 fs3 fc0 sc0 ls18 ws17">La <span class="blank _c"> </span>recta <span class="blank _3"> </span><span class="ff8 wse">\ued54<span class="blank _b"> </span>\uf34c<span class="blank"> </span>\ue973</span> <span class="blank _c"> </span>es <span class="blank _c"> </span>una <span class="blank _c"> </span>asíntota <span class="blank _c"> </span>vertical <span class="blank _3"> </span>de <span class="blank _c"> </span>la <span class="blank _c"> </span>función <span class="blank _c"> </span>y <span class="blank _c"> </span>de <span class="blank _c"> </span>su <span class="blank _c"> </span>derivada. <span class="blank _3"> </span>Lo <span class="blank _c"> </span>tenemos <span class="blank _c"> </span>en <span class="blank _c"> </span>cuenta <span class="blank _3"> </span>al <span class="blank _c"> </span>considerar <span class="blank _3"> </span>los </div><div class="t m0 x1 h13 y2e ff5 fs3 fc0 sc0 ls18 ws17">intervalos donde es<span class="blank _0"></span>tudiamos el signo<span class="blank _0"></span> de la derivad<span class="blank _0"></span>a. </div><div class="t m0 x1 h13 y2f ff5 fs3 fc0 sc0 ls18 ws17">Recordemos <span class="blank _0"></span>que: </div><div class="t m0 x1 h17 y30 ff9 fs3 fc0 sc0 ls18 ws10">\uf0b7<span class="ff5 ws17"> <span class="blank _c"> </span>si <span class="blank _d"> </span><span class="ff8 ws9">\ued42\ue7ef<span class="v7">\udb80\udddb</span><span class="ls6">\ued54<span class="ls7 v7">\udb80\udddc</span></span><span class="ws11">\uf350<span class="blank"> </span>\ue603\ue972</span></span> <span class="blank _d"> </span>para <span class="blank _c"> </span>todo <span class="blank _d"> </span>x <span class="blank _c"> </span>que <span class="blank _d"> </span>pertenece<span class="blank _0"></span> <span class="blank _d"> </span>al <span class="blank _c"> </span>intervalo <span class="blank _c"> </span><span class="ff8 ws9 v7">\udb80\udddb</span><span class="ff8 ws12">\ued3d<span class="blank _3"> </span>\ue7e2<span class="blank"> </span>\ue603\ued3e<span class="blank _3"> </span><span class="ws9 v7">\udb80\udddc</span></span>, <span class="blank _d"> </span>entonces <span class="blank _c"> </span>la <span class="blank _c"> </span>función <span class="blank _d"> </span><span class="ff8 ls16">\ued42</span> <span class="blank _c"> </span>es <span class="blank _d"> </span>creciente <span class="blank _c"> </span>en <span class="blank _d"> </span>el <span class="blank _c"> </span>intervalo </span></div><div class="t m0 x1 h15 y31 ff8 fs3 fc0 sc0 ls18 ws9">\udb80\udddb<span class="ws12 vb">\ued3d\ue7e2<span class="blank"> </span>\ue603\ued3e<span class="blank _3"> </span></span>\udb80\udddc<span class="ff5 ws17 vb"> </span></div><div class="t m0 x1 h15 y32 ff9 fs3 fc0 sc0 ls18 ws10">\uf0b7<span class="ff5 ws17"> si <span class="blank _3"> </span><span class="ff8 wsa">\ued42\ue7ef\udb80\udddb\ued54<span class="blank"> </span>\udb80\udddc<span class="blank _e"> </span>\ue603<span class="blank _e"> </span>\uf34f<span class="blank _9"> </span>\ue603\ue972</span> para <span class="blank _3"> </span>todo x que <span class="blank _3"> </span>perten<span class="blank _0"></span>ece al <span class="blank _3"> </span>intervalo <span class="ff8 ws13">\udb80\udddb\ued3d<span class="blank"> </span>\ue7e2<span class="blank _6"> </span>\ue603\ued3e<span class="blank"> </span>\udb80\udddc\ue7e1</span> entonces la función<span class="ff8 ws9">\ue603\ued42</span> <span class="blank _3"> </span>es decreciente en <span class="blank _3"> </span>el interval<span class="blank _0"></span>o </span></div><div class="t m0 x1 h15 y33 ff8 fs3 fc0 sc0 ls18 ws12">\udb80\udddb\ued3d\ue7e2<span class="blank"> </span>\ue603\ued3e<span class="blank _3"> </span>\udb80\udddc\ue7e4<span class="ff5 ws17"> </span></div><div class="t m0 x1 h17 y34 ff5 fs3 fc0 sc0 ls18 ws17">Analizamos entonce<span class="blank _0"></span>s, los intervalos: <span class="ff8 ws9 v7">\udb80\udddb</span><span class="ff8 ws14">\uf346\ue9bb\ue7e2<span class="blank"> </span>\ue972<span class="ws9 v7">\udb80\udddc</span><span class="ls17">\ue7e1</span><span class="ws9 v7">\udb80\udddb</span><span class="ls3 ws15">\ue972\ue7e2<span class="blank"> </span>\ue973</span><span class="ws9 v7">\udb80\udddc</span><span class="ls17">\ue7e1</span><span class="ws9 v7">\udb80\udddb<span class="blank _0"></span><span class="ws14 vb">\ue973\ue7e2<span class="blank"> </span>\ue974<span class="ws9 v7">\udb80\udddc</span><span class="ls17">\ue7e1<span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls18 ws16">\ue974\ue7e2<span class="blank"> </span>\ue603<span class="blank"> </span>\uf345\ue9bb<span class="ws9 v7">\udb80\udddc<span class="vb">\ue7e4</span></span><span class="ff5 ws17"> </span></span></span></span></span></span></div></div><div class="c x1 y35 w8 h19"><div class="t m0 x19 h2 y36 ff2 fs0 fc0 sc0 ls18 ws17">APELLIDO: </div></div><div class="c x1a y37 w9 h1a"><div class="t m0 xb h2 y38 ff2 fs0 fc0 sc0 ls18 ws17">CALIFICACIÓN:<span class="blank _0"></span> </div></div><div class="c x1 y39 w8 h1b"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls18 ws17">NOMBRE: </div></div><div class="c x1 y37 w8 h1b"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls18 ws17">DNI (registrado en S<span class="blank _0"></span>IU Guaraní): </div></div><div class="c x1 y3a w8 h1c"><div class="t m0 xb h2 y10 ff2 fs0 fc0 sc0 ls18 ws17">E-MAIL: </div></div><div class="c x1a y3b w9 h1d"><div class="t m0 xb h2 y3c ff2 fs0 fc0 sc0 ls18 ws17">DOCENTE (nombre<span class="blank _0"></span> y apellido): </div></div><div class="c x1 y3d w8 h1b"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls18 ws17">TEL: </div></div><div class="c x1 y3b w8 h1b"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls18 ws17">AULA: </div></div><div class="c x0 y3e wa h1e"><div class="t m0 x19 h1f y3f ff4 fs3 fc1 sc0 ls18 ws17"><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 x1b y40 wb h20" alt="" src="https://files.passeidireto.com/c2f1404f-661b-45c9-8d0f-90de15593d63/bg2.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h13 y41 ff5 fs3 fc0 sc0 ls18 ws17">Realiz<span class="blank _0"></span>amos una tabla: </div><div class="t m0 x1 h13 y42 ff5 fs3 fc0 sc0 ls18 ws17"> </div></div><div class="c x1b y43 wc h21"><div class="t m0 x1c h13 y44 ff5 fs3 fc0 sc0 ls18 ws17">Intervalo </div></div><div class="c x1d y43 wd h21"><div class="t m0 x7 h15 y45 ff8 fs3 fc0 sc0 ls18 ws9">\udb80\udddb<span class="ws14 vb">\uf346\ue9bb\ue7e2<span class="blank"> </span>\ue972</span>\udb80\udddc<span class="ff5 ws17 vb"> </span></div></div><div class="c x1e y43 we h21"><div class="t m0 x7 h15 y45 ff8 fs3 fc0 sc0 ls18 ws9">\udb80\udddb<span class="ws14 vb">\ue972\ue7e2<span class="blank"> </span>\ue973</span>\udb80\udddc<span class="ff5 ws17 vb"> </span></div></div><div class="c x1f y43 wf h21"><div class="t m0 x5 h15 y45 ff8 fs3 fc0 sc0 ls18 ws9">\udb80\udddb<span class="ls3 ws15 vb">\ue973\ue7e2<span class="blank"> </span>\ue974</span>\udb80\udddc<span class="ff5 ws17 vb"> </span></div></div><div class="c x20 y43 w10 h21"><div class="t m0 xe h15 y45 ff8 fs3 fc0 sc0 ls18 ws9">\udb80\udddb<span class="ws14 vb">\ue974\ue7e2<span class="blank"> </span>\ue9bb</span>\udb80\udddc<span class="ff5 ws17 vb"> </span></div></div><div class="c x1b y46 wc h22"><div class="t m0 x7 h13 y47 ff5 fs3 fc0 sc0 ls18 ws17">Para </div></div><div class="c x1d y46 wd h22"><div class="t m0 x7 h15 y48 ff8 fs3 fc0 sc0 ls18 wse">\ued54<span class="blank _9"> </span>\uf34c<span class="blank"> </span>\uf346\ue973<span class="ff5 ws17"> </span></div></div><div class="c x1e y46 we h22"><div class="t m0 x7 h23 y49 ff8 fs3 fc0 sc0 ls18 wse">\ued54<span class="blank _9"> </span>\uf34c<span class="blank"> </span><span class="v9">\ue973</span></div><div class="t m0 x21 h15 y4a ff8 fs3 fc0 sc0 ls3">\ue974<span class="ff5 ls18 ws17 vf"> </span></div></div><div class="c x1f y46 wf h22"><div class="t m0 x5 h23 y49 ff8 fs3 fc0 sc0 ls18 ws18">\ued54<span class="blank _9"> </span>\uf34c<span class="blank"> </span><span class="v9">\ue975</span></div><div class="t m0 x22 h15 y4a ff8 fs3 fc0 sc0 ls1b">\ue974<span class="ff5 ls18 ws17 vf"> </span></div></div><div class="c x20 y46 w10 h22"><div class="t m0 x7 h15 y48 ff8 fs3 fc0 sc0 ls18 wse">\ued54<span class="blank _9"> </span>\uf34c<span class="blank"> </span>\ue975<span class="ff5 ws17"> </span></div></div><div class="c x1b y4b wc h24"><div class="t m0 x23 h13 y4c ff6 fs3 fc0 sc0 ls18 ws17">Signo de f\u2019<span class="ff5"> </span></div></div><div class="c x1d y4b wd h24"><div class="t m0 x24 h16 y4d ff8 fs3 fc0 sc0 ls4">\ued42<span class="fs0 ls5 v8">\udb80\udd92</span><span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls6">\ued54<span class="lsb v7">\udb80\udddc</span><span class="lsc">\uf34c<span class="ls18 v9">\ue975</span></span></span></div><div class="t m0 x25 h25 y4e ff8 fs3 fc0 sc0 ls1c">\ue976<span class="ls18 ws19 vf">\uf350<span class="blank"> </span>\ue972<span class="ff5 ws17"> </span></span></div></div><div class="c x1e y4b we h24"><div class="t m0 x23 h17 y4f ff8 fs3 fc0 sc0 ls4">\ued42<span class="fs0 ls12 v8">\udb80\udd92</span><span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls1d">\ued54<span class="ls1e v7">\udb80\udddc</span><span class="ls18 wse">\uf34c<span class="blank"> </span>\uf346\ue975</span></span></div><div class="t m0 x23 h15 y50 ff8 fs3 fc0 sc0 ls18 ws11">\uf34f<span class="blank"> </span>\ue972<span class="ff5 ws17"> </span></div></div><div class="c x1f y4b wf h24"><div class="t m0 x26 h17 y4f ff8 fs3 fc0 sc0 ls4">\ued42<span class="fs0 ls12 v8">\udb80\udd92</span><span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls6">\ued54<span class="lsb v7">\udb80\udddc</span><span class="ls18 wse">\uf34c<span class="blank"> </span>\uf346\ue975</span></span></div><div class="t m0 x26 h15 y50 ff8 fs3 fc0 sc0 ls18 ws19">\uf34f<span class="blank"> </span>\ue972<span class="ff5 ws17"> </span></div></div><div class="c x20 y4b w10 h24"><div class="t m0 x1c h16 y4d ff8 fs3 fc0 sc0 ls4">\ued42<span class="fs0 ls5 v8">\udb80\udd92</span><span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls6">\ued54<span class="lsb v7">\udb80\udddc</span><span class="lsc">\uf34c<span class="ls18 v9">\ue975</span></span></span></div><div class="t m0 x27 h15 y4e ff8 fs3 fc0 sc0 ls18">\ue976</div><div class="t m0 x1c h15 ye ff8 fs3 fc0 sc0 ls18 ws11">\uf350<span class="blank"> </span>\ue972<span class="ff5 ws17"> </span></div></div><div class="c x1b y51 wc h26"><div class="t m0 x24 h13 y52 ff5 fs3 fc0 sc0 ls18 ws17">Conclusión </div></div><div class="c x1d y51 wd h26"><div class="t m0 xc h15 y53 ff8 fs3 fc0 sc0 ls18 ws9">\ued42<span class="blank _3"></span>\ue603<span class="ff5 ws17">crece en </span></div><div class="t m0 x7 h15 y54 ff8 fs3 fc0 sc0 ls18 ws9">\udb80\udddb<span class="ws14 vb">\uf346\ue9bb\ue7e2<span class="blank"> </span>\ue972</span>\udb80\udddc<span class="ff5 ws17 vb"> </span></div></div><div class="c x1e y51 we h26"><div class="t m0 x26 h15 y53 ff8 fs3 fc0 sc0 ls18 ws9">\ued42<span class="blank _3"></span>\ue603<span class="ff5 ws17">decrece </span></div><div class="t m0 x28 h13 y55 ff5 fs3 fc0 sc0 ls25 ws17">en <span class="ffa ls18"> </span></div><div class="t m0 x7 h15 y45 ff8 fs3 fc0 sc0 ls18 ws9">\udb80\udddb<span class="ws14 vb">\ue972\ue7e2<span class="blank"> </span>\ue973</span>\udb80\udddc<span class="ff5 ws17 vb"> </span></div></div><div class="c x1f y51 wf h26"><div class="t m0 x19 h15 y53 ff8 fs3 fc0 sc0 ls18 ws9">\ued42<span class="blank _3"></span>\ue603<span class="ff5 ws17">decrece en <span class="blank _0"></span><span class="ffa"> </span></span></div><div class="t m0 x5 h15 y54 ff8 fs3 fc0 sc0 ls18 ws9">\udb80\udddb<span class="ls3 ws15 vb">\ue973\ue7e2<span class="blank"> </span>\ue974</span>\udb80\udddc<span class="ff5 ws17 vb"> </span></div></div><div class="c x20 y51 w10 h26"><div class="t m0 x26 h15 y53 ff8 fs3 fc0 sc0 ls18 ws9">\ued42<span class="blank _3"></span>\ue603<span class="ff5 ws17">crece en <span class="ffa"> </span></span></div><div class="t m0 xe h15 y54 ff8 fs3 fc0 sc0 ls18 ws9">\udb80\udddb<span class="ws14 vb">\ue974\ue7e2<span class="blank"> </span>\ue9bb</span>\udb80\udddc<span class="ff5 ws17 vb"> </span></div></div><div class="c x0 y1 w2 h0"><div class="t m0 x1 h13 y56 ff5 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h13 y57 ff5 fs3 fc0 sc0 ls18 ws17">Concluimos: </div><div class="t m0 x1 h17 y58 ff8 fs3 fc0 sc0 ls4">\ued42<span class="fs0 ls12 v8">\udb80\udd92</span><span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls1d">\ued54<span class="ls1f v7">\udb80\udddc</span><span class="ls18 ws11">\uf350<span class="blank"> </span>\ue972\ue603</span><span class="ls26 ws1a">\ued41\ued4a<span class="ls20">\ue603</span></span><span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls18 ws14">\uf346\ue9bb\ue7e2<span class="blank"> </span>\ue972<span class="ls21 v7">\udb80\udddc</span></span><span class="ls22 ws1b">\ue603\uebeb<span class="blank _0"></span>\ue603<span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls18 ws14">\ue974\ue7e2<span class="blank"> </span>\ue9bb<span class="ws9 v7">\udb80\udddc</span><span class="ff5 ws17"> por lo que f es c<span class="blank _0"></span>reciente en <span class="ff8 ws9 v7">\udb80\udddb</span><span class="ff8 ws14">\uf346\ue9bb\ue7e2<span class="blank"> </span>\ue972<span class="ls23 v7">\udb80\udddc</span><span class="ls24 ws1c">\ue603\uebeb\ue603</span><span class="ws9 v7">\udb80\udddb</span>\ue974\ue7e2<span class="blank"> </span>\ue9bb<span class="ws9 v7">\udb80\udddc<span class="vb">\ue603\ue7e4</span></span></span> </span></span></span></span></div><div class="t m0 x1 h17 y59 ff8 fs3 fc0 sc0 ls4">\ued42<span class="fs0 ls12 v8">\udb80\udd92</span><span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls1d">\ued54<span class="ls1f v7">\udb80\udddc</span><span class="ls18 ws11">\uf34f<span class="blank"> </span>\ue972\ue603</span><span class="ls26 ws1a">\ued41\ued4a<span class="ls20">\ue603</span></span><span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls3 ws15">\ue972\ue7e2<span class="blank"> </span>\ue973<span class="ls23 v7">\udb80\udddc</span></span><span class="ls24 ws1c">\ue603\uebeb\ue603</span><span class="ls18 ws9 v7">\udb80\udddb</span><span class="ls3 ws15">\ue973\ue7e2<span class="blank"> </span>\ue974</span><span class="ls18 ws9 v7">\udb80\udddc<span class="vb">\ue603\ue603</span></span><span class="ff5 ls18 ws17">por lo que f es<span class="blank _0"></span> decreciente en <span class="ff8 ws9 v7">\udb80\udddb</span><span class="ff8 ls3 ws15">\ue972\ue7e2<span class="blank"> </span>\ue973<span class="ls23 v7">\udb80\udddc</span><span class="ls24 ws1c">\ue603\uebeb\ue603<span class="ls18 ws9 v7">\udb80\udddb</span></span><span class="ws1d">\ue973\ue7e2<span class="blank"> </span>\ue974<span class="ls18 ws9 v7">\udb80\udddc<span class="vb">\ue603\ue7e4\ue603</span></span></span></span> </span></span></div><div class="t m0 x1 h6 y5a ff3 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h6 y5b ff3 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h6 y5c ff3 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h6 y5d ff3 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h6 y5e ff3 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h6 y5f ff3 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h6 y60 ff3 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h6 y61 ff3 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h13 y62 ff5 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h13 y22 ff5 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h13 y63 ff5 fs3 fc0 sc0 ls18 ws17"> <span class="blank _f"> </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 y64 w11 h27" alt="" src="https://files.passeidireto.com/c2f1404f-661b-45c9-8d0f-90de15593d63/bg3.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls18 ws17">MATEMÁTICA (6<span class="ls19 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls27"> <span class="ls28"> </span></span>RECUPERATOR<span class="blank _3"> </span>IO 2° PARC<span class="blank _3"> </span>IAL </div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 ls18 ws17">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 _10"> </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 1 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 ls18 ws17">Hoja 2 de 4 </div><div class="t m0 x3 h2 y65 ff2 fs0 fc0 sc0 ls18 ws17"> </div><div class="t m0 x2 h2 y66 ff1 fs0 fc0 sc0 ls29 ws17"> <span class="ff7 fs2 ls18 v10">2. Calcular el área de la región sombreada, sabiendo que: </span></div><div class="t m0 x1 h28 y67 ff8 fs2 fc0 sc0 ls2a">\uee8d<span class="ls2b v7">\udb80\udddb</span>\uee9e<span class="ls2c v7">\udb80\udddc</span><span class="ls2d">\uf34c<span class="fs7 ls18 v1">\uf0da</span></span></div><div class="t m0 x29 h29 y68 ff8 fs7 fc0 sc0 ls2e">\uf0db<span class="fs2 ls2a v3">\uee9e</span><span class="ls2f v2">\uf0db</span><span class="fs2 ls30 v3">\uf346</span><span class="ls18 v11">\uf0da</span></div><div class="t m0 x2a h2a y68 ff8 fs7 fc0 sc0 ls2e">\uf0db<span class="fs2 ls31 ws1e v3">\uee9e\uf346\uf0dc<span class="blank _11"></span><span class="ffb ls2a ws17"> <span class="blank _0"></span> <span class="ffc fs3 fc3 ls18"> </span></span></span></div><div class="t m0 x1 h2b y69 ff8 fs2 fc0 sc0 ls18 ws1f">\uee8c\udb80\udddb\uee9e\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="v12">\uf0da</span></div><div class="t m0 x2b h2c y6a ff8 fs2 fc0 sc0 ls32">\uf0db<span class="ls18 ws20 v13">\uee9e<span class="blank"> </span>\uf346<span class="blank"> </span><span class="v12">\uf0dc</span></span></div><div class="t m0 x2c h2d y6a ff8 fs2 fc0 sc0 ls18 ws21">\uf0db<span class="ffb ws17 v13"> </span></div><div class="t m0 x1 h2e y6b ffb fs2 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h4 y6c ff7 fs2 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h1f y6d ff4 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h2d y6e ff5 fs2 fc0 sc0 ls18 ws17">El área de la región que se pide calcular es la comprendida por la fu<span class="blank _0"></span>nción <span class="blank _3"> </span><span class="ff8 ws21">\ued43<span class="blank _3"></span>\udb80\udddb\ued54<span class="blank _3"> </span>\udb80\udddc</span><span class="ls33"> <span class="ls58">y </span></span><span class="ff8 ws22">\ued42<span class="blank"> </span>\udb80\udddb<span class="blank"> </span>\ued54\udb80\udddc</span>, e<span class="blank _3"> </span>ntre x=-1 y </div><div class="t m0 x1 h2f y6f ff5 fs2 fc0 sc0 ls18 ws17">x=3. En el gráfico se puede observar q<span class="blank _0"></span>ue <span class="blank _3"> </span><span class="ff8 ls34">\ued42<span class="ls2b v7">\udb80\udddb</span><span class="ls35">\ued54<span class="ls18 ws21 v7">\udb80\udddc</span></span></span><span class="ls33"> </span><span class="ff6">representa el \u201ctecho\u201d de la misma, mientras que <span class="ff8 ls36">\ued43<span class="ls2b v7">\udb80\udddb</span><span class="ls35">\ued54<span class="ls18 ws21 v7">\udb80\udddc</span></span></span></span> el </div><div class="t m0 x1 h30 y70 ff6 fs2 fc0 sc0 ls18 ws17">\u201cpiso\u201d. Por lo tanto, sabemos que:<span class="ff5"> </span></div><div class="t m0 x11 h2f y71 ff8 fs2 fc0 sc0 ls18 ws22">\ued23<span class="blank _b"> </span>\uf34c<span class="blank _b"> </span>\uf3b1<span class="blank _12"> </span>\ued42<span class="blank"> </span><span class="ls2b v7">\udb80\udddb</span><span class="ls37">\ued54<span class="ls38 v7">\udb80\udddc</span></span><span class="ws23">\uf346<span class="blank"> </span>\ued43<span class="ls2b v7">\udb80\udddb</span><span class="ls35">\ued54<span class="ls2b v7">\udb80\udddc</span></span>\ued40\ued54</span></div><div class="t m0 x2d h31 y72 ff8 fs7 fc0 sc0 ls18">\uf137</div><div class="t m0 x18 h32 y73 ff8 fs7 fc0 sc0 ls18 ws24">\uf13f\uf135<span class="blank"> </span><span class="ff5 fs2 ws17 v14"> </span></div><div class="t m0 x1 h2f y74 ff8 fs2 fc0 sc0 ls18 ws25">\ued23<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="ls39 vb">\uebec</span><span class="ls34">\ued42<span class="ls2b v7">\udb80\udddb</span><span class="ls35">\ued54<span class="ls3a v7">\udb80\udddc</span></span></span><span class="ws26">\uf346<span class="blank"> </span>\ued43<span class="blank _3"></span><span class="ls2b v7">\udb80\udddb</span><span class="ls35">\ued54<span class="ls2b v7">\udb80\udddc</span></span>\ued40\ued54</span></div><div class="t m0 x2e h31 y75 ff8 fs7 fc0 sc0 ls18">\uf137</div><div class="t m0 x2f h33 y76 ff8 fs7 fc0 sc0 ls18 ws27">\uf13f\uf135<span class="blank"> </span><span class="fs2 ws28 v15">\uf34c<span class="blank"> </span>\ue603<span class="blank"> </span><span class="ls3b vb">\uebec</span></span><span class="v16">\uf135</span></div><div class="t m0 x30 h29 y77 ff8 fs7 fc0 sc0 ls3c">\uf136<span class="fs2 ls18 ws23 v3">\ued54<span class="blank _9"> </span>\uf346<span class="blank"> </span></span><span class="ls18 v11">\uf137</span></div><div class="t m0 x31 h2a y77 ff8 fs7 fc0 sc0 ls3d">\uf136<span class="fs2 ls18 v3">\uf346</span></div><div class="t m0 x4 h31 y75 ff8 fs7 fc0 sc0 ls18">\uf137</div><div class="t m0 x32 h33 y76 ff8 fs7 fc0 sc0 ls18 ws29">\uf13f\uf135<span class="blank"> </span><span class="fs2 ws21 v15">\udb80\udde1</span><span class="v16">\uf135</span></div><div class="t m0 x33 h29 y77 ff8 fs7 fc0 sc0 ls3e">\uf136<span class="fs2 ls3f v3">\ued54</span><span class="ls40 v2">\uf136</span><span class="fs2 ls31 v3">\uf346</span><span class="ls18 v11">\uf135</span></div><div class="t m0 x1e h29 y77 ff8 fs7 fc0 sc0 ls3e">\uf136<span class="fs2 ls18 ws2a v3">\ued54<span class="blank _7"> </span>\uf346<span class="blank _7"> </span>\ue975\udb80\udde2<span class="blank"> </span>\ued40\ued54<span class="blank _13"> </span>\uf34c<span class="blank _9"> </span><span class="ls41 vb">\uebec</span><span class="ls42">\uf346</span></span><span class="ls18 v11">\uf135</span></div><div class="t m0 x34 h29 y77 ff8 fs7 fc0 sc0 ls3e">\uf136<span class="fs2 ls3f v3">\ued54</span><span class="ls40 v2">\uf136</span><span class="fs2 ls18 ws23 v3">\uf345<span class="blank"> </span>\ued54<span class="blank _9"> </span>\uf345<span class="blank"> </span></span><span class="ls18 v11">\uf137</span></div><div class="t m0 x35 h2a y77 ff8 fs7 fc0 sc0 ls3c">\uf136<span class="fs2 ls18 v3">\ued40\ued54</span></div><div class="t m0 x36 h31 y75 ff8 fs7 fc0 sc0 ls18">\uf137</div><div class="t m0 x37 h34 y76 ff8 fs7 fc0 sc0 ls18 ws2b">\uf13f\uf135<span class="blank"> </span><span class="ff5 fs2 ws17 v15"> </span></div><div class="t m0 x1 h30 y78 ff5 fs2 fc0 sc0 ls18 ws17">Integrando y aplicando la regla de Barrow: </div><div class="t m0 x1 h2b y79 ff8 fs2 fc0 sc0 ls18 ws2c">\ued23<span class="blank _b"> </span>\uf34c<span class="blank _b"> </span>\uf3b1<span class="blank _4"> </span>\uf346<span class="blank"> </span><span class="v12">\ue973</span></div><div class="t m0 x38 h2c y7a ff8 fs2 fc0 sc0 ls43">\ue974<span class="ls44 v13">\ued54</span><span class="fs7 ls40 vd">\uf136</span><span class="ls31 ws1e v13">\uf345\ued54<span class="blank _3"></span>\uf345</span><span class="ls18 v17">\ue975</span></div><div class="t m0 x39 h35 y7a ff8 fs2 fc0 sc0 ls43">\ue974<span class="ls18 v13">\ued40\ued54</span></div><div class="t m0 x3a h31 y62 ff8 fs7 fc0 sc0 ls18">\uf137</div><div class="t m0 x2f h36 y7b ff8 fs7 fc0 sc0 ls18 ws2d">\uf13f\uf135<span class="blank"> </span><span class="fs2 ls2a v14">\uf34c<span class="ff5 ls18 ws17"> </span></span></div><div class="t m0 x1 h2b y7c ff8 fs2 fc0 sc0 ls18 ws2c">\ued23<span class="blank _b"> </span>\uf34c<span class="blank _b"> </span>\uf3b1<span class="blank _4"> </span>\uf346<span class="blank"> </span><span class="v12">\ue973</span></div><div class="t m0 x38 h35 y7d ff8 fs2 fc0 sc0 ls43">\ue974<span class="ls44 v13">\ued54</span><span class="fs7 ls18 vd">\uf136</span></div><div class="t m0 x3a h31 y7e ff8 fs7 fc0 sc0 ls18">\uf137</div><div class="t m0 x2f h36 y7f ff8 fs7 fc0 sc0 ls18 ws2e">\uf13f\uf135<span class="blank"> </span><span class="fs2 ws2f v14">\ued40\ued54<span class="blank _9"> </span>\uf345<span class="blank"> </span>\ue603<span class="blank"> </span>\uf3b1<span class="blank _12"> </span>\ued54<span class="blank _3"></span>\ue603\ued40\ued54</span></div><div class="t m0 x3b h31 y7e ff8 fs7 fc0 sc0 ls18">\uf137</div><div class="t m0 x3c h37 y7f ff8 fs7 fc0 sc0 ls18 ws30">\uf13f\uf135<span class="blank"> </span><span class="fs2 ws23 v14">\uf345<span class="blank"> </span>\uf3b1<span class="blank _4"> </span><span class="v12">\ue975</span></span></div><div class="t m0 x3d h35 y7d ff8 fs2 fc0 sc0 ls43">\ue974<span class="ls18 v13">\ued40\ued54</span></div><div class="t m0 x3e h31 y7e ff8 fs7 fc0 sc0 ls18">\uf137</div><div class="t m0 x3f h36 y7f ff8 fs7 fc0 sc0 ls18 ws31">\uf13f\uf135<span class="blank"> </span><span class="fs2 ws32 v14">\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank"> </span>\udb80\udddb\ued32\ued4b\ued4e<span class="blank _3"></span>\ue603\ued4c\ued4e\ued4b\ued4c\ue7e4<span class="blank _3"></span>\ue603\ue603<span class="ff9 ws33">\uf0f2\uf028<span class="ff8 ws34">\ue688\udb80\udddb\ue603\ue69a\ue603\udb80\udddc<span class="blank"> </span>\ue603<span class="blank"> </span>\uf347<span class="blank _7"> </span>\ue603\ue689\udb80\udddb\ue603\ue69a\udb80\udddc</span>\uf029<span class="ff8 ls59 ws35">\ue686\ue69a<span class="ls18 ws21">\ue603</span></span><span class="ls45">\uf03d</span><span class="ff8 ws21">\ue603</span>\uf0f2<span class="ff8 ws21">\ue688\udb80\udddb\ue603\ue69a\ue603\udb80\udddc<span class="blank _3"></span>\ue603<span class="ls59 ws35">\ue686\ue69a</span><span class="ws17">\ue603<span class="blank"> </span>\uf347<span class="blank"> </span>\ue603</span></span>\uf0f2<span class="ff8 ws21">\ue689\udb80\udddb\ue603\ue69a\udb80\udddc\ue603<span class="ls59 ws35">\ue686\ue69a<span class="ls2b">\udb80\udddc</span></span><span class="ff5 ws17"> </span></span></span></span></div><div class="t m0 x1 h2b y80 ff8 fs2 fc0 sc0 ls18 ws36">\ued23<span class="blank _b"> </span>\uf34c<span class="blank _b"> </span>\uf346<span class="blank"> </span><span class="v12">\ue973</span></div><div class="t m0 x40 h35 y81 ff8 fs2 fc0 sc0 ls43">\ue974<span class="ls18 ws37 v13">\ue7e4<span class="blank _6"> </span>\uf3b1<span class="blank _14"> </span>\ued54<span class="blank"> </span></span><span class="fs7 ls46 vd">\uf136</span><span class="ls18 ws23 v13">\ued40\ued54<span class="blank _7"> </span>\uf345<span class="blank"> </span>\uf3b1<span class="blank _15"> </span>\ued54<span class="blank _3"></span>\ue603\ued40\ued54</span></div><div class="t m0 x3b h31 y82 ff8 fs7 fc0 sc0 ls18">\uf137</div><div class="t m0 x3c h31 y83 ff8 fs7 fc0 sc0 ls18 ws5">\uf13f\uf135</div><div class="t m0 x41 h31 y82 ff8 fs7 fc0 sc0 ls18">\uf137</div><div class="t m0 x38 h37 y83 ff8 fs7 fc0 sc0 ls18 ws38">\uf13f\uf135<span class="blank"> </span><span class="fs2 ws23 v14">\uf345<span class="blank"> </span>\uf3b1<span class="blank _4"> </span><span class="v12">\ue975</span></span></div><div class="t m0 x3d h35 y81 ff8 fs2 fc0 sc0 ls43">\ue974<span class="ls18 ws39 v13">\ued40\ued54<span class="blank"> </span>\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\udb80\udddb\ued32\ued4b\ued4e</span></div><div class="t m0 x3e h31 y82 ff8 fs7 fc0 sc0 ls18">\uf137</div><div class="t m0 x3f h36 y83 ff8 fs7 fc0 sc0 ls18 ws3a">\uf13f\uf135<span class="blank"> </span><span class="fs2 ws21 v14">\ue603\ue692\ue694\ue691\ue692\ue7e4\ue603\ue603\ue603\ue603</span></div><div class="t m1 x42 h38 y80 ff9 fsa fc0 sc0 ls18">\uf0f2</div><div class="t m0 x43 h2d y80 ff8 fs2 fc0 sc0 ls18 ws3b">\ued3d<span class="blank"> </span>\ue603</div><div class="t m1 x44 h38 y80 ff9 fsa fc0 sc0 ls18">\uf0d7</div><div class="t m0 x45 h2f y80 ff8 fs2 fc0 sc0 ls34">\ued42<span class="ls2b v7">\udb80\udddb</span><span class="ls18 ws21">\ue603\ued54\ue603<span class="blank _3"></span><span class="ls2b v7">\udb80\udddc</span>\ued40\ued54\ue603</span></div><div class="t m1 x46 h38 y80 ff9 fsa fc0 sc0 ls18">\uf03d</div><div class="t m0 x47 h2d y80 ff8 fs2 fc0 sc0 ls18 ws21">\ue603\ue603\ued3d<span class="blank _3"></span>\ue603</div><div class="t m1 x48 h38 y80 ff9 fsa fc0 sc0 ls18 ws3c">\uf0d7\uf0f2</div><div class="t m0 x49 h2d y80 ff8 fs2 fc0 sc0 ls18 ws3d">\ued42<span class="blank"> </span>\udb80\udddb\ue603\ued54<span class="blank"> </span>\ue603\udb80\udddc\ue603\ued40\ued54\udb80\udddc<span class="ff5 ws17"> </span></div><div class="t m0 x1 h2b y84 ff8 fs2 fc0 sc0 ls18 ws36">\ued23<span class="blank _b"> </span>\uf34c<span class="blank _b"> </span>\uf346<span class="blank"> </span><span class="v12">\ue973</span></div><div class="t m0 x40 h2c y85 ff8 fs2 fc0 sc0 ls43">\ue974<span class="ls47 v13">\ue7e4</span><span class="ls3f v17">\ued54</span><span class="fs7 ls18 v18">\uf137</span></div><div class="t m0 x4a h2c y85 ff8 fs2 fc0 sc0 ls48">\ue975<span class="ls30 v13">\uf345</span><span class="ls3f v17">\ued54</span><span class="fs7 ls18 v18">\uf136</span></div><div class="t m0 x4b h2c y85 ff8 fs2 fc0 sc0 ls48">\ue974<span class="ls31 v13">\uf345</span><span class="ls18 v17">\ue975</span></div><div class="t m0 x4c h39 y85 ff8 fs2 fc0 sc0 ls43">\ue974<span class="ls18 ws3e v13">\ued54<span class="blank"> </span>\uf42c<span class="blank _13"> </span></span><span class="ls49 v19">\ue975</span><span class="ls18 v1a">\ue603</span></div><div class="t m0 x4d h31 y86 ff8 fs7 fc0 sc0 ls18 ws5">\uf13f\uf135</div><div class="t m0 x4e h3a y87 ff8 fs7 fc0 sc0 ls4a">\ue603<span class="fs2 ls18 ws3f v1a">\uf34c<span class="blank _9"> </span>\uf346<span class="blank"> </span><span class="v12">\ue973</span></span></div><div class="t m0 x4f h2c y85 ff8 fs2 fc0 sc0 ls43">\ue978<span class="ls18 ws37 v13">\ue7e4<span class="blank _6"> </span>\ued54<span class="blank"> </span></span><span class="fs7 ls40 vd">\uf137</span><span class="ls31 v13">\uf345</span><span class="ls3f v17">\ued54</span><span class="fs7 ls18 v18">\uf136</span></div><div class="t m0 x33 h2c y85 ff8 fs2 fc0 sc0 ls48">\ue974<span class="ls31 v13">\uf345</span><span class="ls18 v17">\ue975</span></div><div class="t m0 x50 h39 y85 ff8 fs2 fc0 sc0 ls43">\ue974<span class="ls18 ws3e v13">\ued54<span class="blank"> </span>\uf42c<span class="blank _13"> </span></span><span class="ls49 v19">\ue975</span><span class="ls18 v1a">\ue603</span></div><div class="t m0 x51 h31 y86 ff8 fs7 fc0 sc0 ls18 ws5">\uf13f\uf135</div><div class="t m0 x52 h3b y87 ff8 fs7 fc0 sc0 ls4a">\ue603<span class="fs2 ls18 ws21 v1a">\uf34c<span class="ff5 ws17"> </span></span></div><div class="t m0 x1 h2b y88 ff8 fs2 fc0 sc0 ls18 ws36">\ued23<span class="blank _b"> </span>\uf34c<span class="blank _b"> </span>\uf346<span class="blank"> </span><span class="v12">\ue973</span></div><div class="t m0 x40 h2c y89 ff8 fs2 fc0 sc0 ls43">\ue978<span class="ls18 ws36 v13">\ue7e4<span class="blank"> </span>\ue975</span><span class="fs7 ls40 vd">\uf137</span><span class="ls30 v13">\uf345</span><span class="ls18 ws21 v17">\ue975<span class="fs7 v1b">\uf136</span></span></div><div class="t m0 x4b h2c y89 ff8 fs2 fc0 sc0 ls4b">\ue974<span class="ls4c v13">\uf345</span><span class="ls18 v17">\ue975</span></div><div class="t m0 x4c h2c y89 ff8 fs2 fc0 sc0 ls4d">\ue974<span class="ls18 ws40 v13">\ue7e4\ue603\ue603\ue975<span class="blank _8"> </span>\uf346<span class="blank _7"> </span>\uf36d\uf346<span class="blank"> </span><span class="v12">\ue973</span></span></div><div class="t m0 x1d h3c y89 ff8 fs2 fc0 sc0 ls4e">\ue978<span class="ls18 ws32 v13">\ue603<span class="blank"> </span>\ue7e4<span class="blank _6"> </span></span><span class="ls2b v9">\udb80\udddb</span><span class="ls18 ws21 v13">\uf346\ue973</span><span class="ls2b v9">\udb80\udddc</span><span class="fs7 ls4f vd">\uf137</span><span class="ls31 v13">\uf345</span><span class="ls2b v1c">\udb80\udddb</span><span class="ls18 ws21 v17">\uf346\ue973</span><span class="ls2b v1c">\udb80\udddc</span><span class="fs7 ls18 v18">\uf136</span></div><div class="t m0 x50 h2c y89 ff8 fs2 fc0 sc0 ls50">\ue974<span class="ls31 v13">\uf345</span><span class="ls18 v17">\ue975</span></div><div class="t m0 x53 h3d y89 ff8 fs2 fc0 sc0 ls51">\ue974<span class="ls47 v13">\ue7e4</span><span class="ls2b v9">\udb80\udddb</span><span class="ls18 ws21 v13">\uf346\ue973</span><span class="ls2b v9">\udb80\udddc</span><span class="ls18 ws41 v13">\uf371<span class="blank"> </span>\uf34c<span class="ff5 ws17"> </span></span></div><div class="t m0 x1 h2b y8a ff8 fs2 fc0 sc0 ls18 ws36">\ued23<span class="blank _b"> </span>\uf34c<span class="blank _b"> </span>\uf346<span class="blank"> </span><span class="v12">\ue97b</span></div><div class="t m0 x40 h2c y8b ff8 fs2 fc0 sc0 ls52">\ue974<span class="ls4c v13">\uf345</span><span class="ls18 v17">\ue97b</span></div><div class="t m0 x54 h2c y8b ff8 fs2 fc0 sc0 ls52">\ue974<span class="ls30 v13">\uf345</span><span class="ls18 v17">\ue97b</span></div><div class="t m0 x4b h2c y8b ff8 fs2 fc0 sc0 ls52">\ue974<span class="ls18 ws23 v13">\uf346<span class="blank"> </span>\uf36c<span class="v12">\ue973</span></span></div><div class="t m0 x55 h2c y8b ff8 fs2 fc0 sc0 ls52">\ue978<span class="ls4c v13">\uf345</span><span class="ls18 v17">\ue973</span></div><div class="t m0 x56 h2c y8b ff8 fs2 fc0 sc0 ls52">\ue974<span class="ls31 v13">\uf346</span><span class="ls18 v17">\ue975</span></div><div class="t m0 x57 h35 y8b ff8 fs2 fc0 sc0 ls18 ws21">\ue974<span class="ls53 v13">\uf370</span><span class="ff5 ws17 v13"> </span></div><div class="t m0 x1 h2b y8c ff8 fs2 fc0 sc0 ls18 ws25">\ued23<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="v12">\ue97b</span></div><div class="t m0 x58 h2c y8d ff8 fs2 fc0 sc0 ls54">\ue974<span class="ls31 v13">\uf346</span><span class="ls18 v17">\ue973</span></div><div class="t m0 x59 h2c y8d ff8 fs2 fc0 sc0 ls52">\ue978<span class="ls30 v13">\uf346</span><span class="ls18 v17">\ue973</span></div><div class="t m0 x5a h2c y8d ff8 fs2 fc0 sc0 ls55">\ue974<span class="ls31 v13">\uf345</span><span class="ls18 v17">\ue975</span></div><div class="t m0 x5b h35 y8d ff8 fs2 fc0 sc0 ls56">\ue974<span class="ls2a v13">\uf34c<span class="ff5 ls18 ws17"> </span></span></div><div class="t m0 x1 h3e y8e ff8 fs2 fc0 sc0 ls18 ws25">\ued23<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="ls5a v12">\ue973\ue978</span></div><div class="t m0 x5c h2d y8f ff8 fs2 fc0 sc0 ls57">\ue975<span class="ff5 ls18 ws17 v13"> </span></div><div class="t m0 x1 h13 y90 ff5 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h1f y91 ff4 fs3 fc0 sc0 ls18 ws17"> <span class="blank _16"> </span> </div></div><div class="c x0 y3e wa h1e"><div class="t m0 x19 h1f y3f ff4 fs3 fc1 sc0 ls18 ws17"><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 y92 w12 h3f" alt="" src="https://files.passeidireto.com/c2f1404f-661b-45c9-8d0f-90de15593d63/bg4.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls18 ws17">MATEMÁTICA (6<span class="ls19 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls27"> <span class="ls28"> </span></span>RECUPERATOR<span class="blank _3"> </span>IO 2° PARC<span class="blank _3"> </span>IAL </div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 ls18 ws17">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 _10"> </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 1 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 ls18 ws17">Hoja 3 de 4 </div><div class="t m0 x3 h2 y65 ff2 fs0 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h1f y93 ff4 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h4 y94 ff7 fs2 fc0 sc0 ls18 ws17">3. ¿Cuántas palabras distintas se pueden formar, c<span class="blank _0"></span>on o sin sentido, con las letras de la palabra </div><div class="t m0 x1 h4 y95 ffd fs2 fc0 sc0 ls18 ws42">\u201cAGRARIO\u201d?<span class="ff7 ws17"> </span></div><div class="t m0 x1 h1f y96 ff4 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h40 y97 ff6 fs3 fc0 sc0 ls18 ws17">Buscamos <span class="blank _0"></span>util<span class="blank _0"></span>izar <span class="blank _0"></span>las <span class="blank _0"></span>7 <span class="blank _0"></span>letras<span class="blank _0"></span> de<span class="blank _0"></span> l<span class="blank _0"></span>a <span class="blank _0"></span>palabra <span class="blank _0"></span>\u201cA<span class="blank _0"></span>GRARIO\u201d <span class="blank _0"></span>para <span class="blank _0"></span>ar<span class="blank _0"></span>mar <span class="blank _0"></span>los <span class="blank _0"></span>nuevos <span class="blank _0"></span>v<span class="blank _0"></span>ocablos <span class="blank _0"></span>(indepen<span class="blank _0"></span>dientemente <span class="blank _0"></span>de<span class="blank _0"></span> </div><div class="t m0 x1 h13 y98 ff5 fs3 fc0 sc0 ls18 ws17">si éstos tienen o <span class="blank _3"> </span>no sentido en <span class="blank _3"> </span>nuestro idioma). Por otra parte, importa el orden <span class="blank _3"> </span>en que se eligen <span class="blank _3"> </span>las letras para </div><div class="t m0 x1 h13 y99 ff5 fs3 fc0 sc0 ls18 ws17">formar dichos tér<span class="blank _0"></span>minos. Luego, estamos an<span class="blank _0"></span>te un caso de pe<span class="blank _0"></span>rmutación o r<span class="blank _0"></span>eordenamiento de el<span class="blank _0"></span>ementos. </div><div class="t m0 x1 h40 y9a ff6 fs3 fc0 sc0 ls18 ws17">Sin <span class="blank _3"> </span>embargo, <span class="blank _c"> </span>entre <span class="blank _c"> </span>las <span class="blank _3"> </span>7 <span class="blank _c"> </span>letras <span class="blank _c"> </span>hay <span class="blank _3"> </span>2 <span class="blank _c"> </span>repetidas <span class="blank _3"> </span>(<span class="blank _3"> </span>la <span class="blank _3"> </span>\u201cA\u201d <span class="blank _c"> </span>y <span class="blank _3"> </span>la <span class="blank _c"> </span>\u201cR\u201d) <span class="blank _c"> </span>lo <span class="blank _3"> </span>q<span class="blank _3"> </span>ue <span class="blank _3"> </span>reduce <span class="blank _c"> </span>la <span class="blank _c"> </span>cantidad <span class="blank _3"> </span>de <span class="blank _c"> </span>palabras <span class="blank _3"> </span>distintas </div><div class="t m0 x1 h13 y9b ff5 fs3 fc0 sc0 ls18 ws17">posibles. </div><div class="t m0 x1 h13 y9c ff5 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h13 y9d ff5 fs3 fc0 sc0 ls18 ws17">Recordemos ade<span class="blank _0"></span>más que: </div><div class="t m0 x5d h13 y74 ff5 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h13 y9e ff5 fs3 fc0 sc0 ls18 ws17">Luego, hay: </div><div class="t m0 x57 h15 y9f ff8 fs3 fc0 sc0 ls18">\ued32</div><div class="t m0 x5e h41 ya0 ff8 fs0 fc0 sc0 ls18">\uf13b</div><div class="t m0 x30 h42 ya1 ff8 fs0 fc0 sc0 ls18 ws43">\uf136\ue7e1\uf136\ue7e1\uf135\ue7e1\uf135\ue7e1\uf135<span class="blank"> </span><span class="fs3 ls5b v1d">\uf34c</span><span class="fs3 ws9 vc">\ue979\ue7e8</span></div><div class="t m0 x5f h43 ya2 ff8 fs3 fc0 sc0 ls18 ws44">\ue974\ue7e8<span class="blank"> </span>\ue974\ue7e8<span class="blank"> </span>\ue973\ue7e8<span class="blank"> </span>\ue973\ue7e8<span class="blank"> </span>\ue973\ue7e8<span class="blank _9"> </span><span class="lsc vf">\uf34c</span><span class="ws9 v19">\ue979\ue7e4\ue978\ue7e4\ue977\ue7e4\ue976\ue7e4\ue975\ue7e8</span></div><div class="t m0 x60 h44 ya2 ff8 fs3 fc0 sc0 ls5c">\ue976<span class="ls18 ws18 vf">\uf34c<span class="blank"> </span>\ue979\ue7e4\ue978\ue7e4\ue977\ue7e4\ue975\ue7e4\ue974<span class="blank"> </span>\uf34c<span class="blank"> </span></span><span class="ls3 ws45 vf">\ue973\ue974\ue978\ue972</span><span class="ff5 ls18 ws17 vf"> </span></div><div class="t m0 x1 h6 ya3 ff5 fs3 fc0 sc0 ls18 ws17">palabras distintas <span class="blank _0"></span>que pueden <span class="blank _0"></span>formarse con las<span class="blank _0"></span> 7 letras de la palabra<span class="blank _0"></span> <span class="blank _3"> </span><span class="ffe ws46">\u201cA<span class="blank _0"></span>GRARIO\u201d<span class="ff3 ws17"> </span></span></div><div class="t m0 x1 h13 ya4 ff5 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x61 h13 ya5 ff5 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h13 ya6 ff5 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h13 ya7 ff5 fs3 fc0 sc0 ls18 ws17"> <span class="blank _f"> </span> </div></div><div class="c x0 y3e wa h1e"><div class="t m0 x19 h1f y3f ff4 fs3 fc1 sc0 ls18 ws17"><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 ya8 w13 h45" alt="" src="https://files.passeidireto.com/c2f1404f-661b-45c9-8d0f-90de15593d63/bg5.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h13 y41 ff5 fs3 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h2 ya9 ff1 fs0 fc0 sc0 ls18 ws17">MATEMÁTICA (6<span class="blank _0"></span><span class="ls19 ws0">1)<span class="ff2 ls18 ws17"> Cátedra A: <span class="blank _0"></span>NUÑEZ, MYRIA<span class="blank _0"></span>M<span class="ff1"> RECUPER<span class="blank _0"></span>ATORIO 2° PARCIAL<span class="blank _0"></span> </span></span></span></div><div class="t m0 x1 h2 yaa ff2 fs0 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h2 yab ff2 fs0 fc0 sc0 ls18 ws17">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="ls67 ws47">DN<span class="ls68 ws48">I:</span></span> <span class="blank _10"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _17"> </span> <span class="blank _17"> </span> <span class="blank _17"> </span>TEM<span class="blank _3"> </span>A 1 </div><div class="t m0 x3 h2 yac ff2 fs0 fc0 sc0 ls18 ws17">Hoja 4 de 4 </div><div class="t m0 x3 h2 yad ff2 fs0 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h4 yae fff fs2 fc0 sc0 ls18 ws49">4.<span class="ff7 ws17"> Se<span class="blank _0"></span> encuestar<span class="blank _0"></span>on a <span class="blank _0"></span>250 <span class="blank _0"></span>personas <span class="blank _0"></span>sobre <span class="blank _0"></span>sus <span class="blank _0"></span>hábitos <span class="blank _0"></span>alimenticios <span class="blank _0"></span>en <span class="blank _0"></span>el <span class="blank _0"></span>desayuno y <span class="blank _0"></span>se <span class="blank _0"></span>obtuvieron <span class="blank _0"></span>las <span class="blank _0"></span>siguientes </span></div><div class="t m0 x1 h4 yaf ff7 fs2 fc0 sc0 ls18 ws17">respuestas: <span class="blank _c"> </span>30 <span class="blank _c"> </span>personas <span class="blank _d"> </span>tomaban <span class="blank _c"> </span>té <span class="blank _c"> </span>con <span class="blank _d"> </span>leche, <span class="blank _c"> </span>40 <span class="blank _c"> </span>p<span class="blank _3"> </span>ersonas <span class="blank _c"> </span>tomaban <span class="blank _d"> </span>caf<span class="blank _3"> </span>é <span class="blank _c"> </span>con <span class="blank _c"> </span>leche, <span class="blank _c"> </span>80 <span class="blank _d"> </span>personas <span class="blank _c"> </span>to<span class="blank _3"> </span>maban </div><div class="t m0 x1 h4 yb0 ff7 fs2 fc0 sc0 ls18 ws17">leche, 130 <span class="blank _3"> </span>personas <span class="blank _3"> </span>tomaban té <span class="blank _3"> </span>o <span class="blank _3"> </span>leche y <span class="blank _3"> </span>150 <span class="blank _3"> </span>tom<span class="blank _0"></span>aban <span class="blank _3"> </span>café o <span class="blank _3"> </span>leche. ¿Cuán<span class="blank _3"> </span>tas personas <span class="blank _3"> </span>no tomaba <span class="blank _3"> </span>ninguna </div><div class="t m0 x1 h4 yb1 ff7 fs2 fc0 sc0 ls18 ws17">de estas tres cosas al desayuno? </div><div class="t m0 x1 h30 yb2 ff5 fs2 fc0 sc0 ls18 ws17"> </div><div class="t m0 x61 h13 yb3 ff5 fs3 fc0 sc0 ls18 ws17">Vamos a desi<span class="blank _0"></span>gnar a los conjunto<span class="blank _0"></span>s: <span class="blank _4"> </span><span class="ff8 wse v1e">\ued25<span class="blank _13"> </span>\uf34c<span class="blank"> </span>\ued32\ued41\ued4e\ued4f\ued4b\ued4a\ued3d\ued4f\ue603\ued4d\ued51\ued41\ue603\ued50\ued4b\ued49\ued3d\ued4a\ue603\ued3f\ued3d\ued42\ued41<span class="blank _3"></span>\ue7e1</span><span class="v1e"> </span></div><div class="t m0 x13 h15 yb4 ff8 fs3 fc0 sc0 ls18 wse">\ue603\ued36<span class="blank"> </span>\uf34c<span class="blank"> </span>\ued32\ued41\ued4e\ued4f\ued4b\ued4a\ued3d\ued4f<span class="blank _3"></span>\ue603\ued4d\ued51\ued41\ue603\ued50\ued4b\ued49\ued3d\ued4a\ue603<span class="ls69 ws4a">\ued50\ued41<span class="blank _3"> </span></span><span class="ws9">\ue7e1\ue603<span class="ff5 ws17"> </span></span></div><div class="t m0 x62 h15 yb5 ff8 fs3 fc0 sc0 ls18 ws18">\ued2e<span class="blank _9"> </span>\uf34c<span class="blank"> </span>\ued32\ued41\ued4e\ued4f<span class="blank _3"></span>\ued4b\ued4a\ued3d\ued4f\ue603\ued4d\ued51\ued41\ue603\ued50\ued4b\ued49\ued3d\ued4a\ue603<span class="blank _3"></span>\ued48\ued41\ued3f\ued44\ued41<span class="ff5 ws17"> </span></div><div class="t m0 x61 h17 yb6 ff5 fs3 fc0 sc0 ls18 ws17">Se pide: <span class="ff8 ws9">\ued25\ued3d\ued4e\ued40\ue603<span class="v7">\udb80\udddb</span><span class="ws4b">\ued25<span class="blank _9"> </span>\uebeb<span class="blank"> </span>\ued36<span class="blank"> </span>\uebeb<span class="blank _8"> </span>\ued2e<span class="blank _3"> </span></span><span class="v7">\udb80\udddc</span><span class="fs0 ls5d v8">\uf1d6</span></span> </div><div class="t m0 x61 h13 yb7 ff5 fs3 fc0 sc0 ls18 ws17">Vamos a establece<span class="blank _0"></span>r algunas proposici<span class="blank _0"></span>ones que se deducen<span class="blank _0"></span> del problema </div><div class="t m0 x63 h17 yb8 ff8 fs3 fc0 sc0 ls18 ws9">\ued25\ued3d\ued4e\ued40<span class="v7">\udb80\udddb</span><span class="ws4c">\ued25<span class="blank _9"> </span>\uebea<span class="blank"> </span>\ued36<span class="blank"> </span>\uebea<span class="blank"> </span>\ued2e<span class="blank _3"> </span><span class="ls7 v7">\udb80\udddc</span><span class="ws4d">\uf34c<span class="blank _9"> </span>\ue972\ue7e1<span class="blank"> </span>\ued25\ued3d\ued4e\ued40\ue603</span></span><span class="v7">\udb80\udddb</span><span class="ws4c">\ued25<span class="blank _9"> </span>\uebea<span class="blank"> </span>\ued36<span class="ls7 v7">\udb80\udddc</span><span class="ws4d">\uf34c<span class="blank _9"> </span>\ue972\ue7e1<span class="blank"> </span>\ued25\ued3d\ued4e\ued40\ue603<span class="blank _3"></span></span></span><span class="v7">\udb80\udddb</span><span class="ls5e">\ued37<span class="ls5f v7">\udb80\udddc</span><span class="lsc">\uf34c<span class="ls3">\ue974\ue977\ue972</span></span></span><span class="ff5 ws17"> </span></div><div class="t m0 x64 h17 yb9 ff8 fs3 fc0 sc0 ls18 ws9">\ued25\ued3d\ued4e\ued40\ue603<span class="v7">\udb80\udddb</span><span class="ws4b">\ued25<span class="blank _9"> </span>\uebeb<span class="blank"> </span>\ued36<span class="blank _8"> </span>\uebeb<span class="blank _8"> </span>\ued2e<span class="blank _3"> </span></span><span class="v7">\udb80\udddc</span><span class="fs0 ls60 v8">\uf1d6</span><span class="ws4e">\uf34c<span class="blank"> </span>\ued25\ued3d\ued4e<span class="blank _3"></span></span><span class="v7">\udb80\udddb</span><span class="ls5e">\ued37<span class="ls61 v7">\udb80\udddc</span></span><span class="ws8">\uf346<span class="blank"> </span>\ued25\ued3d\ued4e\ued40<span class="blank _3"></span></span><span class="v7">\udb80\udddb</span><span class="ws4b">\ued25<span class="blank _7"> </span>\uebeb<span class="blank"> </span>\ued36<span class="blank _7"> </span>\uebeb<span class="blank"> </span>\ued2e<span class="blank _3"> </span><span class="ls62 v7">\udb80\udddc</span></span>\uf34c<span class="ff5 ws17"> </span></div><div class="t m0 x61 h12 yba ff8 fs3 fc0 sc0 lsc">\uf34c<span class="ls3 ws4f">\ue974\ue977\ue972<span class="blank"> </span><span class="ls63">\uf346<span class="ls64 v7">\udb80\udddf</span></span></span><span class="ls18 ws9">\ued25\ued3d\ued4e\ued40<span class="v7">\udb80\udddf</span><span class="wsb">\ued25<span class="blank _9"> </span>\uf346<span class="blank"> </span></span><span class="v7">\udb80\udddb</span><span class="ws4c">\ued36<span class="blank"> </span>\uebeb<span class="blank"> </span>\ued2e<span class="blank _3"> </span></span><span class="v7">\udb80\udddc<span class="v0">\udb80\udde0</span></span><span class="ff5 ls65">+</span>\ued25\ued3d\ued4e\ued40<span class="blank _3"> </span><span class="v7">\udb80\udddf</span><span class="wsb">\ued36<span class="blank _7"> </span>\uf346<span class="blank"> </span></span><span class="v7">\udb80\udddb</span><span class="ws4c">\ued25<span class="blank _7"> </span>\uebeb<span class="blank"> </span>\ued2e<span class="blank _3"></span></span><span class="v7">\udb80\udddc</span><span class="ls66 v7">\udb80\udde0</span><span class="wsb">\uf345<span class="blank"> </span>\ued25\ued3d\ued4e\ued40</span><span class="v7">\udb80\udddf</span><span class="wsb">\ued2e<span class="blank _7"> </span>\uf346<span class="blank"> </span></span><span class="v7">\udb80\udddb</span><span class="ws4c">\ued25<span class="blank _7"> </span>\uebeb<span class="blank"> </span>\ued36<span class="blank _3"> </span></span><span class="v7">\udb80\udddc</span><span class="ls66 v7">\udb80\udde0</span>\uf345<span class="ff5 ws17"> </span></span></div><div class="t m0 x61 h12 ybb ff8 fs3 fc0 sc0 ls18 ws9">\ued25\ued3d\ued4e\ued40<span class="v7">\udb80\udddf<span class="vb">\udb80\udddb</span></span><span class="ws4b">\ued25<span class="blank _9"> </span>\uebea<span class="blank"> </span>\ued2e<span class="blank _3"></span><span class="ls9 v7">\udb80\udddc</span><span class="wsb">\uf346<span class="blank"> </span>\ued36<span class="ls66 v7">\udb80\udde0</span><span class="ws50">\uf345<span class="blank _8"> </span>\ued25\ued3d\ued4e\ued40<span class="blank"> </span></span></span></span><span class="v7">\udb80\udddf<span class="vb">\udb80\udddb</span></span><span class="ws4c">\ued36<span class="blank _7"> </span>\uebea<span class="blank"> </span>\ued2e<span class="blank _3"> </span><span class="ls9 v7">\udb80\udddc</span><span class="ws51">\uf346<span class="blank _8"> </span>\ued25<span class="blank"> </span></span></span><span class="v7">\udb80\udde0</span><span class="ff5 ws17">= 250-(70+5<span class="blank _0"></span>0+10+40+30)=50<span class="blank _0"></span> </span></div><div class="t m0 x65 h17 ybc ff8 fs3 fc4 sc0 ls18 ws9">\ued25\ued3d\ued4e\ued40\ue603<span class="v7">\udb80\udddb</span><span class="ws4c">\ued25<span class="blank _9"> </span>\uebeb<span class="blank"> </span>\ued36<span class="blank"> </span>\uebeb<span class="blank"> </span>\ued2e<span class="blank _3"> </span></span><span class="v7">\udb80\udddc</span><span class="fs0 ls60 v8">\uf1d6</span><span class="lsc">\uf34c<span class="ls3 ws45">\ue977\ue972</span></span><span class="ff5 fc0 ws17"> </span></div><div class="t m0 x61 h6 ybd ff3 fs3 fc0 sc0 ls18 ws17">Referencia: Un<span class="blank _0"></span>idad 7: Conj<span class="blank _0"></span>untos </div><div class="t m0 x1 h30 ybe ff5 fs2 fc0 sc0 ls18 ws17"> </div><div class="t m0 x1 h13 ybf ff5 fs3 fc0 sc0 ls18 ws17"> </div></div><div class="c x0 yc0 wa h46"><div class="t m0 x19 h1f y3f ff4 fs3 fc1 sc0 ls18 ws17"><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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