<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/983b1510-9b97-4a18-bbd3-090700f03d0a/bg1.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 lsf ws12">MATEMÁTICA (6<span class="ls10 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM </span></div><div class="t m0 x1 h2 y3 ff1 fs0 fc0 sc0 lsf ws12">RECUPERATORI<span class="blank _0"></span>O 2° PARCIAL </div><div class="t m0 x2 h2 y4 ff1 fs0 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h2 y5 ff2 fs0 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h3 y6 ff2 fs1 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h2 y7 ff2 fs0 fc0 sc0 ls11 ws1">21<span class="lsf ws2">/06/2023<span class="ff1 ws12"> <span class="blank _0"></span> <span class="blank _1"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span>TEMA 2 </span></span></div><div class="t m0 x3 h2 y8 ff2 fs0 fc0 sc0 lsf ws12"> Hoja 1 de 4 </div><div class="t m0 x3 h2 y9 ff2 fs0 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h3 ya ff2 fs1 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h3 yb ff2 fs1 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h4 yc ff3 fs2 fc0 sc0 lsf ws12">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 lsf ws12"> </div></div><div class="c x6 yd w4 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lsf ws12">1 </div></div><div class="c x8 yd w5 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lsf ws12">2 </div></div><div class="c x9 yd w6 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lsf ws12">3 </div></div><div class="c xa yd w7 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lsf ws12">4 </div></div><div class="c x4 yf w3 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsf ws12"> </div></div><div class="c x6 yf w4 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsf ws12"> </div></div><div class="c x8 yf w5 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsf ws12"> </div></div><div class="c x9 yf w6 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsf ws12"> </div></div><div class="c xa yf w7 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsf ws12"> </div></div><div class="c x4 y11 w5 h9"><div class="t m0 xb ha y12 ff4 fs4 fc0 sc0 lsf ws12">Puntaje de cada </div><div class="t m0 xb ha y13 ff4 fs4 fc0 sc0 lsf ws12">ejercicio </div></div><div class="c x6 y11 w4 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lsf ws12">2,50 </div></div><div class="c x8 y11 w5 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lsf ws12">2,50 </div></div><div class="c x9 y11 w6 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lsf ws12">2,50 </div></div><div class="c xa y11 w7 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lsf ws12">2,50 </div></div><div class="c x0 y1 w2 h0"><div class="t m0 x1 hb y15 ff5 fs5 fc0 sc0 lsf ws12">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 lsf ws12">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 ls0 ws12"> <span class="ff7 fs2 lsf v1"> </span></div><div class="t m0 x1 h4 y18 ff7 fs2 fc0 sc0 lsf ws12">1. 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 háb<span class="blank _0"></span>itos <span class="blank _0"></span>alimenticios <span class="blank _0"></span>en <span class="blank _0"></span>el desayuno <span class="blank _0"></span>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 </div><div class="t m0 x1 h4 y19 ff7 fs2 fc0 sc0 lsf ws12">respuestas: <span class="blank _4"> </span>30 <span class="blank _4"> </span>p<span class="blank _3"> </span>ersonas <span class="blank _4"> </span>tomaban <span class="blank _4"> </span>té <span class="blank _5"> </span>con <span class="blank _4"> </span>leche, <span class="blank _5"> </span>40 <span class="blank _4"> </span>personas <span class="blank _5"> </span>tomaban <span class="blank _4"> </span>caf<span class="blank _3"> </span>é <span class="blank _4"> </span>con <span class="blank _4"> </span>leche, <span class="blank _4"> </span>80<span class="blank _3"> </span> <span class="blank _4"> </span>personas <span class="blank _5"> </span>tomaban </div><div class="t m0 x1 h4 y1a ff7 fs2 fc0 sc0 lsf ws12">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. <span class="blank _4"> </span>¿Cuántas p<span class="blank _3"> </span>ersonas no <span class="blank _3"> </span>tomaba ninguna </div><div class="t m0 x1 h4 y1b ff7 fs2 fc0 sc0 lsf ws12">de estas tres cosas al desayuno? </div><div class="t m0 x1 he y1c ff5 fs2 fc0 sc0 lsf ws12"> </div><div class="t m0 xf hf y1d ff5 fs3 fc0 sc0 lsf ws12">Vamos a desi<span class="blank _0"></span>gnar a los conjunto<span class="blank _0"></span>s: <span class="blank _6"> </span><span class="ff8 ws4 v2">\ued25<span class="blank _7"> </span>\uf34c<span class="blank"> </span>\ued32\ued41\ued4e\ued4f\ued4b\ued4a\ued3d\ued4f\ue603\ued4d\ued51\ued41<span class="blank _3"></span>\ue603\ued50\ued4b\ued49\ued3d\ued4a\ue603\ued3f\ued3d\ued42\ued41\ue7e1</span><span class="v2"> </span></div><div class="t m0 x10 h10 y1e ff8 fs3 fc0 sc0 lsf ws4">\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="ls12 ws5">\ued50\ued41<span class="blank _3"> </span></span><span class="ws6">\ue7e1\ue603<span class="ff5 ws12"> </span></span></div><div class="t m0 x11 h10 y1f ff8 fs3 fc0 sc0 lsf ws7">\ued2e<span class="blank _7"> </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<span class="blank _3"></span>\ued48\ued41\ued3f\ued44\ued41<span class="ff5 ws12"> </span></div><div class="t m0 xf h11 y20 ff5 fs3 fc0 sc0 lsf ws12">Se pide: <span class="ff8 ws6">\ued25\ued3d\ued4e\ued40\ue603<span class="v3">\udb80\udddb</span><span class="ws8">\ued25<span class="blank _8"> </span>\uebeb<span class="blank"> </span>\ued36<span class="blank _9"> </span>\uebeb<span class="blank"> </span>\ued2e<span class="blank _3"> </span></span><span class="v3">\udb80\udddc</span><span class="fs0 ls1 v4">\uf1d6</span></span> </div><div class="t m0 xf hf y21 ff5 fs3 fc0 sc0 lsf ws12">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 x12 h11 y22 ff8 fs3 fc0 sc0 lsf ws6">\ued25\ued3d\ued4e\ued40<span class="v3">\udb80\udddb</span><span class="ws9">\ued25<span class="blank _8"> </span>\uebea<span class="blank"> </span>\ued36<span class="blank _9"> </span>\uebea<span class="blank"> </span>\ued2e<span class="blank _3"></span><span class="ls2 v3">\udb80\udddc</span><span class="wsa">\uf34c<span class="blank _8"> </span>\ue972\ue7e1<span class="blank"> </span>\ued25\ued3d\ued4e\ued40\ue603</span></span><span class="v3">\udb80\udddb</span><span class="ws9">\ued25<span class="blank _8"> </span>\uebea<span class="blank"> </span>\ued36<span class="blank _3"></span><span class="ls2 v3">\udb80\udddc</span><span class="wsa">\uf34c<span class="blank _8"> </span>\ue972\ue7e1<span class="blank"> </span>\ued25\ued3d\ued4e\ued40\ue603<span class="blank _3"></span></span></span><span class="v3">\udb80\udddb</span><span class="ls3">\ued37<span class="ls4 v3">\udb80\udddc</span><span class="ls5">\uf34c<span class="ls6">\ue974\ue977\ue972</span></span></span><span class="ff5 ws12"> </span></div><div class="t m0 x13 h11 y23 ff8 fs3 fc0 sc0 lsf ws6">\ued25\ued3d\ued4e\ued40\ue603<span class="v3">\udb80\udddb</span><span class="ws8">\ued25<span class="blank _8"> </span>\uebeb<span class="blank"> </span>\ued36<span class="blank _9"> </span>\uebeb<span class="blank _9"> </span>\ued2e</span><span class="v3">\udb80\udddc</span><span class="fs0 ls7 v4">\uf1d6</span><span class="wsb">\uf34c<span class="blank"> </span>\ued25\ued3d\ued4e<span class="blank _3"></span></span><span class="v3">\udb80\udddb</span><span class="ls3">\ued37<span class="ls8 v3">\udb80\udddc</span></span><span class="wsc">\uf346<span class="blank"> </span>\ued25\ued3d\ued4e\ued40<span class="blank _3"></span></span><span class="v3">\udb80\udddb</span><span class="ws8">\ued25<span class="blank _9"> </span>\uebeb<span class="blank _9"> </span>\ued36<span class="blank _9"> </span>\uebeb<span class="blank"> </span>\ued2e<span class="ls9 v3">\udb80\udddc</span></span>\uf34c<span class="ff5 ws12"> </span></div><div class="t m0 xf h12 y24 ff8 fs3 fc0 sc0 ls5">\uf34c<span class="ls6 wsd">\ue974\ue977\ue972<span class="blank"> </span><span class="lsa">\uf346<span class="lsb v3">\udb80\udddf</span></span></span><span class="lsf ws6">\ued25\ued3d\ued4e\ued40<span class="v3">\udb80\udddf</span><span class="wse">\ued25<span class="blank _8"> </span>\uf346<span class="blank"> </span></span><span class="v3">\udb80\udddb</span><span class="ws9">\ued36<span class="blank _9"> </span>\uebeb<span class="blank"> </span>\ued2e<span class="blank _3"></span></span><span class="v3">\udb80\udddc<span class="v0">\udb80\udde0</span></span><span class="ff5 lsc">+</span>\ued25\ued3d\ued4e\ued40<span class="blank _3"></span><span class="v3">\udb80\udddf</span><span class="wse">\ued36<span class="blank"> </span>\uf346<span class="blank"> </span></span><span class="v3">\udb80\udddb</span><span class="ws9">\ued25<span class="blank _8"> </span>\uebeb<span class="blank"> </span>\ued2e<span class="blank _3"></span></span><span class="v3">\udb80\udddc</span><span class="lsd v3">\udb80\udde0</span><span class="wse">\uf345<span class="blank"> </span>\ued25\ued3d\ued4e\ued40</span><span class="v3">\udb80\udddf</span><span class="wse">\ued2e<span class="blank _9"> </span>\uf346<span class="blank"> </span></span><span class="v3">\udb80\udddb</span><span class="ws9">\ued25<span class="blank _8"> </span>\uebeb<span class="blank"> </span>\ued36</span><span class="v3">\udb80\udddc</span><span class="lsd v3">\udb80\udde0</span>\uf345<span class="ff5 ws12"> </span></span></div><div class="t m0 xf h12 y25 ff8 fs3 fc0 sc0 lsf ws6">\ued25\ued3d\ued4e\ued40<span class="v3">\udb80\udddf<span class="v0">\udb80\udddb</span></span><span class="ws8">\ued25<span class="blank _8"> </span>\uebea<span class="blank"> </span>\ued2e<span class="blank _3"> </span><span class="lse v3">\udb80\udddc</span><span class="wse">\uf346<span class="blank"> </span>\ued36<span class="blank _3"> </span><span class="lsd v3">\udb80\udde0</span><span class="wsf">\uf345<span class="blank _9"> </span>\ued25\ued3d\ued4e\ued40</span></span></span><span class="v3">\udb80\udddf<span class="v0">\udb80\udddb</span></span><span class="ws9">\ued36<span class="blank _9"> </span>\uebea<span class="blank"> </span>\ued2e<span class="blank _3"> </span><span class="lse v3">\udb80\udddc</span><span class="ws10">\uf346<span class="blank _a"> </span>\ued25<span class="blank"> </span></span></span><span class="v3">\udb80\udde0</span><span class="ff5 ws12">= 250-(70+50+10+40<span class="blank _0"></span>+30)=50 </span></div><div class="t m0 x14 h11 y26 ff8 fs3 fc1 sc0 lsf ws6">\ued25\ued3d\ued4e\ued40\ue603<span class="v3">\udb80\udddb</span><span class="ws9">\ued25<span class="blank _8"> </span>\uebeb<span class="blank"> </span>\ued36<span class="blank _9"> </span>\uebeb<span class="blank"> </span>\ued2e<span class="blank _3"></span></span><span class="v3">\udb80\udddc</span><span class="fs0 ls7 v4">\uf1d6</span><span class="ls5">\uf34c<span class="ls6 ws11">\ue977\ue972</span></span><span class="ff5 fc0 ws12"> </span></div><div class="t m0 xf h6 y27 ff3 fs3 fc0 sc0 lsf ws12">Referencia: Un<span class="blank _0"></span>idad 7: Conj<span class="blank _0"></span>untos </div><div class="t m0 x1 h4 y28 ff7 fs2 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h4 y29 ff7 fs2 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h6 y2a ff3 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h6 y2b ff3 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h6 y2c ff3 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h6 y2d ff3 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 hf y2e ff5 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 hf y2f ff5 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 hf y30 ff5 fs3 fc0 sc0 lsf ws12"> <span class="blank _b"> </span> </div></div><div class="c x1 y31 w8 h13"><div class="t m0 x15 h2 y32 ff2 fs0 fc0 sc0 lsf ws12">APELLIDO: </div></div><div class="c x16 y33 w9 h14"><div class="t m0 xb h2 y34 ff2 fs0 fc0 sc0 lsf ws12">CALIFICACIÓN:<span class="blank _0"></span> </div></div><div class="c x1 y35 w8 h15"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lsf ws12">NOMBRE: </div></div><div class="c x1 y33 w8 h15"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lsf ws12">DNI (registrado en S<span class="blank _0"></span>IU Guaraní): </div></div><div class="c x1 y36 w8 h16"><div class="t m0 xb h2 y10 ff2 fs0 fc0 sc0 lsf ws12">E-MAIL: </div></div><div class="c x16 y37 w9 h17"><div class="t m0 xb h2 y38 ff2 fs0 fc0 sc0 lsf ws12">DOCENTE (nombre<span class="blank _0"></span> y apellido): </div></div><div class="c x1 y39 w8 h15"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lsf ws12">TEL: </div></div><div class="c x1 y37 w8 h15"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lsf ws12">AULA: </div></div><div class="c x0 y3a wa h18"><div class="t m0 x15 h19 y3b ff4 fs3 fc2 sc0 lsf ws12"><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 y3c wb h1a" alt="" src="https://files.passeidireto.com/983b1510-9b97-4a18-bbd3-090700f03d0a/bg2.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 lsf ws12">MATEMÁTICA (6<span class="ls10 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls13"> <span class="ls14"> </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 lsf ws12"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 lsf ws12">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 ls15"> <span class="blank _c"></span> <span class="ls34 ws13">TE</span><span class="lsf">MA 2 </span></span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 lsf ws12">Hoja 2 de 4 </div><div class="t m0 x3 h2 y3d ff2 fs0 fc0 sc0 lsf ws12"> </div><div class="t m0 x2 h2 y3e ff1 fs0 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h1b y3f ff7 fs2 fc0 sc0 lsf ws12">2. Encontrar los intervalos de crecimiento y decrecimiento de<span class="blank _0"></span> la función <span class="blank _3"> </span><span class="ff8 ws14">\uee8c\udb80\udddb\uee9e<span class="blank _3"></span>\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank _6"> </span><span class="fs7 ls16 v5">\uee9e</span><span class="fs8 v6">\uf0db</span></span></div><div class="t m0 x17 h1c y40 ff8 fs7 fc0 sc0 lsf ws15">\uee9e\ue603\uf13f\ue603\uf0da<span class="ff7 fs2 ws12 v7"> </span></div><div class="t m0 x1 h6 y41 ff3 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h1d y42 ff5 fs3 fc0 sc0 lsf ws12">Sea <span class="ff8 ws16">\ued42<span class="blank _3"></span>\udb80\udddb\ued54\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank _d"> </span><span class="fs0 ls17 v8">\uf1eb</span><span class="fs9 v9">\uf22e</span></span></div><div class="t m0 x18 h1e y43 ff8 fs0 fc0 sc0 lsf ws17">\uf1eb\ue603\uf13f\ue603<span class="blank _3"> </span>\uf135<span class="ff5 fs3 ws12 va"> </span></div><div class="t m0 x1 h12 y44 ff5 fs3 fc0 sc0 lsf ws12">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 wsc">\ueb39<span class="blank"> </span>\uf346<span class="blank"> </span><span class="ls18 v3">\udb80\udddd</span><span class="ls6">\ue973</span><span class="ws6 v3">\udb80\uddde</span></span>. </div><div class="t m0 x1 hf y45 ff5 fs3 fc0 sc0 lsf ws12">Buscamos la deriv<span class="blank _0"></span>ada y su dominio: </div><div class="t m0 x19 h1f y46 ff8 fs3 fc0 sc0 ls19">\ued42<span class="fs0 ls1a v4">\udb80\udd92</span><span class="lsf ws6 v3">\udb80\udddb</span><span class="ls1b">\ued54<span class="ls2 v3">\udb80\udddc</span><span class="ls1c">\uf34c<span class="lsf ws18 vb">\ue974\ued54<span class="blank"> </span>\ue603\ue7e4<span class="blank _e"> </span></span><span class="lsf ws6 vc">\udb80\udddb</span><span class="lsf wse vb">\ued54<span class="blank _9"> </span>\uf346<span class="blank"> </span>\ue973</span><span class="lse vc">\udb80\udddc</span><span class="lsf ws19 vb">\uf346<span class="blank _a"> </span>\ued54<span class="blank"> </span><span class="fs0 v4">\uf136</span></span></span></span></div><div class="t m0 x1a h10 y47 ff8 fs3 fc0 sc0 lsf ws6">\udb80\udddb<span class="wse vd">\ued54<span class="blank _9"> </span>\uf346<span class="blank"> </span>\ue973</span>\udb80\udddc<span class="fs0 ls1d ve">\uf136</span><span class="ff5 ws12 v5"> </span></div><div class="t m0 x10 h20 y48 ff8 fs3 fc0 sc0 ls19">\ued42<span class="fs0 ls1a v4">\udb80\udd92</span><span class="lsf ws6 v3">\udb80\udddb</span><span class="ls1b">\ued54<span class="ls1e v3">\udb80\udddc</span><span class="ls5">\uf34c<span class="lsf ws1a vb">\ue974\ued54<span class="blank"> </span></span><span class="fs0 ls1f vf">\uf136</span><span class="lsf ws19 vb">\uf346<span class="blank _a"> </span>\ue974\ued54<span class="blank _9"> </span>\uf346<span class="blank _a"> </span>\ued54<span class="blank"> </span><span class="fs0 v4">\uf136</span></span></span></span></div><div class="t m0 x1a h10 y49 ff8 fs3 fc0 sc0 lsf ws6">\udb80\udddb<span class="wse vd">\ued54<span class="blank _9"> </span>\uf346<span class="blank"> </span>\ue973</span>\udb80\udddc<span class="fs0 ls20 ve">\uf136</span><span class="ff5 ws12 v5"> </span></div><div class="t m0 x1b h20 y4a ff8 fs3 fc0 sc0 ls19">\ued42<span class="fs0 ls1a v4">\udb80\udd92</span><span class="lsf ws6 v3">\udb80\udddb</span><span class="ls1b">\ued54<span class="ls1e v3">\udb80\udddc</span><span class="ls21">\uf34c<span class="ls22 vb">\ued54</span><span class="fs0 ls1f vf">\uf136</span><span class="lsf wse vb">\uf346<span class="blank"> </span>\ue974\ued54</span></span></span></div><div class="t m0 x1a h10 y4b ff8 fs3 fc0 sc0 lsf ws6">\udb80\udddb<span class="wse vd">\ued54<span class="blank _9"> </span>\uf346<span class="blank"> </span>\ue973</span>\udb80\udddc<span class="fs0 ls23 ve">\uf136</span><span class="ff5 ws12 v5"> </span></div><div class="t m0 x1c h11 y4c ff8 fs3 fc0 sc0 lsf ws6">\ued26\ued4b\ued49<span class="v3">\udb80\udddb</span><span class="ls19">\ued42<span class="fs0 ls24 v4">\udb80\udd92</span><span class="ls25 v3">\udb80\udddc</span></span><span class="wse">\uf34c<span class="blank _8"> </span>\ueb39<span class="blank"> </span>\uf346<span class="blank"> </span>\udb80\udddd\ue973\udb80\uddde<span class="ff5 ws12"> </span></span></div><div class="t m0 x1 hf y4d ff5 fs3 fc0 sc0 lsf ws12">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 x1d h11 y4e ff8 fs3 fc0 sc0 ls19">\ued42<span class="fs0 ls24 v4">\udb80\udd92</span><span class="lsf ws6 v3">\udb80\udddb</span><span class="ls26">\ued54<span class="ls2 v3">\udb80\udddc</span><span class="lsf ws4">\uf34c<span class="blank"> </span>\ue972<span class="ff5 ws12"> </span></span></span></div><div class="t m0 x1e h10 y4f ff8 fs3 fc0 sc0 ls22">\ued54<span class="fs0 ls1f v4">\uf136</span><span class="lsf wsc">\uf346<span class="blank"> </span>\ue974\ued54</span></div><div class="t m0 x1f h21 y50 ff8 fs3 fc0 sc0 lsf ws6">\udb80\udddb<span class="wse vd">\ued54<span class="blank _9"> </span>\uf346<span class="blank"> </span>\ue973</span>\udb80\udddc<span class="fs0 ls27 ve">\uf136</span><span class="ws4 v5">\uf34c<span class="blank"> </span>\ue972<span class="ff5 ws12"> </span></span></div><div class="t m0 x1e h10 y51 ff8 fs3 fc0 sc0 ls22">\ued54<span class="fs0 ls1f v4">\uf136</span><span class="lsf wsc">\uf346<span class="blank"> </span>\ue974\ued54<span class="blank _7"> </span>\uf34c<span class="blank _8"> </span>\ue972<span class="ff5 ws12"> </span></span></div><div class="t m0 x1f h11 y52 ff8 fs3 fc0 sc0 ls1b">\ued54<span class="lsf ws6 v3">\udb80\udddb</span><span class="lsf ws1b">\ued54<span class="blank _9"> </span>\uf346<span class="blank"> </span>\ue974<span class="ls2 v3">\udb80\udddc</span><span class="ws4">\uf34c<span class="blank"> </span>\ue972<span class="ff5 ws12"> </span></span></span></div><div class="t m0 x1 hf y53 ff5 fs3 fc0 sc0 lsf ws12">Por lo tanto, los<span class="blank _0"></span> puntos crí<span class="blank _0"></span>ticos son: <span class="blank _f"> </span><span class="ff8 ws4 v10">\ued54<span class="blank _7"> </span>\uf34c<span class="blank"> </span>\ue972\ue603\ued55\ue603\ued54<span class="blank _7"> </span>\uf34c<span class="blank"> </span>\ue974</span><span class="v10"> </span></div><div class="t m0 x1 h10 y54 ff5 fs3 fc0 sc0 lsf ws12">La <span class="blank _4"> </span>recta <span class="blank _3"> </span><span class="ff8 ws4">\ued54<span class="blank _7"> </span>\uf34c<span class="blank"> </span>\ue973</span> <span class="blank _4"> </span>es <span class="blank _4"> </span>una <span class="blank _4"> </span>asíntota <span class="blank _4"> </span>vertical <span class="blank _3"> </span>de <span class="blank _4"> </span>la <span class="blank _4"> </span>función <span class="blank _4"> </span>y <span class="blank _4"> </span>de <span class="blank _4"> </span>su <span class="blank _4"> </span>derivada. <span class="blank _3"> </span>Lo <span class="blank _4"> </span>tenemos <span class="blank _4"> </span>en <span class="blank _4"> </span>cuenta <span class="blank _3"> </span>al <span class="blank _4"> </span>considerar <span class="blank _4"> </span>los </div><div class="t m0 x1 hf y55 ff5 fs3 fc0 sc0 lsf ws12">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 hf y56 ff5 fs3 fc0 sc0 lsf ws12">Recordemos <span class="blank _0"></span>que: </div><div class="t m0 x1 h11 y57 ff9 fs3 fc0 sc0 lsf ws1c">\uf0b7<span class="ff5 ws12"> <span class="blank _5"> </span>si <span class="blank _4"> </span><span class="ff8 ws6">\ued42\ue7ef<span class="v3">\udb80\udddb</span><span class="ls1b">\ued54<span class="ls2 v3">\udb80\udddc</span></span><span class="ws1d">\uf350<span class="blank"> </span>\ue603\ue972</span></span> <span class="blank _5"> </span>para <span class="blank _5"> </span>todo <span class="blank _5"> </span>x <span class="blank _4"> </span>que <span class="blank _5"> </span>pertenece <span class="blank _4"> </span>al <span class="blank _5"> </span>intervalo <span class="blank _4"> </span><span class="ff8 ws6 v3">\udb80\udddb</span><span class="ff8 ws1e">\ued3d<span class="blank _3"> </span>\ue7e2<span class="blank"> </span>\ue603\ued3e<span class="blank _3"> </span><span class="ws6 v3">\udb80\udddc</span></span>, <span class="blank _5"> </span>entonces <span class="blank _4"> </span>la <span class="blank _4"> </span>f<span class="blank _3"> </span>unción <span class="blank _4"> </span><span class="ff8 ls28">\ued42</span> <span class="blank _5"> </span>es <span class="blank _5"> </span>creciente <span class="blank _4"> </span>en <span class="blank _5"> </span>el <span class="blank _5"> </span>interval<span class="blank _0"></span>o </span></div><div class="t m0 x1 h10 y58 ff8 fs3 fc0 sc0 lsf ws6">\udb80\udddb<span class="ws1e vd">\ued3d\ue7e2<span class="blank"> </span>\ue603\ued3e<span class="blank _3"> </span></span>\udb80\udddc<span class="ff5 ws12 vd"> </span></div><div class="t m0 x1 h10 y59 ff9 fs3 fc0 sc0 lsf ws1c">\uf0b7<span class="ff5 ws12"> si <span class="blank _3"> </span><span class="ff8 ws18">\ued42\ue7ef\udb80\udddb\ued54<span class="blank"> </span>\udb80\udddc<span class="blank _10"> </span>\ue603<span class="blank _10"> </span>\uf34f<span class="blank _8"> </span>\ue603\ue972</span> <span class="blank _3"> </span>para todo x q<span class="blank _3"> </span>ue pertenece al intervalo <span class="ff8 ws1f">\udb80\udddb\ued3d<span class="blank"> </span>\ue7e2<span class="blank _e"> </span>\ue603\ued3e<span class="blank"> </span>\udb80\udddc\ue7e1</span> entonces la función<span class="ff8 ws6">\ue603\ued42<span class="blank _3"></span></span> es <span class="blank _3"> </span>decreciente en el intervalo </span></div><div class="t m0 x1 h10 y5a ff8 fs3 fc0 sc0 lsf ws1e">\udb80\udddb\ued3d\ue7e2<span class="blank"> </span>\ue603\ued3e<span class="blank _3"> </span>\udb80\udddc\ue7e4<span class="ff5 ws12"> </span></div><div class="t m0 x1 h11 y5b ff5 fs3 fc0 sc0 lsf ws12">Analizamos entonce<span class="blank _0"></span>s, los intervalos: <span class="ff8 ws6 v3">\udb80\udddb</span><span class="ff8 ws20">\uf346\ue9bb\ue7e2<span class="blank"> </span>\ue972<span class="ws6 v3">\udb80\udddc</span><span class="ls29">\ue7e1</span><span class="ws6 v3">\udb80\udddb</span><span class="ls6 ws21">\ue972\ue7e2<span class="blank"> </span>\ue973</span><span class="ws6 v3">\udb80\udddc</span><span class="ls29">\ue7e1</span><span class="ws6 v3">\udb80\udddb<span class="blank _0"></span><span class="ws20 vd">\ue973\ue7e2<span class="blank"> </span>\ue974<span class="ws6 v3">\udb80\udddc</span><span class="ls29">\ue7e1<span class="lsf ws6 v3">\udb80\udddb</span><span class="lsf ws22">\ue974\ue7e2<span class="blank"> </span>\ue603<span class="blank"> </span>\uf345\ue9bb<span class="ws6 v3">\udb80\udddc<span class="vd">\ue7e4</span></span><span class="ff5 ws12"> </span></span></span></span></span></span></div><div class="t m0 x1 hf y5c ff5 fs3 fc0 sc0 lsf ws12">Realizamos una <span class="blank _0"></span>tabla: </div></div><div class="c x20 y5d wc h22"><div class="t m0 x21 hf y5e ff5 fs3 fc0 sc0 lsf ws12"> Intervalo </div></div><div class="c x22 y5d wd h22"><div class="t m0 x7 h10 y5f ff8 fs3 fc0 sc0 lsf ws6">\udb80\udddb<span class="ws20 vd">\uf346\ue9bb\ue7e2<span class="blank"> </span>\ue972</span>\udb80\udddc<span class="ff5 ws12 vd"> </span></div></div><div class="c x23 y5d we h22"><div class="t m0 x7 h10 y5f ff8 fs3 fc0 sc0 lsf ws6">\udb80\udddb<span class="ws20 vd">\ue972\ue7e2<span class="blank"> </span>\ue973</span>\udb80\udddc<span class="ff5 ws12 vd"> </span></div></div><div class="c x24 y5d wf h22"><div class="t m0 x5 h10 y5f ff8 fs3 fc0 sc0 lsf ws6">\udb80\udddb<span class="ls6 ws21 vd">\ue973\ue7e2<span class="blank"> </span>\ue974</span>\udb80\udddc<span class="ff5 ws12 vd"> </span></div></div><div class="c x25 y5d w10 h22"><div class="t m0 xe h10 y5f ff8 fs3 fc0 sc0 lsf ws6">\udb80\udddb<span class="ws20 vd">\ue974\ue7e2<span class="blank"> </span>\ue9bb</span>\udb80\udddc<span class="ff5 ws12 vd"> </span></div></div><div class="c x20 y60 wc h23"><div class="t m0 x7 hf y61 ff5 fs3 fc0 sc0 lsf ws12">Para </div></div><div class="c x22 y60 wd h23"><div class="t m0 x7 h10 y62 ff8 fs3 fc0 sc0 lsf ws4">\ued54<span class="blank _7"> </span>\uf34c<span class="blank"> </span>\uf346\ue973<span class="ff5 ws12"> </span></div></div><div class="c x23 y60 we h23"><div class="t m0 x7 h20 y63 ff8 fs3 fc0 sc0 lsf ws4">\ued54<span class="blank _7"> </span>\uf34c<span class="blank"> </span><span class="vb">\ue973</span></div><div class="t m0 x26 h10 y64 ff8 fs3 fc0 sc0 ls6">\ue974<span class="ff5 lsf ws12 v11"> </span></div></div><div class="c x24 y60 wf h23"><div class="t m0 x5 h20 y63 ff8 fs3 fc0 sc0 lsf ws7">\ued54<span class="blank _7"> </span>\uf34c<span class="blank"> </span><span class="vb">\ue975</span></div><div class="t m0 x27 h10 y64 ff8 fs3 fc0 sc0 ls2a">\ue974<span class="ff5 lsf ws12 v11"> </span></div></div><div class="c x25 y60 w10 h23"><div class="t m0 x7 h10 y62 ff8 fs3 fc0 sc0 lsf ws4">\ued54<span class="blank _7"> </span>\uf34c<span class="blank"> </span>\ue975<span class="ff5 ws12"> </span></div></div><div class="c x20 y65 wc h24"><div class="t m0 x28 hf y66 ff6 fs3 fc0 sc0 lsf ws12">Signo de f\u2019<span class="ff5"> </span></div></div><div class="c x22 y65 wd h24"><div class="t m0 x29 h20 y67 ff8 fs3 fc0 sc0 ls19">\ued42<span class="fs0 ls1a v4">\udb80\udd92</span><span class="lsf ws6 v3">\udb80\udddb</span><span class="ls1b">\ued54<span class="ls1e v3">\udb80\udddc</span><span class="ls5">\uf34c<span class="lsf vb">\ue975</span></span></span></div><div class="t m0 x2a h25 y68 ff8 fs3 fc0 sc0 ls2b">\ue976<span class="lsf ws23 v11">\uf350<span class="blank"> </span>\ue972<span class="ff5 ws12"> </span></span></div></div><div class="c x23 y65 we h24"><div class="t m0 x28 h11 y69 ff8 fs3 fc0 sc0 ls19">\ued42<span class="fs0 ls24 v4">\udb80\udd92</span><span class="lsf ws6 v3">\udb80\udddb</span><span class="ls2c">\ued54<span class="ls2d v3">\udb80\udddc</span><span class="lsf ws4">\uf34c<span class="blank"> </span>\uf346\ue975</span></span></div><div class="t m0 x28 h10 y62 ff8 fs3 fc0 sc0 lsf ws1d">\uf34f<span class="blank"> </span>\ue972<span class="ff5 ws12"> </span></div></div><div class="c x24 y65 wf h24"><div class="t m0 x21 h11 y69 ff8 fs3 fc0 sc0 ls19">\ued42<span class="fs0 ls24 v4">\udb80\udd92</span><span class="lsf ws6 v3">\udb80\udddb</span><span class="ls1b">\ued54<span class="ls1e v3">\udb80\udddc</span><span class="lsf ws4">\uf34c<span class="blank"> </span>\uf346\ue975</span></span></div><div class="t m0 x21 h10 y62 ff8 fs3 fc0 sc0 lsf ws23">\uf34f<span class="blank"> </span>\ue972<span class="ff5 ws12"> </span></div></div><div class="c x25 y65 w10 h24"><div class="t m0 x21 h20 y67 ff8 fs3 fc0 sc0 ls19">\ued42<span class="fs0 ls1a v4">\udb80\udd92</span><span class="lsf ws6 v3">\udb80\udddb</span><span class="ls1b">\ued54<span class="ls1e v3">\udb80\udddc</span><span class="ls5">\uf34c<span class="lsf vb">\ue975</span></span></span></div><div class="t m0 x2b h10 y68 ff8 fs3 fc0 sc0 lsf">\ue976</div><div class="t m0 x21 h10 ye ff8 fs3 fc0 sc0 lsf ws1d">\uf350<span class="blank"> </span>\ue972<span class="ff5 ws12"> </span></div></div><div class="c x20 y6a wc h26"><div class="t m0 x29 hf y6b ff5 fs3 fc0 sc0 lsf ws12">Conclusión </div></div><div class="c x22 y6a wd h26"><div class="t m0 xc h10 y6c ff8 fs3 fc0 sc0 lsf ws6">\ued42<span class="blank _3"></span>\ue603<span class="ff5 ws12">crece en </span></div><div class="t m0 x7 h10 y6d ff8 fs3 fc0 sc0 lsf ws6">\udb80\udddb<span class="ws20 vd">\uf346\ue9bb\ue7e2<span class="blank"> </span>\ue972</span>\udb80\udddc<span class="ff5 ws12 vd"> </span></div></div><div class="c x23 y6a we h26"><div class="t m0 x21 h10 y6c ff8 fs3 fc0 sc0 lsf ws6">\ued42<span class="blank _3"></span>\ue603<span class="ff5 ws12">decrece </span></div><div class="t m0 x2c hf y6e ff5 fs3 fc0 sc0 ls35 ws12">en <span class="ffa lsf"> </span></div><div class="t m0 x7 h10 y6f ff8 fs3 fc0 sc0 lsf ws6">\udb80\udddb<span class="ws20 vd">\ue972\ue7e2<span class="blank"> </span>\ue973</span>\udb80\udddc<span class="ff5 ws12 vd"> </span></div></div><div class="c x24 y6a wf h26"><div class="t m0 x15 h10 y6c ff8 fs3 fc0 sc0 lsf ws6">\ued42<span class="blank _3"></span>\ue603<span class="ff5 ws12">decrece en <span class="blank _0"></span><span class="ffa"> </span></span></div><div class="t m0 x5 h10 y6d ff8 fs3 fc0 sc0 lsf ws6">\udb80\udddb<span class="ls6 ws21 vd">\ue973\ue7e2<span class="blank"> </span>\ue974</span>\udb80\udddc<span class="ff5 ws12 vd"> </span></div></div><div class="c x25 y6a w10 h26"><div class="t m0 x2d h10 y6c ff8 fs3 fc0 sc0 lsf ws6">\ued42<span class="blank _3"></span>\ue603<span class="ff5 ws12">crece en <span class="ffa"> </span></span></div><div class="t m0 xe h10 y6d ff8 fs3 fc0 sc0 lsf ws6">\udb80\udddb<span class="ws20 vd">\ue974\ue7e2<span class="blank"> </span>\ue9bb</span>\udb80\udddc<span class="ff5 ws12 vd"> </span></div></div><div class="c x0 y1 w2 h0"><div class="t m0 x1 hf y70 ff5 fs3 fc0 sc0 lsf ws12">Concluimos: </div><div class="t m0 x1 h11 y71 ff8 fs3 fc0 sc0 ls19">\ued42<span class="fs0 ls24 v4">\udb80\udd92</span><span class="lsf ws6 v3">\udb80\udddb</span><span class="ls2c">\ued54<span class="ls2e v3">\udb80\udddc</span><span class="lsf ws1d">\uf350<span class="blank"> </span>\ue972\ue603</span><span class="ls36 ws24">\ued41\ued4a<span class="ls2f">\ue603</span></span><span class="lsf ws6 v3">\udb80\udddb</span><span class="lsf ws20">\uf346\ue9bb\ue7e2<span class="blank"> </span>\ue972<span class="ls30 v3">\udb80\udddc</span></span><span class="ls31 ws25">\ue603\uebeb<span class="blank _0"></span>\ue603<span class="lsf ws6 v3">\udb80\udddb</span><span class="lsf ws20">\ue974\ue7e2<span class="blank"> </span>\ue9bb<span class="ws6 v3">\udb80\udddc</span><span class="ff5 ws12"> por lo que f es c<span class="blank _0"></span>reciente en <span class="ff8 ws6 v3">\udb80\udddb</span><span class="ff8 ws20">\uf346\ue9bb\ue7e2<span class="blank"> </span>\ue972<span class="ls32 v3">\udb80\udddc</span><span class="ls33 ws26">\ue603\uebeb\ue603</span><span class="ws6 v3">\udb80\udddb</span>\ue974\ue7e2<span class="blank"> </span>\ue9bb<span class="ws6 v3">\udb80\udddc<span class="vd">\ue603\ue7e4</span></span></span> </span></span></span></span></div><div class="t m0 x1 h11 y72 ff8 fs3 fc0 sc0 ls19">\ued42<span class="fs0 ls24 v4">\udb80\udd92</span><span class="lsf ws6 v3">\udb80\udddb</span><span class="ls2c">\ued54<span class="ls2e v3">\udb80\udddc</span><span class="lsf ws1d">\uf34f<span class="blank"> </span>\ue972\ue603</span><span class="ls36 ws24">\ued41\ued4a<span class="ls2f">\ue603</span></span><span class="lsf ws6 v3">\udb80\udddb</span><span class="ls6 ws21">\ue972\ue7e2<span class="blank"> </span>\ue973<span class="ls32 v3">\udb80\udddc</span></span><span class="ls33 ws26">\ue603\uebeb\ue603</span><span class="lsf ws6 v3">\udb80\udddb</span><span class="ls6 ws21">\ue973\ue7e2<span class="blank"> </span>\ue974</span><span class="lsf ws6 v3">\udb80\udddc<span class="vd">\ue603\ue603</span></span><span class="ff5 lsf ws12">por lo que f es<span class="blank _0"></span> decreciente en <span class="ff8 ws6 v3">\udb80\udddb</span><span class="ff8 ls6 ws21">\ue972\ue7e2<span class="blank"> </span>\ue973<span class="ls32 v3">\udb80\udddc</span><span class="ls33 ws26">\ue603\uebeb\ue603<span class="lsf ws6 v3">\udb80\udddb</span></span><span class="ws27">\ue973\ue7e2<span class="blank"> </span>\ue974<span class="lsf ws6 v3">\udb80\udddc<span class="vd">\ue603\ue7e4\ue603</span></span></span></span><span class="ff4"> <span class="blank _11"> </span> </span></span></span></div></div><div class="c x0 y3a wa h18"><div class="t m0 x15 h19 y3b ff4 fs3 fc2 sc0 lsf ws12"><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 y73 w11 h27" alt="" src="https://files.passeidireto.com/983b1510-9b97-4a18-bbd3-090700f03d0a/bg3.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 lsf ws12">MATEMÁTICA (6<span class="ls10 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls13"> <span class="ls14"> </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 lsf ws12"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 lsf ws12">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 _12"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span>TEMA 2 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 lsf ws12">Hoja 3 de 4 </div><div class="t m0 x3 h2 y3d ff2 fs0 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h19 y74 ff4 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h4 y75 ff7 fs2 fc0 sc0 lsf ws12">3. Calcular el área de la región sombreada, sabiendo que: </div><div class="t m0 x1 h28 y76 ff8 fs2 fc0 sc0 ls37">\uee8d<span class="ls38 v3">\udb80\udddb</span>\uee9e<span class="ls39 v3">\udb80\udddc</span><span class="ls3a">\uf34c<span class="fs7 lsf v5">\uf0da</span></span></div><div class="t m0 x2e h29 y77 ff8 fs7 fc0 sc0 ls3b">\uf0db<span class="fs2 ls37 v7">\uee9e</span><span class="ls3c v6">\uf0db</span><span class="fs2 ls3d v7">\uf346</span><span class="lsf v12">\uf0da</span></div><div class="t m0 x2f h2a y77 ff8 fs7 fc0 sc0 ls3b">\uf0db<span class="fs2 ls3e ws28 v7">\uee9e\uf346\uf0dc<span class="blank _13"></span><span class="ffb ls37 ws12"> <span class="blank _0"></span> <span class="ffc fs3 fc4 lsf"> </span></span></span></div><div class="t m0 x1 h2b y78 ff8 fs2 fc0 sc0 lsf ws29">\uee8c\udb80\udddb\uee9e\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="v13">\uf0da</span></div><div class="t m0 x30 h2c y79 ff8 fs2 fc0 sc0 ls3f">\uf0db<span class="lsf ws2a v14">\uee9e<span class="blank"> </span>\uf346<span class="blank"> </span><span class="v13">\uf0dc</span></span></div><div class="t m0 x31 h2d y79 ff8 fs2 fc0 sc0 lsf ws2b">\uf0db<span class="ffb ws12 v14"> </span></div><div class="t m0 x1 h2e y7a ffb fs2 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h4 y7b ff7 fs2 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h19 y7c ff4 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h2d y7d ff5 fs2 fc0 sc0 lsf ws12">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 ws2b">\ued43<span class="blank _3"></span>\udb80\udddb\ued54<span class="blank _3"> </span>\udb80\udddc</span><span class="ls40"> <span class="ls65">y </span></span><span class="ff8 ws2c">\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 y7e ff5 fs2 fc0 sc0 lsf ws12">x=3. En el gráfico se puede observar q<span class="blank _0"></span>ue <span class="blank _3"> </span><span class="ff8 ls41">\ued42<span class="ls38 v3">\udb80\udddb</span><span class="ls42">\ued54<span class="lsf ws2b v3">\udb80\udddc</span></span></span><span class="ls40"> </span><span class="ff6">representa el \u201ctecho\u201d de la misma, mientras que <span class="ff8 ls43">\ued43<span class="ls38 v3">\udb80\udddb</span><span class="ls42">\ued54<span class="lsf ws2b v3">\udb80\udddc</span></span></span></span> el </div><div class="t m0 x1 he y4c ff6 fs2 fc0 sc0 lsf ws12">\u201cpiso\u201d. Por lo tanto, sabemos que:<span class="ff5"> </span></div><div class="t m0 x19 h2f y7f ff8 fs2 fc0 sc0 lsf ws2c">\ued23<span class="blank _7"> </span>\uf34c<span class="blank _7"> </span>\uf3b1<span class="blank _14"> </span>\ued42<span class="blank"> </span><span class="ls38 v3">\udb80\udddb</span><span class="ls44">\ued54<span class="ls45 v3">\udb80\udddc</span></span><span class="ws2d">\uf346<span class="blank"> </span>\ued43<span class="ls38 v3">\udb80\udddb</span><span class="ls42">\ued54<span class="ls38 v3">\udb80\udddc</span></span>\ued40\ued54</span></div><div class="t m0 x32 h30 y80 ff8 fs7 fc0 sc0 lsf">\uf137</div><div class="t m0 x1f h31 y81 ff8 fs7 fc0 sc0 lsf ws2e">\uf13f\uf135<span class="blank"> </span><span class="ff5 fs2 ws12 v15"> </span></div><div class="t m0 x1 h2f y82 ff8 fs2 fc0 sc0 lsf ws2f">\ued23<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="ls46 vd">\uebec</span><span class="ls41">\ued42<span class="ls38 v3">\udb80\udddb</span><span class="ls42">\ued54<span class="ls47 v3">\udb80\udddc</span></span></span><span class="ws30">\uf346<span class="blank"> </span>\ued43<span class="blank _3"></span><span class="ls38 v3">\udb80\udddb</span><span class="ls42">\ued54<span class="ls38 v3">\udb80\udddc</span></span>\ued40\ued54</span></div><div class="t m0 x33 h30 y83 ff8 fs7 fc0 sc0 lsf">\uf137</div><div class="t m0 x34 h32 y84 ff8 fs7 fc0 sc0 lsf ws31">\uf13f\uf135<span class="blank"> </span><span class="fs2 ws32 v16">\uf34c<span class="blank"> </span>\ue603<span class="blank"> </span><span class="ls48 vd">\uebec</span></span><span class="v17">\uf135</span></div><div class="t m0 x35 h29 y85 ff8 fs7 fc0 sc0 ls49">\uf136<span class="fs2 lsf ws2d v7">\ued54<span class="blank _8"> </span>\uf346<span class="blank"> </span></span><span class="lsf v12">\uf137</span></div><div class="t m0 x36 h2a y85 ff8 fs7 fc0 sc0 ls4a">\uf136<span class="fs2 lsf v7">\uf346</span></div><div class="t m0 x4 h30 y83 ff8 fs7 fc0 sc0 lsf">\uf137</div><div class="t m0 x37 h32 y84 ff8 fs7 fc0 sc0 lsf ws33">\uf13f\uf135<span class="blank"> </span><span class="fs2 ws2b v16">\udb80\udde1</span><span class="v17">\uf135</span></div><div class="t m0 x38 h29 y85 ff8 fs7 fc0 sc0 ls4b">\uf136<span class="fs2 ls4c v7">\ued54</span><span class="ls4d v6">\uf136</span><span class="fs2 ls3e v7">\uf346</span><span class="lsf v12">\uf135</span></div><div class="t m0 x23 h29 y85 ff8 fs7 fc0 sc0 ls4b">\uf136<span class="fs2 lsf ws34 v7">\ued54<span class="blank _8"> </span>\uf346<span class="blank _9"> </span>\ue975\udb80\udde2<span class="blank"> </span>\ued40\ued54<span class="blank _7"> </span>\uf34c<span class="blank _7"> </span><span class="ls4e vd">\uebec</span><span class="ls4f">\uf346</span></span><span class="lsf v12">\uf135</span></div><div class="t m0 x39 h29 y85 ff8 fs7 fc0 sc0 ls4b">\uf136<span class="fs2 ls4c v7">\ued54</span><span class="ls4d v6">\uf136</span><span class="fs2 lsf ws2d v7">\uf345<span class="blank"> </span>\ued54<span class="blank _8"> </span>\uf345<span class="blank"> </span></span><span class="lsf v12">\uf137</span></div><div class="t m0 x3a h2a y85 ff8 fs7 fc0 sc0 ls49">\uf136<span class="fs2 lsf v7">\ued40\ued54</span></div><div class="t m0 x3b h30 y83 ff8 fs7 fc0 sc0 lsf">\uf137</div><div class="t m0 x3c h33 y84 ff8 fs7 fc0 sc0 lsf ws35">\uf13f\uf135<span class="blank"> </span><span class="ff5 fs2 ws12 v16"> </span></div><div class="t m0 x1 he y86 ff5 fs2 fc0 sc0 lsf ws12">Integrando y aplicando la regla de Barrow: </div><div class="t m0 x1 h2b y87 ff8 fs2 fc0 sc0 lsf ws36">\ued23<span class="blank _7"> </span>\uf34c<span class="blank _7"> </span>\uf3b1<span class="blank _6"> </span>\uf346<span class="blank"> </span><span class="v13">\ue973</span></div><div class="t m0 x3d h2c y88 ff8 fs2 fc0 sc0 ls50">\ue974<span class="ls51 v14">\ued54</span><span class="fs7 ls4d vf">\uf136</span><span class="ls3e ws28 v14">\uf345\ued54<span class="blank _3"></span>\uf345</span><span class="lsf v18">\ue975</span></div><div class="t m0 x3e h34 y88 ff8 fs2 fc0 sc0 ls50">\ue974<span class="lsf v14">\ued40\ued54</span></div><div class="t m0 x3f h30 y89 ff8 fs7 fc0 sc0 lsf">\uf137</div><div class="t m0 x34 h35 y8a ff8 fs7 fc0 sc0 lsf ws37">\uf13f\uf135<span class="blank"> </span><span class="fs2 ls37 v15">\uf34c<span class="ff5 lsf ws12"> </span></span></div><div class="t m0 x1 h2b y8b ff8 fs2 fc0 sc0 lsf ws36">\ued23<span class="blank _7"> </span>\uf34c<span class="blank _7"> </span>\uf3b1<span class="blank _6"> </span>\uf346<span class="blank"> </span><span class="v13">\ue973</span></div><div class="t m0 x3d h34 y8c ff8 fs2 fc0 sc0 ls50">\ue974<span class="ls51 v14">\ued54</span><span class="fs7 lsf vf">\uf136</span></div><div class="t m0 x3f h30 y8d ff8 fs7 fc0 sc0 lsf">\uf137</div><div class="t m0 x34 h35 y8e ff8 fs7 fc0 sc0 lsf ws38">\uf13f\uf135<span class="blank"> </span><span class="fs2 ws39 v15">\ued40\ued54<span class="blank _8"> </span>\uf345<span class="blank"> </span>\ue603<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 x40 h30 y8d ff8 fs7 fc0 sc0 lsf">\uf137</div><div class="t m0 x41 h36 y8e ff8 fs7 fc0 sc0 lsf ws3a">\uf13f\uf135<span class="blank"> </span><span class="fs2 ws2d v15">\uf345<span class="blank"> </span>\uf3b1<span class="blank _6"> </span><span class="v13">\ue975</span></span></div><div class="t m0 x42 h34 y8c ff8 fs2 fc0 sc0 ls50">\ue974<span class="lsf v14">\ued40\ued54</span></div><div class="t m0 x43 h30 y8d ff8 fs7 fc0 sc0 lsf">\uf137</div><div class="t m0 x44 h35 y8e ff8 fs7 fc0 sc0 lsf ws3b">\uf13f\uf135<span class="blank"> </span><span class="fs2 ws3c v15">\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 ws3d">\uf0f2\uf028<span class="ff8 ws3e">\ue688\udb80\udddb\ue603\ue69a\ue603\udb80\udddc<span class="blank"> </span>\ue603<span class="blank"> </span>\uf347<span class="blank _9"> </span>\ue603\ue689\udb80\udddb\ue603\ue69a\udb80\udddc</span>\uf029<span class="ff8 ls66 ws3f">\ue686\ue69a<span class="lsf ws2b">\ue603</span></span><span class="ls52">\uf03d</span><span class="ff8 ws2b">\ue603</span>\uf0f2<span class="ff8 ws2b">\ue688<span class="blank _3"></span>\udb80\udddb\ue603\ue69a\ue603\udb80\udddc\ue603<span class="ls66 ws3f">\ue686\ue69a</span><span class="ws12">\ue603<span class="blank"> </span>\uf347<span class="blank"> </span>\ue603</span></span>\uf0f2<span class="ff8 ws2b">\ue689\udb80\udddb\ue603\ue69a\udb80\udddc\ue603<span class="ls66 ws3f">\ue686\ue69a<span class="ls38">\udb80\udddc</span></span><span class="ff5 ws12"> </span></span></span></span></div><div class="t m0 x1 h2b y8f ff8 fs2 fc0 sc0 lsf ws40">\ued23<span class="blank _7"> </span>\uf34c<span class="blank _7"> </span>\uf346<span class="blank"> </span><span class="v13">\ue973</span></div><div class="t m0 x45 h34 y90 ff8 fs2 fc0 sc0 ls50">\ue974<span class="lsf ws41 v14">\ue7e4<span class="blank _e"> </span>\uf3b1<span class="blank _6"> </span>\ued54<span class="blank"> </span></span><span class="fs7 ls53 vf">\uf136</span><span class="lsf ws2d v14">\ued40\ued54<span class="blank _8"> </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 x40 h30 y91 ff8 fs7 fc0 sc0 lsf">\uf137</div><div class="t m0 x41 h30 y92 ff8 fs7 fc0 sc0 lsf ws15">\uf13f\uf135</div><div class="t m0 x46 h30 y91 ff8 fs7 fc0 sc0 lsf">\uf137</div><div class="t m0 x3d h36 y92 ff8 fs7 fc0 sc0 lsf ws42">\uf13f\uf135<span class="blank"> </span><span class="fs2 ws2d v15">\uf345<span class="blank"> </span>\uf3b1<span class="blank _6"> </span><span class="v13">\ue975</span></span></div><div class="t m0 x42 h34 y90 ff8 fs2 fc0 sc0 ls50">\ue974<span class="lsf ws43 v14">\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 x43 h30 y91 ff8 fs7 fc0 sc0 lsf">\uf137</div><div class="t m0 x44 h35 y92 ff8 fs7 fc0 sc0 lsf ws44">\uf13f\uf135<span class="blank"> </span><span class="fs2 ws2b v15">\ue603\ue692\ue694\ue691\ue692\ue7e4\ue603\ue603\ue603\ue603</span></div><div class="t m1 x47 h37 y8f ff9 fsa fc0 sc0 lsf">\uf0f2</div><div class="t m0 x48 h2d y8f ff8 fs2 fc0 sc0 lsf ws45">\ued3d<span class="blank"> </span>\ue603</div><div class="t m1 x49 h37 y8f ff9 fsa fc0 sc0 lsf">\uf0d7</div><div class="t m0 x4a h2f y8f ff8 fs2 fc0 sc0 ls41">\ued42<span class="ls38 v3">\udb80\udddb</span><span class="lsf ws2b">\ue603\ued54\ue603<span class="blank _3"></span><span class="ls38 v3">\udb80\udddc</span>\ued40\ued54\ue603</span></div><div class="t m1 x4b h37 y8f ff9 fsa fc0 sc0 lsf">\uf03d</div><div class="t m0 x4c h2d y8f ff8 fs2 fc0 sc0 lsf ws2b">\ue603\ue603\ued3d<span class="blank _3"></span>\ue603</div><div class="t m1 x4d h37 y8f ff9 fsa fc0 sc0 lsf ws46">\uf0d7\uf0f2</div><div class="t m0 x4e h2d y8f ff8 fs2 fc0 sc0 lsf ws47">\ued42<span class="blank"> </span>\udb80\udddb\ue603\ued54<span class="blank"> </span>\ue603\udb80\udddc\ue603\ued40\ued54\udb80\udddc<span class="ff5 ws12"> </span></div><div class="t m0 x1 h2b y93 ff8 fs2 fc0 sc0 lsf ws40">\ued23<span class="blank _7"> </span>\uf34c<span class="blank _7"> </span>\uf346<span class="blank"> </span><span class="v13">\ue973</span></div><div class="t m0 x45 h38 y94 ff8 fs2 fc0 sc0 ls50">\ue974<span class="ls54 v14">\ue7e4</span><span class="ls4c v18">\ued54</span><span class="fs7 lsf v19">\uf137</span></div><div class="t m0 x4f h38 y94 ff8 fs2 fc0 sc0 ls55">\ue975<span class="ls3d v14">\uf345</span><span class="ls4c v18">\ued54</span><span class="fs7 lsf v19">\uf136</span></div><div class="t m0 x50 h38 y94 ff8 fs2 fc0 sc0 ls55">\ue974<span class="ls3e v14">\uf345</span><span class="lsf v18">\ue975</span></div><div class="t m0 x51 h39 y94 ff8 fs2 fc0 sc0 ls50">\ue974<span class="lsf ws48 v14">\ued54<span class="blank"> </span>\uf42c<span class="blank _16"> </span></span><span class="ls56 v1a">\ue975</span><span class="lsf v1b">\ue603</span></div><div class="t m0 x52 h30 y95 ff8 fs7 fc0 sc0 lsf ws15">\uf13f\uf135</div><div class="t m0 x53 h3a y96 ff8 fs7 fc0 sc0 ls57">\ue603<span class="fs2 lsf ws49 v1b">\uf34c<span class="blank _7"> </span>\uf346<span class="blank"> </span><span class="v13">\ue973</span></span></div><div class="t m0 x54 h38 y94 ff8 fs2 fc0 sc0 ls50">\ue978<span class="lsf ws41 v14">\ue7e4<span class="blank _e"> </span>\ued54<span class="blank"> </span></span><span class="fs7 ls4d vf">\uf137</span><span class="ls3e v14">\uf345</span><span class="ls4c v18">\ued54</span><span class="fs7 lsf v19">\uf136</span></div><div class="t m0 x38 h38 y94 ff8 fs2 fc0 sc0 ls55">\ue974<span class="ls3e v14">\uf345</span><span class="lsf v18">\ue975</span></div><div class="t m0 x55 h39 y94 ff8 fs2 fc0 sc0 ls50">\ue974<span class="lsf ws48 v14">\ued54<span class="blank"> </span>\uf42c<span class="blank _16"> </span></span><span class="ls56 v1a">\ue975</span><span class="lsf v1b">\ue603</span></div><div class="t m0 x56 h30 y95 ff8 fs7 fc0 sc0 lsf ws15">\uf13f\uf135</div><div class="t m0 x57 h3b y96 ff8 fs7 fc0 sc0 ls57">\ue603<span class="fs2 lsf ws2b v1b">\uf34c<span class="ff5 ws12"> </span></span></div><div class="t m0 x1 h2b y97 ff8 fs2 fc0 sc0 lsf ws40">\ued23<span class="blank _7"> </span>\uf34c<span class="blank _7"> </span>\uf346<span class="blank"> </span><span class="v13">\ue973</span></div><div class="t m0 x45 h2c y98 ff8 fs2 fc0 sc0 ls50">\ue978<span class="lsf ws40 v14">\ue7e4<span class="blank"> </span>\ue975</span><span class="fs7 ls4d vf">\uf137</span><span class="ls3d v14">\uf345</span><span class="lsf ws2b v18">\ue975<span class="fs7 v1c">\uf136</span></span></div><div class="t m0 x50 h2c y98 ff8 fs2 fc0 sc0 ls58">\ue974<span class="ls59 v14">\uf345</span><span class="lsf v18">\ue975</span></div><div class="t m0 x51 h2c y98 ff8 fs2 fc0 sc0 ls5a">\ue974<span class="lsf ws4a v14">\ue7e4\ue603\ue603\ue975<span class="blank _9"> </span>\uf346<span class="blank _9"> </span>\uf36d\uf346<span class="blank"> </span><span class="v13">\ue973</span></span></div><div class="t m0 x22 h3c y98 ff8 fs2 fc0 sc0 ls5b">\ue978<span class="lsf ws3c v14">\ue603<span class="blank"> </span>\ue7e4<span class="blank _e"> </span></span><span class="ls38 vb">\udb80\udddb</span><span class="lsf ws2b v14">\uf346\ue973</span><span class="ls38 vb">\udb80\udddc</span><span class="fs7 ls5c vf">\uf137</span><span class="ls3e v14">\uf345</span><span class="ls38 v1d">\udb80\udddb</span><span class="lsf ws2b v18">\uf346\ue973</span><span class="ls38 v1d">\udb80\udddc</span><span class="fs7 lsf v19">\uf136</span></div><div class="t m0 x55 h2c y98 ff8 fs2 fc0 sc0 ls5d">\ue974<span class="ls3e v14">\uf345</span><span class="lsf v18">\ue975</span></div><div class="t m0 x58 h3d y98 ff8 fs2 fc0 sc0 ls5e">\ue974<span class="ls54 v14">\ue7e4</span><span class="ls38 vb">\udb80\udddb</span><span class="lsf ws2b v14">\uf346\ue973</span><span class="ls38 vb">\udb80\udddc</span><span class="lsf ws4b v14">\uf371<span class="blank"> </span>\uf34c<span class="ff5 ws12"> </span></span></div><div class="t m0 x1 h2b y99 ff8 fs2 fc0 sc0 lsf ws40">\ued23<span class="blank _7"> </span>\uf34c<span class="blank _7"> </span>\uf346<span class="blank"> </span><span class="v13">\ue97b</span></div><div class="t m0 x45 h2c y9a ff8 fs2 fc0 sc0 ls5f">\ue974<span class="ls59 v14">\uf345</span><span class="lsf v18">\ue97b</span></div><div class="t m0 x59 h2c y9a ff8 fs2 fc0 sc0 ls5f">\ue974<span class="ls3d v14">\uf345</span><span class="lsf v18">\ue97b</span></div><div class="t m0 x50 h2c y9a ff8 fs2 fc0 sc0 ls5f">\ue974<span class="lsf ws2d v14">\uf346<span class="blank"> </span>\uf36c<span class="v13">\ue973</span></span></div><div class="t m0 x5a h2c y9a ff8 fs2 fc0 sc0 ls5f">\ue978<span class="ls59 v14">\uf345</span><span class="lsf v18">\ue973</span></div><div class="t m0 x5b h2c y9a ff8 fs2 fc0 sc0 ls5f">\ue974<span class="ls3e v14">\uf346</span><span class="lsf v18">\ue975</span></div><div class="t m0 x5c h34 y9a ff8 fs2 fc0 sc0 lsf ws2b">\ue974<span class="ls60 v14">\uf370</span><span class="ff5 ws12 v14"> </span></div><div class="t m0 x1 h2b y9b ff8 fs2 fc0 sc0 lsf ws2f">\ued23<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="v13">\ue97b</span></div><div class="t m0 x5d h2c y9c ff8 fs2 fc0 sc0 ls61">\ue974<span class="ls3e v14">\uf346</span><span class="lsf v18">\ue973</span></div><div class="t m0 x5e h2c y9c ff8 fs2 fc0 sc0 ls5f">\ue978<span class="ls3d v14">\uf346</span><span class="lsf v18">\ue973</span></div><div class="t m0 x5f h2c y9c ff8 fs2 fc0 sc0 ls62">\ue974<span class="ls3e v14">\uf345</span><span class="lsf v18">\ue975</span></div><div class="t m0 x60 h34 y9c ff8 fs2 fc0 sc0 ls63">\ue974<span class="ls37 v14">\uf34c<span class="ff5 lsf ws12"> </span></span></div><div class="t m0 x1 h3e y9d ff8 fs2 fc0 sc0 lsf ws2f">\ued23<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="ls67 v13">\ue973\ue978</span></div><div class="t m0 x61 h2d y9e ff8 fs2 fc0 sc0 ls64">\ue975<span class="ff5 lsf ws12 v14"> </span></div><div class="t m0 x1 hf y9f ff5 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 hf ya0 ff5 fs3 fc0 sc0 lsf ws12"> <span class="blank _b"> </span> </div></div><div class="c x0 y3a wa h18"><div class="t m0 x15 h19 y3b ff4 fs3 fc2 sc0 lsf ws12"><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 ya1 w12 h3f" alt="" src="https://files.passeidireto.com/983b1510-9b97-4a18-bbd3-090700f03d0a/bg4.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 hf ya2 ff5 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h2 ya3 ff1 fs0 fc0 sc0 lsf ws12">MATEMÁTICA (6<span class="blank _0"></span><span class="ls10 ws0">1)<span class="ff2 lsf ws12"> 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 ya4 ff2 fs0 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h2 ya5 ff2 fs0 fc0 sc0 lsf ws12">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="ls68"> <span class="ls6b ws4c">DN<span class="ls6c ws4d">I:</span></span></span> <span class="blank _12"> </span> <span class="blank _17"> </span> <span class="blank _17"> </span> <span class="blank _2"> </span> <span class="blank _17"> </span> <span class="blank _2"> </span>TEMA 2 </div><div class="t m0 x3 h2 ya6 ff2 fs0 fc0 sc0 lsf ws12">Hoja 4 de 4 </div><div class="t m0 x3 h2 ya7 ff2 fs0 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h4 ya8 ffd fs2 fc0 sc0 lsf ws4e">4.<span class="ff7 ws12"> ¿Cuántas palabras distintas se pueden formar, c<span class="blank _0"></span>on o sin sentido, con las letras de la palabra </span></div><div class="t m0 x1 h4 ya9 ffe fs2 fc0 sc0 lsf ws4f">\u201cAGRARIO\u201d?<span class="ff7 ws12"> </span></div><div class="t m0 x1 h19 yaa ff4 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h40 yab ff6 fs3 fc0 sc0 lsf ws12">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 hf yac ff5 fs3 fc0 sc0 lsf ws12">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 hf yad ff5 fs3 fc0 sc0 lsf ws12">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 yae ff6 fs3 fc0 sc0 lsf ws12">Sin <span class="blank _3"> </span>embargo, <span class="blank _4"> </span>entre <span class="blank _4"> </span>las <span class="blank _3"> </span>7 <span class="blank _4"> </span>letras <span class="blank _4"> </span>hay <span class="blank _3"> </span>2 <span class="blank _4"> </span>repetidas <span class="blank _4"> </span>(la <span class="blank _3"> </span>\u201cA\u201d <span class="blank _4"> </span>y <span class="blank _4"> </span>la <span class="blank _4"> </span>\u201cR\u201d) <span class="blank _3"> </span>lo <span class="blank _4"> </span>que <span class="blank _3"> </span>r<span class="blank _3"> </span>educe <span class="blank _3"> </span>la <span class="blank _4"> </span>cantidad <span class="blank _3"> </span>de <span class="blank _4"> </span>palabras <span class="blank _4"> </span>distintas<span class="blank _0"></span> </div><div class="t m0 x1 hf yaf ff5 fs3 fc0 sc0 lsf ws12">posibles. </div><div class="t m0 x1 hf yb0 ff5 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 hf yb1 ff5 fs3 fc0 sc0 lsf ws12">Recordemos ade<span class="blank _0"></span>más que: </div><div class="t m0 x62 hf yb2 ff5 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 hf yb3 ff5 fs3 fc0 sc0 lsf ws12">Luego, hay: </div><div class="t m0 x5c h10 yb4 ff8 fs3 fc0 sc0 lsf">\ued32</div><div class="t m0 x63 h41 yb5 ff8 fs0 fc0 sc0 lsf">\uf13b</div><div class="t m0 x35 h42 yb6 ff8 fs0 fc0 sc0 lsf ws50">\uf136\ue7e1\uf136\ue7e1\uf135\ue7e1\uf135\ue7e1\uf135<span class="blank"> </span><span class="fs3 ls69 v1e">\uf34c</span><span class="fs3 ws6 v1f">\ue979\ue7e8</span></div><div class="t m0 x64 h43 yb7 ff8 fs3 fc0 sc0 lsf ws51">\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 _8"> </span><span class="ls5 v11">\uf34c</span><span class="ws6 v1a">\ue979\ue7e4\ue978\ue7e4<span class="blank _3"></span>\ue977\ue7e4\ue976\ue7e4\ue975\ue7e8</span></div><div class="t m0 x65 h25 yb7 ff8 fs3 fc0 sc0 ls6a">\ue976<span class="lsf ws7 v11">\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="ls6 ws11 v11">\ue973\ue974\ue978\ue972</span><span class="ff5 lsf ws12 v11"> </span></div><div class="t m0 x1 h6 yb8 ff5 fs3 fc0 sc0 lsf ws12">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="fff ws52">\u201cA<span class="blank _0"></span>GRARIO\u201d<span class="ff3 ws12"> </span></span></div><div class="t m0 x1 hf yb9 ff5 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 xf hf yba ff5 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 h6 ybb ff3 fs3 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 he ybc ff5 fs2 fc0 sc0 lsf ws12"> </div><div class="t m0 x1 hf ybd ff5 fs3 fc0 sc0 lsf ws12"> </div></div><div class="c x0 ybe wa h44"><div class="t m0 x15 h19 y3b ff4 fs3 fc2 sc0 lsf ws12"><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>
Compartilhar