<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/df4bfa75-d5d4-4062-b1c9-910d885c99d6/bg1.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls15 ws12">MATEMÁTICA (6<span class="ls16 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM </span></div><div class="t m0 x1 h2 y3 ff1 fs0 fc0 sc0 ls15 ws12">RECUPERATORI<span class="blank _0"></span>O 2° PARCIAL </div><div class="t m0 x2 h2 y4 ff1 fs0 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h2 y5 ff2 fs0 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h3 y6 ff2 fs1 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h2 y7 ff2 fs0 fc0 sc0 ls17 ws1">21<span class="ls15 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 4 </span></span></div><div class="t m0 x3 h2 y8 ff2 fs0 fc0 sc0 ls15 ws12"> Hoja 1 de 4 </div><div class="t m0 x3 h2 y9 ff2 fs0 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h3 ya ff2 fs1 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h3 yb ff2 fs1 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h4 yc ff3 fs2 fc0 sc0 ls15 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 ls15 ws12"> </div></div><div class="c x6 yd w4 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls15 ws12">1 </div></div><div class="c x8 yd w5 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls15 ws12">2 </div></div><div class="c x9 yd w6 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls15 ws12">3 </div></div><div class="c xa yd w7 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls15 ws12">4 </div></div><div class="c x4 yf w3 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls15 ws12"> </div></div><div class="c x6 yf w4 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls15 ws12"> </div></div><div class="c x8 yf w5 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls15 ws12"> </div></div><div class="c x9 yf w6 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls15 ws12"> </div></div><div class="c xa yf w7 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls15 ws12"> </div></div><div class="c x4 y11 w5 h9"><div class="t m0 xb ha y12 ff4 fs4 fc0 sc0 ls15 ws12">Puntaje de cada </div><div class="t m0 xb ha y13 ff4 fs4 fc0 sc0 ls15 ws12">ejercicio </div></div><div class="c x6 y11 w4 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls15 ws12">2,50 </div></div><div class="c x8 y11 w5 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls15 ws12">2,50 </div></div><div class="c x9 y11 w6 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls15 ws12">2,50 </div></div><div class="c xa y11 w7 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls15 ws12">2,50 </div></div><div class="c x0 y1 w2 h0"><div class="t m0 x1 hb y15 ff5 fs5 fc0 sc0 ls15 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 ls15 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 ls15 v1">1. Calcular el área de la región sombreada sabiendo que </span></div><div class="t m0 x1 he y18 ff8 fs2 fc0 sc0 ls15 ws4">\uee8c<span class="ls1 v2">\udb80\udddb</span><span class="ls2">\uee9e<span class="ls3 v2">\udb80\udddc</span><span class="ls4">\uf34c</span></span><span class="fs7 v3">\uee9e</span></div><div class="t m0 xf hf y19 ff8 fs7 fc0 sc0 ls5">\uf0db<span class="ff7 fs2 ls15 ws12 v4"> </span></div><div class="t m0 x1 he y1a ff8 fs2 fc0 sc0 ls2">\uee8d<span class="ls1 v2">\udb80\udddb</span>\uee9e<span class="ls6 v2">\udb80\udddc</span><span class="ls7">\uf34c<span class="fs7 ls15 v3">\uf0da</span></span></div><div class="t m0 x10 hf y1b ff8 fs7 fc0 sc0 ls15 ws5">\uf0db<span class="ls8 v5">\ue9be</span>\uee9e<span class="ff7 fs2 ws12 v4"> </span></div><div class="t m0 x1 h10 y1c ff5 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h10 y1d ff5 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h10 y1e ff5 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h10 y1f ff5 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h10 y20 ff5 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h10 y21 ff5 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h10 y22 ff5 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h11 y23 ff9 fs2 fc0 sc0 ls15 ws12">Para <span class="blank _0"></span>la <span class="blank _0"></span>realización de <span class="blank _0"></span>este <span class="blank _0"></span>ejercicio, <span class="blank _0"></span>recomendamos ver <span class="blank _0"></span>apuntes <span class="blank _0"></span>de: I<span class="blank _0"></span>ntegrales - Integ<span class="blank _0"></span>ral definida <span class="blank _0"></span><span class="ffa ws6">\u2013<span class="ff9 ws12"> <span class="blank _0"></span>Cálculo de <span class="blank _0"></span>área </span></span></div><div class="t m0 x1 h12 y24 ff9 fs2 fc0 sc0 ls15 ws12">En <span class="blank _0"></span>primer <span class="blank _4"></span>lugar, <span class="blank _4"></span>debemo<span class="blank _3"> </span>s <span class="blank _0"></span>hallar <span class="blank _4"></span>la <span class="blank _4"></span>int<span class="blank _3"> </span>ersección <span class="blank _4"></span>entre <span class="blank _0"></span><span class="ff8 ls9">\ued42<span class="ff9 ls15"> <span class="blank _0"></span><span class="ls18">y <span class="ff8 lsa">\ued43</span><span class="ls15"> <span class="blank _4"></span>para <span class="blank _0"></span>luego <span class="blank _4"></span>calcular e<span class="blank _0"></span>l <span class="blank _0"></span>área <span class="blank _4"></span>sombreada <span class="blank _0"></span>mediante <span class="blank _4"></span>la <span class="blank _0"></span>suma </span></span></span></span></div><div class="t m0 x1 h11 y25 ff9 fs2 fc0 sc0 ls15 ws12">de dos integrales: </div><div class="t m0 x1 h13 y26 ff8 fs2 fc0 sc0 ls9">\ued42<span class="ls1 v2">\udb80\udddb</span><span class="lsb">\ued54<span class="ls3 v2">\udb80\udddc</span><span class="ls15 ws7">\uf34c<span class="blank"> </span>\ued43<span class="ls1 v2">\udb80\udddb</span></span>\ued54<span class="ls1 v2">\udb80\udddc</span><span class="ff9 ls15 ws12"> </span></span></div><div class="t m0 x1 h12 y27 ff8 fs2 fc0 sc0 ls15">\ued54</div><div class="t m0 x1 h14 y28 ff8 fs2 fc0 sc0 lsc">\ue974<span class="lsd v6">\uf34c</span><span class="ls15 v7">\ue973</span></div><div class="t m0 x11 h15 y29 ff8 fs2 fc0 sc0 ls15 ws4">\ue974<span class="ls2 v5">\ue9be</span><span class="ws8">\ued54<span class="blank"> </span>\ue603</span><span class="v8">\ue603<span class="ff9 ws12"> </span></span></div><div class="t m0 x1 h16 y2a ff8 fs2 fc0 sc0 ls15 ws9">\ued54<span class="blank"> </span>\uf34c<span class="blank _5"> </span><span class="v9">\ue973</span></div><div class="t m0 x11 h17 y2b ff8 fs2 fc0 sc0 ls1">\ue9be<span class="ls15 ws4 va">\ued54\ue603</span><span class="ff9 ls15 ws12 vb"> </span></div><div class="t m0 x1 h16 y2c ff8 fs2 fc0 sc0 lse">\ued54<span class="fs7 lsf vc">\uf136</span><span class="ls10">\uf34c<span class="ls15 v9">\ue973</span></span></div><div class="t m0 x12 h18 y2d ff8 fs2 fc0 sc0 ls11">\ued54<span class="ls15 wsa v6">\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank"> </span>\udb80\udddb\ued41\ued48\ued41\ued52\ued3d\ued4a\ued40\ued4b\ue603</span><span class="ls2 ws8 v6">\ued3d\ued48<span class="blank"> </span></span><span class="ls15 ws4 v6">\ue603\ued3f\ued51\ued3d\ued40\ued4e\ued3d<span class="blank _3"></span>\ued40\ued4b\ue603\ued49\ued45<span class="blank _3"></span>\ued41\ued49\ued3e\ued4e\ued4b\ue603\ued3d<span class="blank _3"> </span>\ue603\ued49\ued45\ued41\ued49\ued3e<span class="blank _3"></span>\ued4e\ued4b\udb80\udddc<span class="ff9 ws12"> </span></span></div><div class="t m0 x1 h16 y2e ff8 fs2 fc0 sc0 lse">\ued54<span class="fs7 ls12 vc">\uf136</span><span class="ls15 wsb">\ue603\ue7e4\ue603\ue603\ued54<span class="blank _6"> </span>\uf34c<span class="blank"> </span><span class="v9">\ue973</span></span></div><div class="t m0 x13 h18 y2f ff8 fs2 fc0 sc0 ls13">\ued54<span class="ls15 wsc v6">\ue603\ue7e4\ue603\ue603\ued54<span class="blank"> </span>\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\udb80\udddb\ued2f\ued51\ued48\ued50\ued45\ued4c\ued48\ued45\ued3f\ued3d\ued49\ued4b\ued4f<span class="blank"> </span>\ue603\ued49\ued45\ued41\ued49\ued3e\ued4e\ued4b<span class="blank"> </span>\ue603\ued3d\ue603\ued49\ued45<span class="blank"> </span>\ued41\ued49\ued3e\ued4e\ued4b\ue603\ued4c\ued4b\ued4e<span class="blank"> </span>\ue603\ue936\ued54\ue936\ue7e1<span class="blank _7"> </span></span><span class="ls19 wsd v6">\ued55\ued3d<span class="blank _3"></span></span><span class="ls15 wse v6">\ue603\ued4d\ued51\ued41\ue603\ued54<span class="blank _8"> </span>\uf34d<span class="blank"> </span>\ue972\ue603</span><span class="ls1a wsf v6">\ued41\ued4a</span><span class="ls15 ws4 v6">\ue603</span><span class="ls1b ws10 v6">\ued4f\ued51<span class="blank"> </span></span><span class="ls15 ws4 v6">\ue603\ued45\ued4a\ued50\ued41\ued4e\ued4f\ued41\ued3f\ued3f\ued45\ue6d7\ued4a<span class="blank _3"> </span>\udb80\udddc<span class="ff9 ws12"> </span></span></div><div class="t m0 x1 h12 y30 ff8 fs2 fc0 sc0 lse">\ued54<span class="fs7 lsf vc">\uf137</span><span class="ls15 ws11">\uf34c<span class="blank"> </span>\ue973<span class="ff9 ws12"> </span></span></div><div class="t m0 x1 h12 y31 ff8 fs2 fc0 sc0 ls15 ws9">\ued54<span class="blank"> </span>\uf34c<span class="blank _9"> </span><span class="ls1 v0">\ue9be</span>\ue973</div><div class="t m0 x11 h19 y32 ff8 fs8 fc0 sc0 ls14">\uf22f<span class="ff9 fs2 ls15 ws12 vd"> </span></div><div class="t m0 x1 h12 y33 ff8 fs2 fc0 sc0 ls15 wsb">\ued54<span class="blank _6"> </span>\uf34c<span class="blank"> </span>\ue973<span class="ff9 ws12"> </span></div><div class="t m0 x1 h11 y34 ff9 fs2 fc0 sc0 ls15 ws12">Por lo <span class="blank _0"></span>tanto, <span class="blank _0"></span>teniendo <span class="blank _0"></span>en cue<span class="blank _0"></span>nta que <span class="blank _0"></span>el <span class="blank _0"></span>área de <span class="blank _4"></span>un<span class="blank _3"> </span>a integ<span class="blank _0"></span>ral puede <span class="blank _0"></span>calcularse como <span class="blank _0"></span>la <span class="blank _0"></span>integral <span class="blank _0"></span>de la <span class="blank _0"></span>fun<span class="blank _3"> </span><span class="ffa">ción \u201c<span class="blank _0"></span>techo\u201d </span></div><div class="t m0 x1 h11 y35 ffa fs2 fc0 sc0 ls15 ws12">menos la función que hace de \u201cpiso\u201d, podríamos expresar el área total de la siguiente<span class="blank _0"></span> manera:<span class="blank _3"> </span><span class="ff9"> </span></div></div><div class="c x1 y36 w8 h1a"><div class="t m0 x14 h2 y37 ff2 fs0 fc0 sc0 ls15 ws12">APELLIDO: </div></div><div class="c x15 y38 w9 h1b"><div class="t m0 xb h2 y39 ff2 fs0 fc0 sc0 ls15 ws12">CALIFICACIÓN:<span class="blank _0"></span> </div></div><div class="c x1 y3a w8 h1c"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls15 ws12">NOMBRE: </div></div><div class="c x1 y38 w8 h1c"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls15 ws12">DNI (registrado en S<span class="blank _0"></span>IU Guaraní): </div></div><div class="c x1 y3b w8 h1d"><div class="t m0 xb h2 y10 ff2 fs0 fc0 sc0 ls15 ws12">E-MAIL: </div></div><div class="c x15 y3c w9 h1e"><div class="t m0 xb h2 y3d ff2 fs0 fc0 sc0 ls15 ws12">DOCENTE (nombre<span class="blank _0"></span> y apellido): </div></div><div class="c x1 y3e w8 h1c"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls15 ws12">TEL: </div></div><div class="c x1 y3c w8 h1c"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls15 ws12">AULA: </div></div><div class="c x0 y3f wa h1f"><div class="t m0 x14 h20 y40 ff4 fs3 fc1 sc0 ls15 ws12"><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 x16 y41 wb h21" alt="" src="https://files.passeidireto.com/df4bfa75-d5d4-4062-b1c9-910d885c99d6/bg2.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h13 y42 ff8 fs2 fc0 sc0 ls15 wsb">\ued23<span class="blank"> </span>\uf34c<span class="blank"> </span>\ued23<span class="fs7 ls1c ve">\uf135</span><span class="ws13">\uf345<span class="blank"> </span>\ued23<span class="fs7 ls1d ve">\uf136</span><span class="ws10">\uf34c<span class="blank _a"> </span>\ue603<span class="blank _a"> </span>\uf3b1<span class="blank _b"> </span>\ued42<span class="blank"> </span><span class="ls1 v2">\udb80\udddb</span><span class="lsb">\ued54<span class="ls1e v2">\udb80\udddc</span></span></span>\uf346<span class="blank"> </span>\ue972\ue603\ued40\ued54<span class="blank _c"> </span>\uf345<span class="blank"> </span>\uf3b1<span class="blank _d"> </span>\ued43<span class="ls1 v2">\udb80\udddb</span><span class="lsb">\ued54<span class="ls1e v2">\udb80\udddc</span></span>\uf346<span class="blank"> </span>\ue972\ue603\ued40\ued54<span class="blank _6"> </span>\uf34c\ue603</span></div><div class="t m0 x17 h22 y43 ff8 fs7 fc0 sc0 ls15">\uf138</div><div class="t m0 x18 h22 y44 ff8 fs7 fc0 sc0 ls15">\uf135</div><div class="t m0 x19 h22 y43 ff8 fs7 fc0 sc0 ls15">\uf135</div><div class="t m0 x1a h23 y44 ff8 fs7 fc0 sc0 ls1f">\uf134<span class="fs2 ls15 ws10 vf">\uf3b1<span class="blank _b"> </span>\ued42<span class="ls1 v2">\udb80\udddb</span><span class="lsb">\ued54<span class="ls1 v2">\udb80\udddc</span><span class="ls15 ws13">\ue603\ued40\ued54<span class="blank _c"> </span>\uf345<span class="blank"> </span>\uf3b1<span class="blank _d"> </span>\ued43<span class="ls1 v2">\udb80\udddb</span></span>\ued54<span class="ls1 v2">\udb80\udddc</span><span class="ls15 ws8">\ued40\ued54<span class="blank"> </span>\ue603</span></span></span></div><div class="t m0 x1b h22 y43 ff8 fs7 fc0 sc0 ls15">\uf138</div><div class="t m0 x1c h22 y44 ff8 fs7 fc0 sc0 ls15">\uf135</div><div class="t m0 x1d h22 y43 ff8 fs7 fc0 sc0 ls15">\uf135</div><div class="t m0 x1e h24 y44 ff8 fs7 fc0 sc0 ls20">\uf134<span class="ff9 fs2 ls15 ws12 vf"> </span></div><div class="t m0 x1 h16 y45 ff8 fs2 fc0 sc0 ls15 ws14">\ued23<span class="blank _6"> </span>\uf34c<span class="blank"> </span>\ue603<span class="blank"> </span>\uf3b1<span class="blank _e"> </span><span class="v9">\ued54</span></div><div class="t m0 x1f h25 y46 ff8 fs2 fc0 sc0 ls21">\ue974<span class="ls15 ws15 v6">\ue603\ued40\ued54<span class="blank"> </span>\uf345</span></div><div class="t m0 x20 h22 y47 ff8 fs7 fc0 sc0 ls15">\uf135</div><div class="t m0 x21 h26 y48 ff8 fs7 fc0 sc0 ls22">\uf134<span class="fs2 ls23 vf">\uf3b1<span class="ls15 v9">\ue973</span></span></div><div class="t m0 x22 h12 y49 ff8 fs2 fc0 sc0 ls15 ws4">\ue974<span class="ls2 v5">\ue9be</span>\ued54</div><div class="t m0 x19 h22 y47 ff8 fs7 fc0 sc0 ls15">\uf138</div><div class="t m0 x1a h27 y48 ff8 fs7 fc0 sc0 ls24">\uf135<span class="fs2 ls15 ws8 vf">\ue603\ued40\ued54<span class="blank"> </span><span class="ff9 ws12"> </span></span></div><div class="t m0 x1 h11 y4a ff9 fs2 fc0 sc0 ls15 ws12">Resolviendo cada integral y aplicando la regla de Barrow: </div><div class="t m0 x1 h16 y4b ff8 fs2 fc0 sc0 ls15 wsb">\ued23<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="v9">\ue973</span></div><div class="t m0 x11 h14 y4c ff8 fs2 fc0 sc0 ls25">\ue974<span class="ls15 ws8 v6">\uf3b1<span class="blank _e"> </span>\ued54<span class="blank"> </span>\ue603\ued40\ued54<span class="blank _c"> </span>\uf345<span class="blank _c"> </span><span class="v9">\ue973</span></span></div><div class="t m0 x1a h14 y4c ff8 fs2 fc0 sc0 ls26">\ue974<span class="ls27 v6">\uf3b1</span><span class="ls15 v7">\ue973</span></div><div class="t m0 x23 h28 y4d ff8 fs2 fc0 sc0 ls2">\ue9be<span class="ls28 va">\ued54</span><span class="ls15 ws4 vb">\ue603\ued40\ued54</span></div><div class="t m0 x24 h22 y4e ff8 fs7 fc0 sc0 ls15">\uf138</div><div class="t m0 x25 h22 y4f ff8 fs7 fc0 sc0 ls15">\uf135</div><div class="t m0 x1f h22 y4e ff8 fs7 fc0 sc0 ls15">\uf135</div><div class="t m0 x26 h29 y4f ff8 fs7 fc0 sc0 ls29">\uf134<span class="fs2 ls15 ws16 vf">\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank"> </span>\udb80\udddb\ued32\ued4b\ued4e\ue603\ue692<span class="blank _3"></span>\ue694\ue691\ue692\ue7e4\ue603\ue603\ue603\ue603</span></div><div class="t m1 x27 h2a y4b ffb fs9 fc0 sc0 ls15">\uf0f2</div><div class="t m0 x8 h12 y4b ff8 fs2 fc0 sc0 ls15 ws17">\ued3d<span class="blank"> </span>\ue603</div><div class="t m1 x28 h2a y4b ffb fs9 fc0 sc0 ls15">\uf0d7</div><div class="t m0 x29 h13 y4b ff8 fs2 fc0 sc0 ls9">\ued42<span class="ls2a v2">\udb80\udddb</span><span class="ls15 ws8">\ue603\ued54<span class="blank"> </span>\ue603<span class="ls1 v2">\udb80\udddc</span><span class="ws4">\ued40\ued54\ue603</span></span></div><div class="t m1 x2a h2a y4b ffb fs9 fc0 sc0 ls15">\uf03d</div><div class="t m0 x2b h12 y4b ff8 fs2 fc0 sc0 ls15 ws17">\ue603\ue603\ued3d<span class="blank"> </span>\ue603</div><div class="t m1 x2c h2a y4b ffb fs9 fc0 sc0 ls15 ws18">\uf0d7\uf0f2</div><div class="t m0 x2d h12 y4b ff8 fs2 fc0 sc0 ls15 ws8">\ued42<span class="blank"> </span>\udb80\udddb\ue603\ued54<span class="blank"> </span>\ue603\udb80\udddc<span class="blank"> </span>\ue603\ued40\ued54\udb80\udddc<span class="ff9 ws12"> </span></div><div class="t m0 x1 h16 y50 ff8 fs2 fc0 sc0 ls15 wsb">\ued23<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="v9">\ue973</span></div><div class="t m0 x11 h14 y51 ff8 fs2 fc0 sc0 ls2b">\ue974<span class="ls15 ws16 v6">\ue603<span class="blank"> </span>\ue7e4<span class="blank _7"> </span>\udb80\udde7</span><span class="lse v7">\ued54</span><span class="fs7 ls15 v10">\uf136</span></div><div class="t m0 x2e h2b y51 ff8 fs2 fc0 sc0 ls2c">\ue974<span class="ls15 ws19 v6">\udb80\udde8<span class="blank"> </span>\uf42c<span class="blank _f"> </span><span class="v3">\ue603</span></span></div><div class="t m0 x2f h22 y52 ff8 fs7 fc0 sc0 ls15">\ue603</div><div class="t m0 x30 h22 y53 ff8 fs7 fc0 sc0 ls15 ws5">\uf135<span class="fs2 v11">\ue603</span></div><div class="t m0 x30 h22 y54 ff8 fs7 fc0 sc0 ls15">\uf134</div><div class="t m0 x2f h2c y55 ff8 fs7 fc0 sc0 ls2d">\ue603<span class="fs2 ls2e v12">\uf345<span class="ls15 v9">\ue973</span></span></div><div class="t m0 x31 h2d y51 ff8 fs2 fc0 sc0 ls2f">\ue974<span class="ls15 ws16 v6">\ue603\ue603<span class="blank"> </span>\ue7e4<span class="blank _7"> </span>\uf36b\ue974\ue603</span><span class="ls2 v3">\ue9be</span><span class="ls15 ws8 v6">\ued54\uf36f<span class="blank _7"> </span>\uf42c<span class="blank _f"> </span><span class="v3">\ue603</span></span></div><div class="t m0 x32 h22 y56 ff8 fs7 fc0 sc0 ls15">\ue603</div><div class="t m0 x33 h22 y57 ff8 fs7 fc0 sc0 ls15 ws5">\uf138<span class="fs2 v11">\ue603</span></div><div class="t m0 x33 h22 y58 ff8 fs7 fc0 sc0 ls15">\uf135</div><div class="t m0 x32 h2e y59 ff8 fs7 fc0 sc0 ls30">\ue603<span class="fs2 ls4 v12">\uf34c<span class="ls15 v9">\ue973</span></span></div><div class="t m0 x34 h14 y51 ff8 fs2 fc0 sc0 ls31">\ue974<span class="ls15 wsa v6">\ue603<span class="blank"> </span>\ue7e4<span class="blank _7"> </span>\udb80\udde7</span><span class="ls15 ws4 v7">\ue973<span class="fs7 vc">\uf136</span></span></div><div class="t m0 x35 h14 y51 ff8 fs2 fc0 sc0 ls32">\ue974<span class="ls2e v6">\uf346</span><span class="ls15 ws4 v7">\ue972<span class="fs7 vc">\uf136</span></span></div><div class="t m0 x36 h14 y51 ff8 fs2 fc0 sc0 ls33">\ue974<span class="ls15 ws1a v6">\udb80\udde8<span class="blank"> </span>\uf345<span class="blank"> </span><span class="v9">\ue973</span></span></div><div class="t m0 x29 h18 y51 ff8 fs2 fc0 sc0 ls2f">\ue974<span class="ls15 ws1b v6">\ue603\ue603<span class="blank"> </span>\ue7e4<span class="blank _7"> </span>\uf36b\ue974</span><span class="ls2 v6">\ue9be</span><span class="ls15 ws1c v6">\ue976<span class="blank"> </span>\uf346<span class="blank"> </span>\ue974</span><span class="ls2 v6">\ue9be</span><span class="ls15 ws1d v6">\ue973\uf36f<span class="blank"> </span>\uf34c<span class="ff9 ws12"> </span></span></div><div class="t m0 x1 h16 y5a ff8 fs2 fc0 sc0 ls15 wsb">\ued23<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="v9">\ue973</span></div><div class="t m0 x11 h14 y5b ff8 fs2 fc0 sc0 ls2b">\ue974<span class="ls15 ws16 v6">\ue603<span class="blank"> </span>\ue7e4<span class="blank _7"> </span><span class="v9">\ue973</span></span></div><div class="t m0 xf h14 y5b ff8 fs2 fc0 sc0 ls34">\ue974<span class="ls2e v6">\uf345</span><span class="ls15 v7">\ue973</span></div><div class="t m0 x37 h14 y5b ff8 fs2 fc0 sc0 ls35">\ue974<span class="ls15 wsa v6">\ue603<span class="blank"> </span>\ue7e4<span class="blank _7"> </span></span><span class="ls1 v13">\udb80\udddb</span><span class="ls15 ws1a v6">\ue976<span class="blank"> </span>\uf346<span class="blank"> </span>\ue974</span><span class="ls10 v13">\udb80\udddc</span><span class="ls36 v6">\uf34c</span><span class="ls15 v7">\ue973</span></div><div class="t m0 x38 h18 y5b ff8 fs2 fc0 sc0 ls34">\ue976<span class="ls15 ws1e v6">\uf345<span class="blank"> </span>\ue973<span class="ff9 ws12"> </span></span></div><div class="t m0 x1 h16 y5c ff8 fs2 fc0 sc0 ls15 wsb">\ued23<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="v9">\ue977</span></div><div class="t m0 x11 h2f y5d ff8 fs2 fc0 sc0 ls15 ws4">\ue976<span class="ff9 ws12 v6"> </span></div><div class="t m0 x1 h4 y5e ff7 fs2 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h4 y5f ff7 fs2 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 y60 ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 y61 ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 y62 ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 y63 ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 y64 ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 y65 ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 y66 ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 y67 ff3 fs3 fc0 sc0 ls15 ws12"> <span class="blank _10"> </span> </div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y68 wc h30" alt="" src="https://files.passeidireto.com/df4bfa75-d5d4-4062-b1c9-910d885c99d6/bg3.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls15 ws12">MATEMÁTICA (6<span class="ls16 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls37"> <span class="ls38"> </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 ls15 ws12"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 ls15 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 _11"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span>TEMA 4 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 ls15 ws12">Hoja 2 de 4 </div><div class="t m0 x3 h2 y69 ff2 fs0 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 he y6a ff7 fs2 fc0 sc0 ls15 ws12">2. Hallar los intervalos de crecimiento y decrecimiento de la función <span class="ff8 ws7">\uee8c\udb80\udddb\uee9e\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="fs7 v3">\uf0da</span></span></div><div class="t m0 x15 h31 y6b ff8 fs7 fc0 sc0 ls39">\uf0dd<span class="fs2 ls15 ws13 v4">\uee9e<span class="blank"> </span>\uf345<span class="blank _12"> </span></span><span class="ls15 v14">\uf0e2</span></div><div class="t m0 x39 h32 y6b ff8 fs7 fc0 sc0 ls15 ws5">\uee9e\uf13e\uf0da<span class="ff7 fs2 ws12 v4"> </span></div><div class="t m0 x1 h6 y6c ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 y6d ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 y6e ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 y6f ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 y70 ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 y71 ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h11 y58 ff9 fs2 fc0 sc0 ls15 ws12">Igualamos a cero la derivada para obtener los puntos críticos: </div><div class="t m0 x8 h13 y72 ff8 fs2 fc0 sc0 ls3a">\ued42<span class="fs7 ls3b vc">\udb80\udd92</span><span class="ls1 v2">\udb80\udddb</span><span class="ls3c">\ued54<span class="ls10 v2">\udb80\udddc</span><span class="ls15 ws7">\uf34c<span class="blank"> </span>\ue972<span class="ff9 ws12"> </span></span></span></div><div class="t m0 x3a h12 y73 ff8 fs2 fc0 sc0 ls15">\ue973</div><div class="t m0 x3a h33 y74 ff8 fs2 fc0 sc0 ls33">\ue976<span class="ls3d v6">\uf345</span><span class="ls15 ws4 v7">\uf346\ue97b</span></div><div class="t m0 x3b h34 y75 ff8 fs2 fc0 sc0 ls1">\udb80\udddb<span class="ls15 ws1f v5">\ued54<span class="blank _c"> </span>\uf345<span class="blank"> </span>\ue973</span>\udb80\udddc<span class="fs7 ls3e v15">\uf136</span><span class="ls15 ws7 v16">\uf34c<span class="blank"> </span>\ue972<span class="ff9 ws12"> </span></span></div><div class="t m0 x3c h12 y76 ff8 fs2 fc0 sc0 ls1">\udb80\udddb<span class="ls15 ws13 v5">\ued54<span class="blank _c"> </span>\uf345<span class="blank"> </span>\ue973</span>\udb80\udddc<span class="fs7 ls1c v17">\uf136</span><span class="ls15 ws20 v5">\uf346<span class="blank _13"> </span>\ue97b\ue603\ue7e4<span class="blank"> </span>\ue976</span></div><div class="t m0 x3d h18 y77 ff8 fs2 fc0 sc0 ls15 ws4">\ue976<span class="ls1 v2">\udb80\udddb</span><span class="ws1f">\ued54<span class="blank"> </span>\uf345<span class="blank"> </span>\ue973<span class="ls1 v2">\udb80\udddc</span><span class="fs7 ls3f v18">\uf136</span><span class="ws7 v6">\uf34c<span class="blank"> </span>\ue972<span class="blank _3"></span><span class="ff9 ws12"> </span></span></span></div><div class="t m0 x3e h12 y78 ff8 fs2 fc0 sc0 lse">\ued54<span class="fs7 ls40 vc">\uf136</span><span class="ls15 ws13">\uf345<span class="blank"> </span>\ue974\ued54<span class="blank _c"> </span>\uf345<span class="blank"> </span>\ue973<span class="blank"> </span>\uf346<span class="blank"> </span><span class="ls4a">\ue975\ue978</span></span></div><div class="t m0 x3d h18 y79 ff8 fs2 fc0 sc0 ls15 ws4">\ue976<span class="ls1 v2">\udb80\udddb</span><span class="ws1f">\ued54<span class="blank"> </span>\uf345<span class="blank"> </span>\ue973<span class="ls1 v2">\udb80\udddc</span><span class="fs7 ls41 v18">\uf136</span><span class="wsb v6">\uf34c<span class="blank"> </span>\ue972<span class="blank _3"></span><span class="ff9 ws12"> </span></span></span></div><div class="t m0 x36 h12 y7a ff8 fs2 fc0 sc0 lse">\ued54<span class="fs7 ls40 vc">\uf136</span><span class="ls15 ws13">\uf345<span class="blank"> </span>\ue974\ued54<span class="blank _c"> </span>\uf346<span class="blank"> </span></span><span class="ls4a ws21">\ue975\ue977<span class="blank"> </span></span><span class="ls15 wsb">\uf34c<span class="blank"> </span>\ue972<span class="ff9 ws12"> </span></span></div><div class="t m0 x1 h12 y7b ff9 fs2 fc0 sc0 ls15 ws12">Utilizando <span class="ff8">\ued54</span></div><div class="t m0 x37 h35 y7c ff8 fs7 fc0 sc0 ls15 ws22">\uf135\ue7e1\uf136<span class="blank"> </span><span class="fs2 ls4 v12">\uf34c</span><span class="ws5 v8">\uf13f\uf1d5<span class="blank _3"> </span>\uf347</span><span class="ls8 v19">\ue9be</span><span class="ls42 v8">\uf1d5</span><span class="fs8 ls43 v1a">\uf22e</span><span class="ws5 v8">\uf13f\uf138<span class="ls4b">\uf1d4\uf1d6</span></span></div><div class="t m0 x3f h36 y7d ff8 fs7 fc0 sc0 ls15 ws23">\uf136\uf1d4<span class="blank"> </span><span class="fs2 wsb v4">\ue7e1<span class="blank _7"> </span>\ued3f\ued4b\ued4a\ue603\ued3d<span class="blank _6"> </span>\uf34c<span class="blank"> </span>\ue973\ue7e1<span class="blank _7"> </span>\ued3e<span class="blank"> </span>\uf34c<span class="blank"> </span>\ue974\ue7e1<span class="blank _7"> </span>\ued3f<span class="blank"> </span>\uf34c<span class="blank"> </span>\uf346<span class="ls4a ws24">\ue975\ue977<span class="ff9 ls15 ws12"> </span></span></span></div><div class="t m0 x6 h12 y7e ff8 fs2 fc0 sc0 ls15">\ued54</div><div class="t m0 x40 h37 y7f ff8 fs7 fc0 sc0 ls15 ws22">\uf135\ue7e1\uf136<span class="blank"> </span><span class="fs2 ls4 v12">\uf34c</span><span class="fs2 ws13 vf">\uf346\ue974<span class="blank"> </span>\uf347<span class="blank"> </span><span class="ws4 v0">\uf3a5<span class="v0">\ue974</span></span></span><span class="ls40 v1b">\uf136</span><span class="fs2 ws20 vf">\uf346<span class="blank _13"> </span>\ue976\ue603\ue7e4\ue973\ue603\ue7e4<span class="blank"> </span>\udb80\udddb\uf346<span class="ls4a ws24">\ue975\ue977<span class="ls15">\udb80\udddc</span></span></span></div><div class="t m0 x41 h2f y80 ff8 fs2 fc0 sc0 ls15 ws25">\ue974\ue7e4\ue973<span class="blank"> </span><span class="ff9 ws12 v6"> </span></div><div class="t m0 x3e h12 y81 ff8 fs2 fc0 sc0 ls15">\ued54</div><div class="t m0 x3c h38 y82 ff8 fs7 fc0 sc0 ls15 ws26">\uf135\ue7e1\uf136<span class="blank"> </span><span class="fs2 ls36 v12">\uf34c</span><span class="fs2 ws1a vf">\uf346\ue974<span class="blank"> </span>\uf347<span class="blank"> </span><span class="ls2 v5">\ue9be</span>\ue976<span class="blank"> </span>\uf345<span class="blank _c"> </span><span class="ls4a">\ue973\ue976\ue972</span></span></div><div class="t m0 x42 h2f y83 ff8 fs2 fc0 sc0 ls44">\ue974<span class="ff9 ls15 ws12 v6"> </span></div><div class="t m0 x36 h12 y84 ff8 fs2 fc0 sc0 ls15">\ued54</div><div class="t m0 x43 h38 y85 ff8 fs7 fc0 sc0 ls15 ws26">\uf135\ue7e1\uf136<span class="blank"> </span><span class="fs2 ls36 v12">\uf34c</span><span class="fs2 ws1a vf">\uf346\ue974<span class="blank"> </span>\uf347<span class="blank"> </span><span class="ls2 v5">\ue9be</span><span class="ls4a">\ue973\ue976\ue976</span></span></div><div class="t m0 x42 h2f y86 ff8 fs2 fc0 sc0 ls45">\ue974<span class="ff9 ls15 ws12 v6"> </span></div><div class="t m0 x44 h12 y87 ff8 fs2 fc0 sc0 ls15">\ued54</div><div class="t m0 x3e h38 y88 ff8 fs7 fc0 sc0 ls3e">\uf135<span class="fs2 ls4 v12">\uf34c<span class="ls15 ws1f v9">\uf346\ue974<span class="blank"> </span>\uf345<span class="blank"> </span><span class="ls4a">\ue973\ue974</span></span></span></div><div class="t m0 x45 h14 y89 ff8 fs2 fc0 sc0 ls46">\ue974<span class="ls36 v6">\uf34c</span><span class="ls4a v7">\ue973\ue972</span></div><div class="t m0 x46 h18 y89 ff8 fs2 fc0 sc0 ls47">\ue974<span class="ls15 wsb v6">\uf34c<span class="blank"> </span>\ue977<span class="ff9 ws12"> </span></span></div><div class="t m0 x35 h16 y8a ff8 fs2 fc0 sc0 ls15 ws4">\ued54<span class="fs7 ls3e ve">\uf136</span><span class="ls4">\uf34c</span><span class="ws13 v9">\uf346\ue974<span class="blank"> </span>\uf346<span class="blank"> </span><span class="ls4a">\ue973\ue974</span></span></div><div class="t m0 x8 h14 y8b ff8 fs2 fc0 sc0 ls46">\ue974<span class="ls15 ws27 v6">\uf34c<span class="blank _14"> </span>\uf346<span class="blank"> </span></span><span class="ls4a v7">\ue973\ue976</span></div><div class="t m0 x47 h18 y8b ff8 fs2 fc0 sc0 ls48">\ue974<span class="ls15 ws7 v6">\uf34c<span class="blank"> </span>\uf346\ue979<span class="ff9 ws12"> </span></span></div><div class="t m0 x1 h11 y8c ff9 fs2 fc0 sc0 ls15 ws12">Luego, </div><div class="t m0 x48 h12 y8d ff8 fs2 fc0 sc0 ls1">\udb80\udddb<span class="ls15 ws13 v5">\ued54<span class="blank _c"> </span>\uf346<span class="blank"> </span>\ue977</span>\udb80\udddc\udb80\udddb<span class="ls15 ws13 v5">\ued54<span class="blank"> </span>\uf345<span class="blank"> </span>\ue979</span><span class="ls49">\udb80\udddc<span class="ls15 ws7 v5">\uf34c<span class="blank"> </span>\ue972<span class="ff9 ws12"> </span></span></span></div><div class="t m0 x1 h11 y8e ff9 fs2 fc0 sc0 ls15 ws12">De donde es: </div><div class="t m0 x49 h12 y8f ff8 fs2 fc0 sc0 ls15 ws13">\ued54<span class="blank _c"> </span>\uf346<span class="blank"> </span>\ue977<span class="blank _c"> </span>\uf34c<span class="blank _14"> </span>\ue972\ue603<span class="blank"> </span>\uebe9<span class="blank"> </span>\ue603\ued54<span class="blank _c"> </span>\uf345<span class="blank"> </span>\ue979<span class="blank _14"> </span>\uf34c<span class="blank _14"> </span>\ue972<span class="ff9 ws12"> </span></div><div class="t m0 x1 h12 y90 ff9 fs2 fc0 sc0 ls15 ws12">Luego, los puntos críticos son <span class="ff8 ws7">\ued54<span class="blank _6"> </span>\uf34c<span class="blank"> </span>\ue977\ue7e1<span class="blank _15"> </span>\ued54<span class="blank _6"> </span>\uf34c<span class="blank"> </span>\uf346\ue979\ue603\ued55<span class="blank _3"></span>\ue603\ued54<span class="blank _6"> </span>\uf34c<span class="blank"> </span>\uf346\ue973\ue7e4\ue603</span> </div><div class="t m0 x1 h12 y91 ff9 fs2 fc0 sc0 ls15 ws12">La <span class="blank _3"> </span>r<span class="blank _3"> </span>ecta <span class="blank _16"> </span><span class="ff8 ws28">\ued54<span class="blank _6"> </span>\uf34c<span class="blank"> </span>\uf346\ue973</span> <span class="blank _16"> </span>es <span class="blank _16"> </span>una <span class="blank _16"> </span>asíntota <span class="blank _16"> </span>vertica<span class="blank _0"></span>l <span class="blank _16"> </span>de <span class="blank _16"> </span>la <span class="blank _16"> </span>función <span class="blank _16"> </span>y<span class="blank _0"></span> <span class="blank _16"> </span>de <span class="blank _16"> </span>su <span class="blank _16"> </span>derivada. <span class="blank _16"> </span>Lo <span class="blank _3"> </span>tenemos <span class="blank _16"> </span>en <span class="blank _16"> </span>cuenta <span class="blank _16"> </span>al <span class="blank _16"> </span>considera<span class="blank _0"></span>r <span class="blank _16"> </span>los </div><div class="t m0 x1 h11 y92 ff9 fs2 fc0 sc0 ls15 ws12">intervalos donde estudiamos el signo de la derivada. </div><div class="t m0 x1 h11 y93 ff9 fs2 fc0 sc0 ls15 ws12">Recordemos que: </div><div class="t m0 x1 h13 y94 ffb fs2 fc0 sc0 ls15 ws29">\uf0b7<span class="ff9 ws12"> <span class="blank _16"> </span>si <span class="blank _17"> </span><span class="ff8 ws4">\ued42\ue7ef<span class="ls1 v2">\udb80\udddb</span><span class="lsb">\ued54<span class="ls10 v2">\udb80\udddc</span></span><span class="ws1d">\uf350<span class="blank"> </span>\ue603\ue972</span></span> <span class="blank _16"> </span>para <span class="blank _16"> </span>todo <span class="blank _16"> </span>x<span class="blank _3"> </span> <span class="blank _16"> </span>que <span class="blank _16"> </span>pertenece <span class="blank _17"> </span>al <span class="blank _16"> </span>intervalo <span class="blank _17"> </span><span class="ff8 ls2a v2">\udb80\udddb</span><span class="ff8 ws2a">\ued3d\ue7e2<span class="blank"> </span>\ue603\ued3e<span class="blank _3"> </span><span class="ls1 v2">\udb80\udddc</span></span>, <span class="blank _17"> </span>entonces <span class="blank _16"> </span>la <span class="blank _16"> </span>función <span class="blank _17"> </span><span class="ff8 ls9">\ued42</span> <span class="blank _17"> </span>es <span class="blank _16"> </span>creciente <span class="blank _16"> </span>en <span class="blank _16"> </span>el<span class="blank _3"> </span> <span class="blank _16"> </span>intervalo </span></div><div class="t m0 x1 h12 y95 ff8 fs2 fc0 sc0 ls1">\udb80\udddb<span class="ls15 ws2a v5">\ued3d<span class="blank _3"></span>\ue7e2<span class="blank"> </span>\ue603\ued3e</span><span class="ls15 ws4">\udb80\udddc<span class="ff9 ws12 v5"> </span></span></div><div class="t m0 x1 h12 y96 ffb fs2 fc0 sc0 ls15 ws29">\uf0b7<span class="ff9 ws12"> si <span class="blank _3"> </span><span class="ff8 ws8">\ued42\ue7ef\udb80\udddb\ued54<span class="blank"> </span>\udb80\udddc<span class="blank _18"> </span>\ue603<span class="blank _a"> </span>\uf34f<span class="blank _14"> </span>\ue603\ue972</span> <span class="blank _3"> </span>para todo <span class="blank _3"> </span>x <span class="blank _3"> </span>que <span class="blank _3"> </span>pertenece al <span class="blank _3"> </span>intervalo <span class="blank _3"> </span><span class="ff8 ws2b">\udb80\udddb\ued3d<span class="blank"> </span>\ue7e2<span class="blank _18"> </span>\ue603\ued3e<span class="blank"> </span>\udb80\udddc\ue7e1</span> <span class="blank _3"> </span>entonces la <span class="blank _3"> </span>función<span class="ff8 ws10">\ue603\ued42<span class="blank"> </span></span> <span class="blank _3"> </span>es <span class="blank _3"> </span>decreciente en <span class="blank _3"> </span>el <span class="blank _3"> </span>intervalo </span></div><div class="t m0 x1 h12 y97 ff8 fs2 fc0 sc0 ls15 ws2a">\udb80\udddb\ued3d<span class="blank _3"> </span>\ue7e2<span class="blank"> </span>\ue603\ued3e<span class="blank _3"></span>\udb80\udddc\ue7e4<span class="ff9 ws12"> </span></div></div><div class="c x0 y3f wa h1f"><div class="t m0 x14 h20 y40 ff4 fs3 fc1 sc0 ls15 ws12"><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 x4a y98 wd h39" alt="" src="https://files.passeidireto.com/df4bfa75-d5d4-4062-b1c9-910d885c99d6/bg4.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h13 y99 ff9 fs2 fc0 sc0 ls15 ws12">Analizamos entonces, los intervalos: <span class="ff8 ls1 v2">\udb80\udddb</span><span class="ff8 ws2a">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346\ue979<span class="ls1 v2">\udb80\udddc</span><span class="ls4c">\ue7e1<span class="ls1 v2">\udb80\udddb</span></span>\uf346\ue979\ue7e2<span class="blank"> </span>\uf346\ue973<span class="ls1 v2">\udb80\udddc</span><span class="ls4d">\ue7e1<span class="ls1 v2">\udb80\udddb</span></span><span class="ws2c">\uf346\ue973\ue7e2<span class="blank"> </span>\ue977<span class="ls1 v2">\udb80\udddc</span><span class="ls4d">\ue7e1<span class="ls1 v2">\udb80\udddb</span></span><span class="wsa">\ue977\ue7e2<span class="blank"> </span>\ue603<span class="blank"> </span>\uf345\ue9bb<span class="ls1 v2">\udb80\udddc</span><span class="ws4">\ue7e4</span></span></span></span> </div><div class="t m0 x1 h11 y9a ff9 fs2 fc0 sc0 ls15 ws12">Realizamos una tabla: </div></div><div class="c x4a y9b we h3a"><div class="t m0 x4b h11 y14 ff9 fs2 fc0 sc0 ls15 ws12">Intervalo </div></div><div class="c x4 y9b wf h3a"><div class="t m0 x4c h12 y37 ff8 fs2 fc0 sc0 ls1">\udb80\udddb<span class="ls15 ws2c v5">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346\ue979</span>\udb80\udddc<span class="ff9 ls15 ws12 v5"> </span></div></div><div class="c x4d y9b w10 h3a"><div class="t m0 x4b h12 y37 ff8 fs2 fc0 sc0 ls1">\udb80\udddb<span class="ls15 ws2a v5">\uf346\ue979\ue7e2<span class="blank"> </span>\uf346\ue973</span>\udb80\udddc<span class="ls15 ws4 v5">\ue603<span class="ff9 ws12"> </span></span></div></div><div class="c x2a y9b w11 h3a"><div class="t m0 x7 h13 y9c ff8 fs2 fc0 sc0 ls15 ws4">\ue603<span class="ls1 v2">\udb80\udddb</span><span class="ws2a">\uf346\ue973\ue7e2<span class="blank"> </span>\ue977<span class="ls1 v2">\udb80\udddc</span><span class="ff9 ws12"> </span></span></div></div><div class="c x15 y9b w12 h3a"><div class="t m0 x7 h13 y9c ff8 fs2 fc0 sc0 ls15 ws4">\ue603<span class="ls1 v2">\udb80\udddb</span><span class="ws2d">\ue977\ue7e2<span class="blank"> </span>\ue603<span class="blank"> </span>\uf345\ue9bb</span><span class="v2">\udb80\udddc</span><span class="ff9 ws12"> </span></div></div><div class="c x4a y9d we h3b"><div class="t m0 x4e h11 y14 ff9 fs2 fc0 sc0 ls15 ws12">Para </div></div><div class="c x4 y9d wf h3b"><div class="t m0 x4f h12 y9c ff8 fs2 fc0 sc0 ls15 ws7">\ued54<span class="blank _6"> </span>\uf34c<span class="blank"> </span>\uf346\ue97a<span class="ff9 ws12"> </span></div></div><div class="c x4d y9d w10 h3b"><div class="t m0 x7 h12 y9c ff8 fs2 fc0 sc0 ls15 wsb">\ued54<span class="blank _6"> </span>\uf34c<span class="blank"> </span>\uf346\ue974<span class="ff9 ws12"> </span></div></div><div class="c x2a y9d w11 h3b"><div class="t m0 x4e h12 y9c ff8 fs2 fc0 sc0 ls15 wsb">\ued54<span class="blank _6"> </span>\uf34c<span class="blank"> </span>\ue972<span class="ff9 ws12"> </span></div></div><div class="c x15 y9d w12 h3b"><div class="t m0 x50 h12 y9c ff8 fs2 fc0 sc0 ls15 wsb">\ued54<span class="blank _6"> </span>\uf34c<span class="blank"> </span>\ue978<span class="ff9 ws12"> </span></div></div><div class="c x4a y9e we h3c"><div class="t m0 x51 h11 y9f ffa fs2 fc0 sc0 ls15 ws12">Signo de f\u2019<span class="ff9"> </span></div></div><div class="c x4 y9e wf h3c"><div class="t m0 x14 h16 ya0 ff8 fs2 fc0 sc0 ls3a">\ued42<span class="fs7 ls4e vc">\udb80\udd92</span><span class="ls1 v2">\udb80\udddb</span><span class="lsb">\ued54<span class="ls10 v2">\udb80\udddc</span><span class="ls4f">\uf34c<span class="ls4a v9">\ue973\ue975</span></span></span></div><div class="t m0 x52 h12 ya1 ff8 fs2 fc0 sc0 ls4a">\ue973\ue97b\ue978</div><div class="t m0 x14 h12 ya2 ff8 fs2 fc0 sc0 ls15 ws2e">\uf350<span class="blank"> </span>\ue972<span class="ff9 ws12"> </span></div></div><div class="c x4d y9e w10 h3c"><div class="t m0 x53 h16 ya3 ff8 fs2 fc0 sc0 ls3a">\ued42<span class="fs7 ls3b vc">\udb80\udd92</span><span class="ls1 v2">\udb80\udddb</span><span class="lsb">\ued54<span class="ls10 v2">\udb80\udddc</span><span class="ls15 ws2f">\uf34c<span class="blank _c"> </span>\uf346<span class="blank"> </span><span class="ls4a v9">\ue975\ue977</span></span></span></div><div class="t m0 x21 h12 ya4 ff8 fs2 fc0 sc0 ls15">\ue976</div><div class="t m0 x53 h12 y9c ff8 fs2 fc0 sc0 ls15 ws1d">\uf34f<span class="blank"> </span>\ue972<span class="ff9 ws12"> </span></div></div><div class="c x2a y9e w11 h3c"><div class="t m0 x53 h16 ya3 ff8 fs2 fc0 sc0 ls3a">\ued42<span class="fs7 ls4e vc">\udb80\udd92</span><span class="ls1 v2">\udb80\udddb</span><span class="lsb">\ued54<span class="ls10 v2">\udb80\udddc</span><span class="ls15 ws27">\uf34c<span class="blank _14"> </span>\uf346<span class="blank"> </span><span class="ls4a v9">\ue975\ue977</span></span></span></div><div class="t m0 x21 h12 ya4 ff8 fs2 fc0 sc0 ls15">\ue976</div><div class="t m0 x53 h12 y9c ff8 fs2 fc0 sc0 ls15 ws1d">\uf34f<span class="blank"> </span>\ue972<span class="ff9 ws12"> </span></div></div><div class="c x15 y9e w12 h3c"><div class="t m0 x4c h16 ya0 ff8 fs2 fc0 sc0 ls3a">\ued42<span class="fs7 ls3b vc">\udb80\udd92</span><span class="ls1 v2">\udb80\udddb</span><span class="lsb">\ued54<span class="ls10 v2">\udb80\udddc</span><span class="ls50">\uf34c<span class="ls4a v9">\ue973\ue975</span></span></span></div><div class="t m0 x11 h12 ya1 ff8 fs2 fc0 sc0 ls4a">\ue973\ue97b\ue978</div><div class="t m0 x4c h12 ya2 ff8 fs2 fc0 sc0 ls15 ws1d">\uf350<span class="blank"> </span>\ue972<span class="ff9 ws12"> </span></div></div><div class="c x4a ya5 we h3d"><div class="t m0 x51 h11 ya6 ff9 fs2 fc0 sc0 ls15 ws12">Conclusión </div></div><div class="c x4 ya5 wf h3d"><div class="t m0 x4c h12 ya7 ff8 fs2 fc0 sc0 ls15 ws10">\ued42<span class="blank"> </span>\ue603<span class="ff9 ws12">crece en <span class="ffc"> </span></span></div><div class="t m0 x4c h12 y37 ff8 fs2 fc0 sc0 ls1">\udb80\udddb<span class="ls15 ws2c v5">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346\ue979</span>\udb80\udddc<span class="ff9 ls15 ws12 v5"> </span></div></div><div class="c x4d ya5 w10 h3d"><div class="t m0 x51 h12 ya7 ff8 fs2 fc0 sc0 ls15 ws10">\ued42<span class="blank"> </span>\ue603<span class="ff9 ws12">decrece en <span class="ffc"> </span></span></div><div class="t m0 x4f h12 y37 ff8 fs2 fc0 sc0 ls1">\udb80\udddb<span class="ls15 ws2a v5">\uf346\ue979\ue7e2<span class="blank"> </span>\uf346\ue973</span><span class="ls15 ws4">\udb80\udddc<span class="ff9 ws12 v5"> </span></span></div></div><div class="c x2a ya5 w11 h3d"><div class="t m0 x51 h12 ya7 ff8 fs2 fc0 sc0 ls15 ws10">\ued42<span class="blank"> </span>\ue603<span class="ff9 ws12">decrece en <span class="ffc"> </span></span></div><div class="t m0 x7 h12 y37 ff8 fs2 fc0 sc0 ls1">\udb80\udddb<span class="ls15 ws2a v5">\uf346\ue973\ue7e2<span class="blank"> </span>\ue977</span><span class="ls15 ws4">\udb80\udddc<span class="ff9 ws12 v5"> </span></span></div></div><div class="c x15 ya5 w12 h3d"><div class="t m0 xe h12 ya7 ff8 fs2 fc0 sc0 ls15 ws10">\ued42<span class="blank"> </span>\ue603<span class="ff9 ws12">crece en <span class="ffc"> </span></span></div><div class="t m0 x54 h12 y37 ff8 fs2 fc0 sc0 ls1">\udb80\udddb<span class="ls15 ws2d v5">\ue977\ue7e2<span class="blank"> </span>\ue603<span class="blank"> </span>\uf345\ue9bb</span><span class="ls15 ws4">\udb80\udddc<span class="ff9 ws12 v5"> </span></span></div></div><div class="c x0 y1 w2 h0"><div class="t m0 x1 h11 ya8 ff9 fs2 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h11 ya9 ff9 fs2 fc0 sc0 ls15 ws12">Concluimos: </div><div class="t m0 x1 h13 yaa ff8 fs2 fc0 sc0 ls3a">\ued42<span class="fs7 ls4e vc">\udb80\udd92</span><span class="ls1 v2">\udb80\udddb</span><span class="lsb">\ued54<span class="ls51 v2">\udb80\udddc</span><span class="ls15 ws2e">\uf350<span class="blank"> </span>\ue972\ue603</span><span class="ls1a wsf">\ued41\ued4a<span class="ls1 v2">\udb80\udddb</span></span><span class="ls15 ws2a">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346\ue979<span class="ls52 v2">\udb80\udddc</span></span><span class="ls53 ws30">\ue603\uebeb\ue603<span class="ls1 v2">\udb80\udddb</span></span><span class="ls15 ws31">\ue977\ue7e2<span class="blank"> </span>\ue603<span class="blank _17"> </span>\uf345\ue9bb<span class="ws4 v2">\udb80\udddc</span><span class="ff9 ws12">por lo que f es creciente en </span><span class="ls1 v2">\udb80\udddb</span><span class="ws2a">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346\ue979<span class="ls52 v2">\udb80\udddc</span></span></span><span class="ls53 ws30">\ue603\uebeb\ue603<span class="ls1 v2">\udb80\udddb</span></span><span class="ls15 ws31">\ue977\ue7e2<span class="blank"> </span>\ue603<span class="blank _17"> </span>\uf345\ue9bb<span class="ls1 v2">\udb80\udddc</span><span class="ws4">\ue603\ue7e4<span class="ff9 ws12"> </span></span></span></span></div><div class="t m0 x1 h13 yab ff8 fs2 fc0 sc0 ls3a">\ued42<span class="fs7 ls4e vc">\udb80\udd92</span><span class="ls1 v2">\udb80\udddb</span><span class="lsb">\ued54<span class="ls51 v2">\udb80\udddc</span><span class="ls15 ws2e">\uf34f<span class="blank"> </span>\ue972\ue603</span><span class="ls1a wsf">\ued41\ued4a</span><span class="ls15 ws4">\ue603<span class="ls1 v2">\udb80\udddb</span><span class="ws2a">\uf346\ue979\ue7e2<span class="blank"> </span>\uf346\ue973<span class="ls54 v2">\udb80\udddc</span></span></span><span class="ls53 ws30">\ue603\uebeb\ue603<span class="ls1 v2">\udb80\udddb</span></span><span class="ls15 ws2a">\uf346\ue973\ue7e2<span class="blank"> </span>\ue977<span class="ls1 v2">\udb80\udddc</span><span class="ws4">\ue603\ue603<span class="ff9 ws12">por lo que f es decreciente en </span><span class="ls1 v2">\udb80\udddb</span></span>\uf346\ue979\ue7e2<span class="blank"> </span>\uf346\ue973<span class="ls54 v2">\udb80\udddc</span></span><span class="ls53 ws30">\ue603\uebeb\ue603<span class="ls1 v2">\udb80\udddb</span></span><span class="ls15 ws2a">\uf346\ue973\ue7e2<span class="blank"> </span>\ue977<span class="ls1 v2">\udb80\udddc</span><span class="ws4">\ue603\ue7e4\ue603<span class="ff9 ws12"> </span></span></span></span></div><div class="t m0 x1 h6 yac ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 yad ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h11 yae ff9 fs2 fc0 sc0 ls15 ws12"> <span class="blank _10"> </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 yaf wc h3e" alt="" src="https://files.passeidireto.com/df4bfa75-d5d4-4062-b1c9-910d885c99d6/bg5.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h11 yb0 ff9 fs2 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h2 yb1 ff1 fs0 fc0 sc0 ls15 ws12">MATEMÁTICA (6<span class="blank _0"></span><span class="ls16 ws0">1)<span class="ff2 ls15 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 yb2 ff2 fs0 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h2 yb3 ff2 fs0 fc0 sc0 ls15 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="blank _11"> </span> <span class="blank _19"> </span> <span class="blank _19"> </span> <span class="blank _2"> </span> <span class="blank _19"> </span> <span class="blank _2"> </span>TEMA 4 </div><div class="t m0 x3 h2 y7 ff2 fs0 fc0 sc0 ls15 ws12">Hoja 3 de 4 </div><div class="t m0 x3 h2 yb4 ff2 fs0 fc0 sc0 ls15 ws12"> </div><div class="t m0 x2 h2 y9 ff2 fs0 fc0 sc0 ls55 ws12"> <span class="ff7 fs2 ls15 v1c">3. Al p<span class="blank _3"> </span>rimer parcial de <span class="blank _3"> </span>una <span class="blank _3"> </span>sede <span class="blank _3"> </span>de UBAXXI s<span class="blank _3"> </span>e presentaron 100 <span class="blank _3"> </span>estudiantes, d<span class="blank _3"> </span>e los cuales<span class="blank _3"> </span> 65 <span class="blank _3"> </span>aprobaron el </span></div><div class="t m0 x1 h4 yb5 ff7 fs2 fc0 sc0 ls15 ws12">examen <span class="blank _16"> </span>de <span class="blank _17"> </span>Matemáticas, <span class="blank _17"> </span>25 <span class="blank _16"> </span>el <span class="blank _17"> </span>de <span class="blank _16"> </span>Matemáticas <span class="blank _17"> </span>y <span class="blank _17"> </span>Biofísica; <span class="blank _16"> </span>y <span class="blank _17"> </span>15 <span class="blank _17"> </span>aprobaron <span class="blank _16"> </span>sólo <span class="blank _17"> </span>el <span class="blank _17"> </span>de <span class="blank _16"> </span>Biofísi<span class="blank _3"> </span>ca. <span class="blank _16"> </span>¿Cuántos </div><div class="t m0 x1 h4 yb6 ff7 fs2 fc0 sc0 ls15 ws12">estudiantes no aprobaron ninguno de los exámenes mencionados? </div><div class="t m0 x1 h6 yb7 ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 yb8 ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 yb9 ff3 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x20 h10 yba ff5 fs3 fc0 sc0 ls15 ws12">Vamos a desi<span class="blank _0"></span>gnar a los conjunto<span class="blank _0"></span>s: </div><div class="t m0 x55 h3f ybb ff8 fs3 fc0 sc0 ls15 ws32">\ue603\ue603\ue603\ue603\ue603\ue603\ued2f<span class="blank _c"> </span>\uf34c<span class="blank"> </span>\ued23\ued48\ued51\ued49\ued4a\ued4b\ued4f<span class="blank _3"> </span>\ue603\ued4d\ued51\ued41\ue603\ued3d\ued4c\ued4e\ued51\ued41\ued3e\ued3d\ued4a\ue603\ued49\ued3d\ued50\ued41\ued49\ued3d\ued50\ued45\ued3f\ued3d\ue7e1<span class="blank _3"></span>\ue603<span class="ff5 ws12"> </span></div><div class="t m0 x6 h3f ybc ff8 fs3 fc0 sc0 ls15 ws33">\ued24<span class="blank _c"> </span>\uf34c<span class="blank"> </span>\ued23\ued48\ued51\ued49\ued4a\ued4b\ued4f<span class="blank _3"> </span>\ue603\ued4d\ued51\ued41\ue603\ued3d\ued4c\ued4e\ued4b\ued3e\ued3d\ued4e\ued4b\ued4a\ue603\ued24\ued45\ued4b\ued42\ued45\ued4f\ued45\ued3f\ued3d<span class="ff5 ws12"> </span></div><div class="t m0 x56 h40 ybd ff8 fs3 fc0 sc0 ls15 ws34">\ued3f\ued3d\ued4e\ued40<span class="blank"> </span><span class="ws35 v2">\udb80\udddb</span><span class="ls56">\ued37<span class="ls57 v2">\udb80\udddc</span><span class="ls58">\uf34c<span class="ls59">\ue973\ue972\ue972</span></span></span><span class="ws36">\ue7e1<span class="blank _18"> </span>\ued3f\ued3d\ued4e\ued40<span class="blank"> </span><span class="ws35 v2">\udb80\udddb</span><span class="ls5a">\ued2f<span class="ls57 v2">\udb80\udddc</span><span class="ls58">\uf34c<span class="ls59 ws37">\ue978\ue977</span></span></span>\ue7e1<span class="blank _18"> </span>\ued3f\ued3d\ued4e\ued40<span class="blank"> </span><span class="ws35 v2">\udb80\udddb</span><span class="ws38">\ued2f<span class="blank"> </span>\uebea<span class="blank"> </span>\ued24<span class="blank _3"> </span><span class="ls5b v2">\udb80\udddc</span><span class="ls58">\uf34c<span class="ls59">\ue974\ue977</span></span></span>\ue7e1<span class="blank _18"> </span>\ued3f\ued3d\ued4e\ued40<span class="blank"> </span><span class="ls5c v2">\udb80\udddb</span><span class="ws39">\ued24<span class="blank _13"> </span>\uf346<span class="blank"> </span>\ued2f<span class="blank _3"> </span><span class="ls57 v2">\udb80\udddc</span><span class="ls58">\uf34c<span class="ls59">\ue973\ue977</span></span><span class="ffd ws12"> </span></span></span></div><div class="t m0 x20 h10 ybe ff5 fs3 fc0 sc0 ls15 ws12">Se pide: </div><div class="t m0 x20 h40 ybf ff8 fs3 fc0 sc0 ls15 ws35">\ued25\ued3d\ued4e\ued40<span class="v2">\udb80\udddb</span><span class="ws38">\ued2f<span class="blank _c"> </span>\uebeb<span class="blank"> </span>\ued24<span class="ls5d v2">\udb80\udddc</span><span class="fs0 ls5e v17">\uf1bc</span><span class="ws3a">\uf34c<span class="blank _c"> </span>\ued25\ued3d\ued4e\ued40<span class="blank"> </span><span class="ls5c v2">\udb80\udddb</span><span class="ls56">\ued37<span class="ls5f v2">\udb80\udddc</span></span><span class="ws39">\uf346<span class="blank"> </span>\ued25\ued3d\ued4e\ued40</span></span></span><span class="v2">\udb80\udddb</span><span class="ws38">\ued2f<span class="blank _c"> </span>\uebeb<span class="blank"> </span>\ued24</span><span class="v2">\udb80\udddc</span><span class="ff5 ws12">= </span></div><div class="t m0 x22 h41 yc0 ff8 fs3 fc0 sc0 ls58">\uf34c<span class="ls59 ws3b">\ue973\ue972\ue972<span class="blank"> </span><span class="ls60">\uf346</span></span><span class="ls15 ws35 v2">\udb80\udddf</span><span class="ls15 ws3c">\ued25\ued3d\ued4e\ued40<span class="blank"> </span><span class="ws35 v2">\udb80\udddb</span><span class="ws39">\ued2f<span class="blank"> </span>\uf346<span class="blank"> </span>\ued24<span class="blank _3"> </span><span class="ls61 v2">\udb80\udddc</span>\uf345<span class="blank"> </span>\ued25\ued3d\ued4e\ued40<span class="ws35 v2">\udb80\udddb</span><span class="ws3d">\ued2f<span class="blank _c"> </span>\uebea<span class="blank"> </span>\ued24<span class="ls61 v2">\udb80\udddc</span></span>\uf345<span class="blank"> </span>\ued25\ued3d\ued4e\ued40<span class="ws35 v2">\udb80\udddb</span>\ued24<span class="blank _c"> </span>\uf346<span class="blank"> </span>\ued2f<span class="ls5b v2">\udb80\udddc</span></span></span>\uf34c<span class="ls59 ws3e">\ue973\ue972\ue972<span class="blank"> </span></span><span class="ls15 ws39">\uf346<span class="blank"> </span>\udb80\udddb</span><span class="ls59 ws3f">\ue976\ue972<span class="blank"> </span><span class="ls60">\uf345</span>\ue974\ue977<span class="blank"> </span><span class="ls60">\uf345</span>\ue973\ue977</span><span class="ls15 ws35">\udb80\udddc<span class="v2">\udb80\udde0</span><span class="ff5 ws12"> </span></span></div><div class="t m0 x20 h40 yc1 ff8 fs3 fc0 sc0 ls15 ws35">\ued25\ued3d\ued4e\ued40<span class="v2">\udb80\udddb</span><span class="ls56">\ued37<span class="ls61 v2">\udb80\udddc</span></span><span class="ws39">\uf346<span class="blank"> </span>\ued25\ued3d\ued4e\ued40<span class="blank _3"> </span></span><span class="v2">\udb80\udddb</span><span class="ws38">\ued2f<span class="blank _13"> </span>\uebeb<span class="blank"> </span>\ued24<span class="blank _3"> </span></span><span class="v2">\udb80\udddc</span><span class="ff5 ls62">=</span><span class="ls59 ws3b">\ue973\ue972\ue972<span class="blank"> </span><span class="ls60">\uf346</span><span class="ws40">\ue97a\ue972<span class="blank"> </span><span class="ls58">\uf34c</span>\ue974\ue972<span class="ff5 ls63 ws12"> </span></span></span><span class="fc3 ws3a v1d">\ued25\ued3d\ued4e\ued40<span class="blank"> </span></span><span class="fc3 v1e">\udb80\udddb<span class="ws38 v5">\ued2f<span class="blank _13"> </span>\uebeb<span class="blank"> </span>\ued24<span class="blank _3"> </span></span><span class="ls5d">\udb80\udddc<span class="fs0 ls5e v18">\uf1bc</span><span class="ls58 v5">\uf34c<span class="ls59">\ue974\ue972<span class="ff5 ls15 ws12"> </span></span></span></span></span></div><div class="t m0 x20 h42 yc2 ffd fs3 fc0 sc0 ls15 ws12">Referencia: Unida<span class="blank _0"></span>d 7: Conjuntos </div><div class="t m0 x20 h10 yc3 ff5 fs3 fc3 sc0 ls15 ws12"> </div><div class="t m0 x1 h42 yc4 ffd fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h6 yc5 ff3 fs3 fc0 sc0 ls15 ws12"> <span class="blank _10"> </span> </div></div><div class="c x0 yc6 wa h43"><div class="t m0 x14 h20 y40 ff4 fs3 fc1 sc0 ls15 ws12"><span class="fc2 sc0"> </span></div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 yc7 w13 h44" alt="" src="https://files.passeidireto.com/df4bfa75-d5d4-4062-b1c9-910d885c99d6/bg6.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls15 ws12">MATEMÁTICA (6<span class="ls16 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls37"> <span class="ls38"> </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 ls15 ws12"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 ls15 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 _11"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span>TEMA 4 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 ls15 ws12">Hoja 4 de 4 </div><div class="t m0 x3 h2 y69 ff2 fs0 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h20 yc8 ff4 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h4 yc9 ff7 fs2 fc0 sc0 ls15 ws12">4. <span class="ffe">¿Cuántas palabras distintas se pueden formar, c<span class="blank _0"></span>on o sin sentido, que comiencen con la letra \u201cC\u201d, ¿con </span></div><div class="t m0 x1 h11 yca ffe fs2 fc0 sc0 ls15 ws12">las letras de la palabra \u201cCAMISA\u201d?<span class="ff9"> </span></div><div class="t m0 x1 h10 ycb ff5 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h10 ycc ff6 fs3 fc0 sc0 ls15 ws12">Buscamos utilizar las <span class="blank _3"> </span>6 <span class="blank _3"> </span>letras de <span class="blank _3"> </span>la palabra \u201cCAM<span class="blank _0"></span>ISA\u201d <span class="blank _3"> </span>para <span class="blank _3"> </span>arma<span class="blank _0"></span>r <span class="blank _3"> </span>los <span class="blank _3"> </span><span class="ff5">nuevos vocablos (independientemente de </span></div><div class="t m0 x1 h10 ycd ff5 fs3 fc0 sc0 ls15 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 h10 yce ff5 fs3 fc0 sc0 ls15 ws12">formar dichos tér<span class="blank _0"></span>minos. Luego, es<span class="blank _0"></span>tamos ante un <span class="blank _0"></span>caso de permutación<span class="blank _0"></span> o reordenamiento<span class="blank _0"></span> de elementos.<span class="blank _0"></span> </div><div class="t m0 x21 h10 ycf ff5 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h10 yd0 ff5 fs3 fc0 sc0 ls15 ws41">S<span class="ff6 ws12">iendo <span class="blank _3"> </span>además <span class="blank _3"> </span>que <span class="blank _3"> </span>buscamos <span class="blank _3"> </span>palabras q<span class="blank _3"> </span>ue <span class="blank _3"> </span>comienzan<span class="blank _0"></span> <span class="blank _16"> </span>con <span class="blank _3"> </span>la <span class="blank _3"> </span>letra <span class="blank _3"> </span>\u201cC\u201d, <span class="blank _3"> </span>en <span class="blank _3"> </span>lugar <span class="blank _16"> </span>d<span class="blank _0"></span>e <span class="blank _3"> </span>permutar <span class="blank _3"> </span>los <span class="blank _3"> </span>6 <span class="blank _3"> </span>caracteres </span></div><div class="t m0 x1 h10 yd1 ff5 fs3 fc0 sc0 ls15 ws12">disponibles, debemos re<span class="blank _0"></span>ordenar solo 5 de ellos, aquellos que justamente<span class="blank _0"></span> ocupan las posiciones 2 a 6 dentro de </div><div class="t m0 x1 h10 yd2 ff5 fs3 fc0 sc0 ls15 ws12">cada nueva palab<span class="blank _0"></span>ra. </div><div class="t m0 x1 h10 yd3 ff5 fs3 fc0 sc0 ls15 ws12">Por otra parte,<span class="blank _0"></span> recordemos que: </div><div class="t m0 x57 h10 yd4 ff5 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h10 yd5 ff6 fs3 fc0 sc0 ls15 ws12">Luego, como hay<span class="blank _0"></span> 2 letras \u201cA\u201d disponi<span class="blank _0"></span>bles entre las 5 a<span class="blank _0"></span> reordenar, tendrem<span class="blank _0"></span>os: <span class="ff5"> </span></div><div class="t m0 x58 h3f yd6 ff8 fs3 fc0 sc0 ls15">\ued32</div><div class="t m0 x59 h45 yd7 ff8 fs0 fc0 sc0 ls15">\uf139</div><div class="t m0 x5a h46 yd8 ff8 fs0 fc0 sc0 ls15 ws42">\uf136\ue7e1\uf135\ue7e1\uf135\ue7e1\uf135<span class="blank"> </span><span class="fs3 ls64 v1f">\uf34c</span><span class="fs3 ws35 v15">\ue977\ue7e8</span></div><div class="t m0 x3e h47 yd9 ff8 fs3 fc0 sc0 ls15 ws43">\ue974\ue7e8<span class="blank"> </span>\ue973\ue7e8<span class="blank"> </span>\ue973\ue7e8<span class="blank"> </span>\ue973\ue7e8<span class="blank _c"> </span><span class="ls65 v16">\uf34c</span><span class="ws35 v20">\ue977\ue7e4\ue976\ue7e4\ue975\ue7e4\ue974\ue7e8</span></div><div class="t m0 x42 h48 yd9 ff8 fs3 fc0 sc0 ls15 ws44">\ue974\ue7e8<span class="blank"> </span><span class="ws33 v16">\uf34c<span class="blank"> </span>\ue977\ue7e4\ue976\ue7e4\ue975<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="ls59 ws37">\ue978\ue972<span class="ff5 ls15 ws12"> </span></span></span></div><div class="t m0 x1 h49 yda ff6 fs3 fc0 sc0 ls15 ws12">palabras <span class="blank _3"> </span>distintas q<span class="blank _3"> </span>ue <span class="blank _3"> </span>pueden f<span class="blank _3"> </span>ormarse con <span class="blank _3"> </span>las <span class="blank _3"> </span>6 <span class="blank _3"> </span>letras <span class="blank _16"> </span>de la <span class="blank _3"> </span>palabra <span class="blank _3"> </span>\u201cCAMISA\u201d <span class="blank _3"> </span>y <span class="blank _3"> </span>que <span class="blank _3"> </span>además <span class="blank _3"> </span>comienzan<span class="blank _0"></span> <span class="blank _3"> </span>con </div><div class="t m0 x1 h10 ydb ff5 fs3 fc0 sc0 ls15 ws12">la letr<span class="ff6">a \u201cC\u201d.</span> </div><div class="t m0 x20 h10 ydc ff5 fs3 fc0 sc0 ls15 ws12"> </div><div class="t m0 x1 h10 ydd ff5 fs3 fc3 sc0 ls15 ws12"> </div><div class="t m0 x1 h42 yde ffd fs3 fc0 sc0 ls15 ws12"> </div></div><div class="c x0 y3f wa h1f"><div class="t m0 x14 h20 y40 ff4 fs3 fc1 sc0 ls15 ws12"><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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