<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/46e9e1ad-a4aa-4675-b347-4f90f436463f/bg1.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls22 ws1e">MATEMÁTICA (6<span class="ls23 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM </span></div><div class="t m0 x1 h2 y3 ff1 fs0 fc0 sc0 ls22 ws1e">FINAL </div><div class="t m0 x2 h2 y4 ff1 fs0 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h2 y5 ff2 fs0 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h3 y6 ff2 fs1 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h2 y7 ff2 fs0 fc0 sc0 ls22 ws1">12/07/2023<span class="ff1 ws1e"> <span class="blank _0"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span>TEMA 2 </span></div><div class="t m0 x3 h2 y8 ff2 fs0 fc0 sc0 ls22 ws1e"> Hoja 1 de 4 </div><div class="t m0 x3 h2 y9 ff2 fs0 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h3 ya ff2 fs1 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h3 yb ff2 fs1 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h4 yc ff3 fs2 fc0 sc0 ls22 ws1e">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 ls22 ws1e"> </div></div><div class="c x6 yd w4 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls22 ws1e">1 </div></div><div class="c x8 yd w5 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls22 ws1e">2 </div></div><div class="c x9 yd w6 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls22 ws1e">3 </div></div><div class="c xa yd w7 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 ls22 ws1e">4 </div></div><div class="c x4 yf w3 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls22 ws1e"> </div></div><div class="c x6 yf w4 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls22 ws1e"> </div></div><div class="c x8 yf w5 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls22 ws1e"> </div></div><div class="c x9 yf w6 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls22 ws1e"> </div></div><div class="c xa yf w7 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 ls22 ws1e"> </div></div><div class="c x4 y11 w5 h9"><div class="t m0 xb ha y12 ff4 fs4 fc0 sc0 ls22 ws1e">Puntaje de cada </div><div class="t m0 xb ha y13 ff4 fs4 fc0 sc0 ls22 ws1e">ejercicio </div></div><div class="c x6 y11 w4 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls22 ws1e">2,50 </div></div><div class="c x8 y11 w5 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls22 ws1e">2,50 </div></div><div class="c x9 y11 w6 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls22 ws1e">2,50 </div></div><div class="c xa y11 w7 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 ls22 ws1e">2,50 </div></div><div class="c x0 y1 w2 h0"><div class="t m0 x1 hb y15 ff5 fs5 fc0 sc0 ls22 ws1e">Duración del exam<span class="blank _2"> </span>en: 1h <span class="ff6 ws2">40\u2019.</span> Com<span class="blank _2"> </span>pletar los datos<span class="blank _2"> </span> personales<span class="blank _2"> </span> con letra clara, m<span class="blank _2"> </span>ayúscula e imprenta. <span class="blank _2"> </span> </div><div class="t m0 xd hc y16 ff3 fs5 fc0 sc0 ls22 ws1e">No se aceptarán respue<span class="blank _2"> </span>stas en lápiz.<span class="blank _2"> </span> </div><div class="t m0 xe hd y17 ff2 fs6 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 he y18 ff3 fs2 fc0 sc0 ls22 ws1e">1. <span class="blank _3"> </span>Dada <span class="blank _3"> </span><span class="ff7 ws3">\uee8c\udb80\udddb\uee9e\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank"> </span>\uee8b<span class="fs7 ws4 v1">\uf13f\uee9e</span><span class="fs8 ls0 v2">\uf0dc</span><span class="fs7 ws4 v1">\uf13e<span class="ls24 ws5">\uf0db\uf0da\uee9e<span class="blank"> </span></span></span></span>, <span class="blank _3"> </span>determinar <span class="blank _3"> </span>los <span class="blank _3"> </span>intervalos <span class="blank _3"> </span>de <span class="blank _4"> </span>crecimiento <span class="blank _3"> </span>y <span class="blank _4"> </span>de <span class="blank _3"> </span>decrecimiento, <span class="blank _3"> </span>y<span class="blank _5"></span> <span class="blank _3"> </span>los </div><div class="t m0 x1 h4 y19 ff3 fs2 fc0 sc0 ls22 ws1e">máximos y mínimos relativos. </div><div class="t m0 x1 h4 y1a ff3 fs2 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 hf y1b ff4 fs3 fc0 sc0 ls22 ws1e">Lo primero que nec<span class="blank _5"></span>esitamos conocer<span class="blank _5"></span> es el domini<span class="blank _5"></span>o de la fu<span class="blank _5"></span>nción. Como su expr<span class="blank _5"></span>esión no present<span class="blank _5"></span>a ninguna res<span class="blank _5"></span>tricción, el </div><div class="t m0 x1 h10 y1c ff4 fs3 fc0 sc0 ls22 ws1e">dominio es <span class="ff7 ws6">\ued26\ued4b\ued49<span class="v3">\udb80\udddb</span><span class="ls1">\ued42<span class="ls2 v3">\udb80\udddc</span></span><span class="ws7">\uf34c<span class="blank"> </span>\ueb39</span></span>. </div><div class="t m0 x1 hf y1d ff4 fs3 fc0 sc0 ls22 ws1e">Para hallar los in<span class="blank _5"></span>tervalos de crecimi<span class="blank _5"></span>ento y de decr<span class="blank _5"></span>ecimiento, analiz<span class="blank _5"></span>amos el sign<span class="blank _5"></span>o de la derivada. </div><div class="t m0 x1 h11 y1e ff7 fs3 fc0 sc0 ls3">\ued42<span class="fs0 ls4 v4">\udb80\udd92</span><span class="ls22 ws6 v3">\udb80\udddb</span><span class="ls5">\ued54<span class="ls6 v3">\udb80\udddc</span><span class="ls22 ws8">\uf34c<span class="blank"> </span>\ue603<span class="blank"> </span><span class="fs2 ls7">\ued41</span><span class="fs7 ws4 v4">\uf346\ued54</span><span class="fs8 ls8 v5">\ue975</span><span class="fs7 ws4 v4">\uf345<span class="ls25 ws9">\ue974\ue973<span class="ls9">\ued54</span></span></span><span class="ff4 ws1e">. (-3</span><span class="lsa">\ued54<span class="fs0 lsb v4">\uf136</span><span class="lsc">\uf345</span></span></span><span class="ls13 wsa">\ue974\ue973</span><span class="ff4 ls22 ws1e">). Notamos qu<span class="blank _5"></span>e para hallar la deriv<span class="blank _5"></span>ada aplica<span class="blank _5"></span>mos la regla de l<span class="blank _5"></span>a cadena por tra<span class="blank _5"></span>tarse de una </span></span></div><div class="t m0 x1 hf y1f ff4 fs3 fc0 sc0 ls22 ws1e">función compuesta, <span class="blank _5"></span>y que el dominio de e<span class="blank _5"></span>sta coincide con <span class="blank _5"></span>el dominio de la<span class="blank _5"></span> función origin<span class="blank _5"></span>al. Utilizamos ahora el t<span class="blank _5"></span>eorema </div><div class="t m0 x1 h12 y20 ff4 fs3 fc0 sc0 ls22 ws1e">de Bolzano aplicad<span class="blank _5"></span>o a <span class="ff7 ws6">\ued42\ueb22</span> para saber c<span class="blank _5"></span>ómo varía su sig<span class="blank _5"></span>no en <span class="ls26 wsb">su</span> dominio.<span class="blank _5"></span> </div><div class="t m0 x1 h12 y21 ff4 fs3 fc0 sc0 ls22 ws1e">Calculamos el c<span class="blank _5"></span>onjunto de ceros de <span class="ff7 ws6">\ued42\ueb22<span class="blank _5"></span><span class="ff4 ws1e">: </span></span></div><div class="t m0 x1 he y22 ff7 fs2 fc0 sc0 lsd">\ued41<span class="fs7 ls22 wsc v1">\uf13f\uf1eb<span class="blank"> </span></span><span class="fs8 lse v2">\uf22f</span><span class="fs7 lsf v1">\uf13e<span class="ls27 wsd">\uf136\uf135<span class="ls10">\uf1eb</span></span></span><span class="fs3 ls22 wse">\ue7e4<span class="blank"> </span>\udb80\udddb\uf346\ue975\ued54<span class="fs0 ls11 v1">\ue974</span><span class="ls12">\uf345<span class="ls13">\ue974\ue973</span></span><span class="wsf">\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank"> </span>\ue972<span class="ff4 ws1e"> </span></span></span></div><div class="t m0 x1 hf y23 ff4 fs3 fc0 sc0 ls22 ws1e">Como la exponencial<span class="blank _5"></span> siempre t<span class="blank _5"></span>oma valores po<span class="blank _5"></span>sitivos, l<span class="blank _5"></span>a ecuación anterior <span class="blank _5"></span>es equivalente a </div><div class="t m0 x1 h13 y24 ff7 fs3 fc0 sc0 ls22 ws10">\uf346\ue975\ued54<span class="blank"> </span><span class="fs0 ls14 v4">\uf136</span><span class="lsc">\uf345<span class="ls13 ws11">\ue974\ue973<span class="blank"> </span></span></span><span class="ws12">\uf34c<span class="blank"> </span>\ue972<span class="ff4 ws1e"> </span></span></div><div class="t m0 x1 h13 y25 ff7 fs3 fc0 sc0 ls22 ws10">\uf346\ued54<span class="blank"> </span><span class="fs0 ls15 v4">\uf136</span><span class="ws13">\uf345<span class="blank"> </span>\ue979<span class="blank _3"> </span>\uf34c<span class="blank _6"> </span>\ue972<span class="ff4 ws1e"> </span></span></div><div class="t m0 x1 h12 y26 ff7 fs3 fc0 sc0 ls22 ws14">\ue801\ued54<span class="blank"> </span>\ue801<span class="blank _3"> </span>\uf34c<span class="blank _6"> </span><span class="ws6 v6">\ue9be</span><span class="ls13">\ue979</span><span class="ff4 ws1e"> </span></div><div class="t m0 x1 h12 y27 ff7 fs3 fc0 sc0 ls22 ws8">\ued54<span class="blank _6"> </span>\uf34c<span class="blank"> </span>\ue603<span class="blank"> </span><span class="ws6 v6">\ue9be</span><span class="ls13">\ue979</span><span class="ff4 ws1e">, </span>\ued54<span class="blank _7"> </span>\uf34c<span class="blank"> </span>\ue603<span class="blank"> </span>\uf346<span class="ws6 v6">\ue9be</span><span class="ls13">\ue979</span><span class="ff4 ws1e"> </span></div><div class="t m0 x1 h12 y28 ff4 fs3 fc0 sc0 ls22 ws1e">Luego, el conjunt<span class="blank _5"></span>o de ceros de la deri<span class="blank _5"></span>vada es <span class="ff7">\ued25</span></div><div class="t m0 xf h14 y29 ff7 fs0 fc0 sc0 ls16">\uf134<span class="fs3 ls22 ws6 v7">\udb80\udddb<span class="lsd v6">\ued42</span></span><span class="ls17 v8">\udb80\udd92</span><span class="fs3 ls2 v7">\udb80\udddc<span class="ls18 v6">\uf34c<span class="ls19 v6">\uf35b</span><span class="ls1a">\uf346<span class="ls22 ws6 v6">\ue9be</span><span class="ls22 ws15">\ue979\ue7e2<span class="blank"> </span><span class="ws6 v6">\ue9be</span><span class="ls13">\ue979<span class="ls19 v6">\uf35f</span></span><span class="ws6">\ue7e4<span class="ff4 ws1e"> </span></span></span></span></span></span></div><div class="t m0 x1 h12 y2a ff4 fs3 fc0 sc0 ls22 ws1e">Evaluamos <span class="ff7 ws6">\ued42\ueb22</span> en alg<span class="blank _5"></span>ún punto del c<span class="blank _5"></span>onjunto <span class="ff7 ws6 v6">\uf36b</span><span class="ff7 ws16">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346<span class="ws6 v6">\ue9be</span><span class="ls13">\ue979</span><span class="ws6 v6">\uf36f</span></span> para <span class="blank _5"></span>ver su sign<span class="blank _5"></span>o: </div><div class="t m0 x1 h15 y2b ff7 fs3 fc0 sc0 ls3">\ued42<span class="fs0 ls4 v4">\udb80\udd92</span><span class="ls22 ws6 v3">\udb80\udddb<span class="v6">\uf346\ue975</span><span class="ls1b">\udb80\udddc</span></span><span class="ls18">\uf34c<span class="fs2 ls7">\ued41<span class="fs7 ls25 ws9 v4">\ue974\ue979<span class="ls22 ws4">\uf346<span class="ls25 ws17">\ue978\ue975<span class="blank"> </span></span></span></span></span><span class="ls1c">\ue7e4<span class="ls22 ws6 v3">\udb80\udddb</span><span class="ls22 ws18">\uf346\ue975\ue7e4\ue97b<span class="blank"> </span>\uf345<span class="blank"> </span><span class="ls13">\ue974\ue973<span class="ls2 v3">\udb80\udddc</span></span><span class="ws19">\uf34f<span class="blank"> </span>\ue972<span class="ff4 ws1e">, luego, </span><span class="ws6">\ued42\ueb22<span class="ff4 ws1e"> es negati<span class="blank _5"></span>va en <span class="ff7 ws6 v6">\uf36b</span><span class="ff7 ws16">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346<span class="ws6 v6">\ue9be</span><span class="ls13">\ue979</span><span class="ws6 v6">\uf36f</span></span>. </span></span></span></span></span></span></div><div class="t m0 x1 h12 y2c ff4 fs3 fc0 sc0 ls22 ws1e">Análogamente, en el<span class="blank _5"></span> interv<span class="blank _5"></span>alo <span class="ff7 ws6 v6">\uf36b</span><span class="ff7 ls1d">\uf346<span class="ls22 ws6 v6">\ue9be</span><span class="ls22 ws16">\ue979\ue7e2<span class="blank"> </span><span class="ws6 v6">\ue9be</span><span class="ls13">\ue979</span><span class="ws6 v6">\uf36f<span class="v0">\ue7e3</span></span></span></span> </div><div class="t m0 x1 h15 y2d ff7 fs3 fc0 sc0 ls3">\ued42<span class="fs0 ls4 v4">\udb80\udd92</span><span class="ls22 ws6 v3">\udb80\udddb<span class="v6">\ue972</span><span class="ls6">\udb80\udddc</span></span><span class="ls18">\uf34c<span class="fs2 ls7">\ued41<span class="fs7 ls1e v4">\ue972</span></span><span class="ls1c">\ue7e4<span class="ls22 ws6 v3">\udb80\udddb</span><span class="ls22 ws1a">\ue972<span class="blank"> </span>\uf345<span class="blank"> </span><span class="ls13">\ue974\ue973<span class="ls2 v3">\udb80\udddc</span></span></span></span>\uf34c<span class="ls13 ws1b">\ue974\ue973<span class="blank"> </span></span><span class="ls22 ws1c">\uf350<span class="blank"> </span>\ue972<span class="ff4 ws1e">, por l<span class="blank _5"></span>o que <span class="ff7 ws6">\ued42\ueb22</span> es positi<span class="blank _5"></span>va en <span class="ff7 ws6 v6">\uf36b</span><span class="ff7 ls1a">\uf346<span class="ls22 ws6 v6">\ue9be</span><span class="ls22 ws16">\ue979\ue7e2<span class="blank"> </span><span class="ws6 v6">\ue9be<span class="blank _5"></span><span class="ls13 v3">\ue979<span class="ls22 v6">\uf36f<span class="ff4 ws1e v0">. </span></span></span></span></span></span></span></span></span></div><div class="t m0 x1 h12 y2e ff4 fs3 fc0 sc0 ls22 ws1e">En <span class="ff7 ws6 v6">\uf36b<span class="v6">\ue9be</span></span><span class="ff7 ws16">\ue979\ue7e2<span class="blank"> </span>\uf345\ue9bb<span class="ws6 v6">\uf36f</span></span> la derivada e<span class="blank _5"></span>s nuevame<span class="blank _5"></span>nte negativa ya qu<span class="blank _5"></span>e, por ej<span class="blank _5"></span>emplo, </div><div class="t m0 x1 h15 y2f ff7 fs3 fc0 sc0 ls3">\ued42<span class="fs0 ls4 v4">\udb80\udd92</span><span class="ls22 ws6 v3">\udb80\udddb<span class="v6">\ue975</span><span class="ls6">\udb80\udddc</span></span><span class="ls18">\uf34c<span class="fs2 ls7">\ued41<span class="fs7 ls22 ws4 v4">\uf346<span class="ls25 ws9">\ue974\ue979</span>\uf345<span class="ls25 ws1d">\ue978\ue975<span class="blank"> </span></span></span></span><span class="ls1c">\ue7e4<span class="ls22 ws6 v3">\udb80\udddb</span><span class="ls22 ws18">\uf346\ue975\ue7e4\ue97b<span class="blank"> </span>\uf345<span class="blank"> </span><span class="ls13">\ue974\ue973<span class="ls2 v3">\udb80\udddc</span></span><span class="ws19">\uf34f<span class="blank"> </span>\ue972<span class="ff4 ws1e">. </span></span></span></span></span></div><div class="t m0 x1 h12 y30 ff4 fs3 fc0 sc0 ls22 ws1e">De esta forma, p<span class="blank _5"></span>or el criter<span class="blank _5"></span>io de la derivada el in<span class="blank _5"></span>terval<span class="blank _5"></span>o de crecimien<span class="blank _5"></span>to de la función <span class="ff7 ls1f">\ued42</span> es <span class="ff7 ls20 v6">\uf36b</span><span class="ff7 ls1a">\uf346<span class="ls22 ws6 v6">\ue9be</span><span class="ls22 ws15">\ue979\ue7e2<span class="blank"> </span><span class="ws6 v6">\ue9be</span><span class="ls13">\ue979</span><span class="ws6 v6">\uf36f</span></span></span> y los inter<span class="blank _5"></span>valos de </div><div class="t m0 x1 h12 y31 ff4 fs3 fc0 sc0 ls22 ws1e">decrecimiento s<span class="blank _5"></span>on <span class="ff7 ws6 v6">\uf36b</span><span class="ff7 ws16">\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346<span class="ws6 v6">\ue9be</span><span class="ls13">\ue979</span><span class="ws6 v6">\uf36f</span></span><span class="ls21"> <span class="ls28">y <span class="ff7 ls20 v6">\uf36b</span></span></span><span class="ff7 ws6 v6">\ue9be<span class="blank _5"></span><span class="ws16 v3">\ue979\ue7e2<span class="blank"> </span>\uf345\ue9bb<span class="ws6 v6">\uf36f<span class="v0">\ue7e4<span class="ff4 ws1e"> Ade<span class="blank _5"></span>más, como la funci<span class="blank _5"></span>ón decrece a la<span class="blank _5"></span> izquierda de -</span></span></span></span></span></div><div class="t m0 x10 h16 y32 ff7 fs3 fc0 sc0 ls22 ws6">\ue9be<span class="ls13 v3">\ue979</span><span class="ff4 ws1e v3"> y crece a su d<span class="blank _5"></span>erecha, </span></div><div class="t m0 x1 h12 y33 ff4 fs3 fc0 sc0 ls22 ws1e">entonces <span class="ff7 ws7">\ued54<span class="blank"> </span>\uf34c<span class="blank"> </span>\uf346<span class="ws6 v6">\ue9be<span class="v3">\ue979</span></span></span> es un mínimo relativ<span class="blank _5"></span>o; y como <span class="ff7 ls1f">\ued42</span> crece<span class="blank _5"></span> a la izquierd<span class="blank _5"></span>a de <span class="ff7 ws6 v6">\ue9be</span><span class="ff7 ls13">\ue979</span> y decrece a su d<span class="blank _5"></span>erecha, la abscisa <span class="blank _5"></span><span class="ff7 ws7">\ued54<span class="blank _6"> </span>\uf34c<span class="blank"> </span><span class="ws6 v6">\ue9be</span><span class="ls13">\ue979</span><span class="ff4 ws1e"> </span></span></div><div class="t m0 x1 hf y34 ff4 fs3 fc0 sc0 ls22 ws1e">es un máximo relati<span class="blank _5"></span>vo. </div><div class="t m0 x1 h17 y35 ff5 fs3 fc0 sc0 ls22 ws1e"> <span class="blank _8"> </span> </div></div><div class="c x1 y36 w8 h18"><div class="t m0 x11 h2 y37 ff2 fs0 fc0 sc0 ls22 ws1e">APELLIDO: </div></div><div class="c x12 y38 w9 h19"><div class="t m0 xb h2 y39 ff2 fs0 fc0 sc0 ls22 ws1e">CALIFICACIÓN:<span class="blank _5"></span> </div></div><div class="c x1 y3a w8 h1a"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls22 ws1e">NOMBRE: </div></div><div class="c x1 y38 w8 h1a"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls22 ws1e">DNI (registrado en S<span class="blank _5"></span>IU Guaraní<span class="blank _5"></span>): </div></div><div class="c x1 y3b w8 h1b"><div class="t m0 xb h2 y10 ff2 fs0 fc0 sc0 ls22 ws1e">E-MAIL: </div></div><div class="c x12 y3c w9 h1c"><div class="t m0 xb h2 y3d ff2 fs0 fc0 sc0 ls22 ws1e">DOCENTE (nombre<span class="blank _5"></span> y apellido<span class="blank _5"></span>): </div></div><div class="c x1 y3e w8 h1a"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls22 ws1e">TEL: </div></div><div class="c x1 y3c w8 h1a"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 ls22 ws1e">AULA: </div></div><div class="c x0 y3f wa h1d"><div class="t m0 x11 hf y40 ff4 fs3 fc1 sc0 ls22 ws1e"><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 x0 y41 wb h1e" alt="" src="https://files.passeidireto.com/46e9e1ad-a4aa-4675-b347-4f90f436463f/bg2.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls22 ws1e">MATEMÁTICA (6<span class="ls23 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls29"> <span class="ls2a"> </span></span> FINAL </div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 ls22 ws1e">APELLIDO Y NOMB<span class="blank _5"></span>RE: <span class="blank _5"></span> <span class="blank _5"></span> <span class="blank _5"></span> <span class="blank _5"></span> DNI<span class="blank _5"></span>:<span class="ff1"> <span class="blank _9"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span>TEMA 2 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 ls22 ws1e">Hoja 2 de 4 </div><div class="t m0 x3 h2 y42 ff2 fs0 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x2 h2 y43 ff1 fs0 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h1f y44 ff3 fs2 fc0 sc0 ls22 ws1e">2. Calcular la siguiente integral<span class="ff7 ws1f v6">\uebec</span><span class="ff7 ws20">\uf36b\uee9e\ue7e4<span class="blank"> </span><span class="ls2b v0">\ue9be<span class="v6">\uee9e</span><span class="fs7 ls2c v9">\uf0db</span></span><span class="ws21">\uf345<span class="blank _3"> </span>\uf0de\uf36f<span class="blank"> </span><span class="ls36 ws22">\uee8a\uee9e</span></span></span> </div><div class="t m0 x1 h6 y45 ff3 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 hf y46 ff4 fs3 fc0 sc0 ls22 ws1e">Para <span class="blank"> </span>resolver <span class="blank"> </span>est<span class="blank _5"></span>os <span class="blank"> </span>ejercicios <span class="blank"> </span>se <span class="blank"> </span>tendrán <span class="blank"> </span>en <span class="blank"> </span>cuent<span class="blank _5"></span>a <span class="blank"> </span>los <span class="blank"> </span>temas <span class="blank"> </span>abordad<span class="blank _5"></span>os <span class="blank"> </span>durante <span class="blank"> </span>todo <span class="blank"> </span>el <span class="blank"> </span>cuatrimest<span class="blank _5"></span>re: <span class="blank"> </span>Funciones- </div><div class="t m0 x1 hf y47 ff4 fs3 fc0 sc0 ls22 ws1e">Operaciones con p<span class="blank _5"></span>olinomios- Integrales<span class="blank _5"></span> inmediatas- Integ<span class="blank _5"></span>rales por sustituci<span class="blank _5"></span>ón. </div><div class="t m0 x13 h13 y48 ff4 fs3 fc0 sc0 ls22 ws1e">Designamos a: <span class="blank _5"></span><span class="ff7 ws7">\ued50<span class="blank _6"> </span>\uf34c<span class="blank"> </span>\uee9e<span class="fs0 ls2d v4">\uf0db</span><span class="ws23">\uf345<span class="blank"> </span>\uf0de<span class="ff8 ls21 ws1e"> <span class="ff4 ls22">y luego derivam<span class="blank _5"></span>os la expresi<span class="blank _5"></span>ón<span class="ff8">: </span></span></span></span></span></div><div class="t m0 x14 h12 y49 ff7 fs3 fc0 sc0 ls37 ws24">\ued40\ued50<span class="blank"> </span><span class="ls22 ws25">\uf34c<span class="blank _3"> </span>\ue974\ued54<span class="blank"> </span>\ue603</span><span class="ws26">\ued40\ued54<span class="blank"> </span><span class="ff4 ls22 ws1e"> </span></span></div><div class="t m0 x15 h12 y4a ff7 fs3 fc0 sc0 ls37">\ued40\ued50</div><div class="t m0 x16 h20 y4b ff7 fs3 fc0 sc0 ls2e">\ue974<span class="ls22 ws14 v2">\uf34c<span class="blank _3"> </span>\ued54<span class="blank"> </span>\ue603</span><span class="ls37 ws27 v2">\ued40\ued54<span class="blank"> </span></span><span class="ff4 ls22 ws1e v2"> </span></div><div class="t m0 x13 h21 y4c ff8 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x13 hf y4d ff4 fs3 fc0 sc0 ls22 ws1e">Vemos que: </div><div class="t m0 x17 h22 y4e ff7 fs3 fc0 sc0 ls22 ws14">\uf3b1<span class="blank _a"> </span>\ued54<span class="blank"> </span>\ue7e4<span class="blank _a"> </span><span class="ws6 va">\uf3a5</span><span class="lsa">\ued54<span class="fs0 ls2f v9">\uf136</span></span><span class="ws23">\uf345<span class="blank"> </span>\ue977\ue603<span class="ls37 ws28">\ued40\ued54<span class="blank"> </span></span><span class="ws29">\uf34c<span class="blank _3"> </span>\uf3b1<span class="blank"> </span><span class="ws6 vb">\ue9be</span><span class="ws2a">\ued50<span class="blank _b"> </span>\ue603<span class="blank"> </span><span class="ls37 vc">\ued40\ued50</span></span></span></span></div><div class="t m0 x18 h23 y4f ff7 fs3 fc0 sc0 ls30">\ue974<span class="ff4 ls22 ws1e v2"> </span></div><div class="t m0 x19 h22 y50 ff7 fs3 fc0 sc0 ls22 ws25">\uf3b1<span class="blank _a"> </span>\ued54<span class="blank"> </span>\ue7e4<span class="blank _a"> </span><span class="ws6 va">\uf3a5</span><span class="lsa">\ued54<span class="fs0 lsb v9">\uf136</span></span><span class="ws2b">\uf345<span class="blank"> </span>\ue977\ue603<span class="ls37 ws28">\ued40\ued54<span class="blank"> </span><span class="ls18">\uf34c</span></span><span class="vc">\ue973</span></span></div><div class="t m0 x1a h24 y51 ff7 fs3 fc0 sc0 ls31">\ue974<span class="ls22 ws2c v2">\uf3b1<span class="blank _a"> </span>\ued50<span class="blank"> </span></span><span class="fs0 ls22 ws2d vd">\uf135\ue800\uf136<span class="blank"> </span></span><span class="ls22 ws6 v2">\ue603</span><span class="ls37 ws2e v2">\ued40\ued50</span><span class="ff4 ls22 ws1e v2"> </span></div><div class="t m0 x1b h22 y52 ff7 fs3 fc0 sc0 ls22 ws25">\uf3b1<span class="blank _a"> </span>\ued54\ue7e4<span class="blank _c"> </span><span class="ls32 va">\uf3a5</span><span class="lsa">\ued54<span class="fs0 ls15 v9">\uf136</span></span><span class="ws2b">\uf345<span class="blank"> </span>\ue977\ue603<span class="ls37 ws28">\ued40\ued54<span class="blank"> </span><span class="ls18">\uf34c</span></span><span class="vc">\ue973</span></span></div><div class="t m0 x1c h25 y53 ff7 fs3 fc0 sc0 ls31">\ue974<span class="ls33 v2">\ue7e4</span><span class="ls34 ve">\ued50</span><span class="fs0 ls22 ws2f vf">\uf137\ue800\uf136</span></div><div class="t m0 x1d h12 y54 ff7 fs3 fc0 sc0 ls22">\ue975</div><div class="t m0 x1d h26 y55 ff7 fs3 fc0 sc0 ls35">\ue974<span class="ls22 ws30 v10">\uf345<span class="blank _4"> </span>\ued25<span class="blank"> </span><span class="ff4 ws1e"> </span></span></div><div class="t m0 x13 hf y56 ff4 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 hf y57 ff4 fs3 fc0 sc0 ls22 ws1e">Volvemos a realizar la<span class="blank _5"></span> sustitución c<span class="blank _5"></span>orrespondient<span class="blank _5"></span>e y nos queda<span class="blank _5"></span>: </div><div class="t m0 x1e h22 y58 ff7 fs3 fc0 sc0 ls22 ws14">\uf3b1<span class="blank _a"> </span>\ued54<span class="blank"> </span>\ue7e4<span class="blank _a"> </span><span class="ws6 va">\uf3a5</span><span class="lsa">\ued54<span class="fs0 ls15 v9">\uf136</span></span><span class="ws23">\uf345<span class="blank"> </span>\ue977\ue603<span class="ls37 ws31">\ued40\ued54<span class="blank"> </span><span class="ls18">\uf34c</span></span><span class="vc">\ue973</span></span></div><div class="t m0 x1f h27 y59 ff7 fs3 fc0 sc0 ls31">\ue974<span class="ls1c v2">\ue7e4</span><span class="ls22 ve">\ue974</span></div><div class="t m0 x20 h28 y59 ff7 fs3 fc0 sc0 ls31">\ue975<span class="ls22 ws6 v2">\udb80\udddb</span><span class="lsa v2">\ued54</span><span class="fs0 lsb vd">\uf136</span><span class="ls22 ws23 v2">\uf345<span class="blank"> </span>\ue977</span><span class="ls22 ws6 v2">\udb80\udddc<span class="fs0 v11">\uf137</span></span></div><div class="t m0 x21 h29 y5a ff7 fs0 fc0 sc0 ls15">\uf136<span class="fs3 ls22 ws30 v12">\uf345<span class="blank _4"> </span>\ued25<span class="blank"> </span><span class="ff4 ws1e"> </span></span></div><div class="t m0 x1 hf y5b ff4 fs3 fc0 sc0 ls22 ws1e">Por lo tanto: </div><div class="t m0 x22 h22 y5c ff7 fs3 fc0 sc0 ls22 ws14">\uf3b1<span class="blank _a"> </span>\ued54<span class="blank"> </span>\ue7e4<span class="blank _a"> </span><span class="ws6 va">\uf3a5</span><span class="lsa">\ued54<span class="fs0 ls15 v9">\uf136</span></span><span class="ws23">\uf345<span class="blank"> </span>\ue977\ue603<span class="ls37 ws28">\ued40\ued54<span class="blank"> </span><span class="ls18">\uf34c</span></span><span class="vc">\ue973</span></span></div><div class="t m0 x23 h28 y5d ff7 fs3 fc0 sc0 ls31">\ue975<span class="ls1c v2">\ue7e4</span><span class="ls22 ws6 v2">\udb80\udddb</span><span class="lsa v2">\ued54</span><span class="fs0 lsb vd">\uf136</span><span class="ls22 ws23 v2">\uf345<span class="blank"> </span>\ue977</span><span class="ls22 ws6 v2">\udb80\udddc<span class="fs0 v11">\uf137</span></span></div><div class="t m0 x24 h29 y5e ff7 fs0 fc0 sc0 ls15">\uf136<span class="fs3 ls22 ws30 v12">\uf345<span class="blank _4"> </span>\ued25<span class="blank"> </span><span class="ff5 ws1e"> </span></span></div><div class="t m0 x1 h6 y5f ff3 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h4 y60 ff3 fs2 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h4 y61 ff3 fs2 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h6 y62 ff3 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x13 h17 y63 ff5 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x13 hf y64 ff4 fs3 fc0 sc0 ls22 ws1e"> <span class="blank _d"> </span> </div></div><div class="c x0 y3f wa h1d"><div class="t m0 x11 hf y40 ff4 fs3 fc1 sc0 ls22 ws1e"><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="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y65 wc h2a" alt="" src="https://files.passeidireto.com/46e9e1ad-a4aa-4675-b347-4f90f436463f/bg3.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls22 ws1e">MATEMÁTICA (6<span class="ls23 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls29"> <span class="ls2a"> </span></span>FINAL </div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 ls22 ws1e">APELLIDO Y NOMB<span class="blank _5"></span>RE: <span class="blank _5"></span> <span class="blank _5"></span> <span class="blank _5"></span> <span class="blank _5"></span> DNI<span class="blank _5"></span>:<span class="ff1"> <span class="blank _9"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span>TEMA 2 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 ls22 ws1e">Hoja 3 de 4 </div><div class="t m0 x3 h2 y42 ff2 fs0 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 hf y66 ff4 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h4 y67 ff3 fs2 fc0 sc0 ls7 ws32">3.<span class="ls38 ws1e"> <span class="fs3 ls22">¿Cuántas<span class="blank _5"></span> palabras dist<span class="blank _5"></span>intas, con o s<span class="blank _5"></span>in sentido, se<span class="blank _5"></span> pueden forma<span class="blank _5"></span>r con las letras<span class="blank _5"></span> de la pala<span class="blank _5"></span>bra </span></span></div><div class="t m0 x1 h6 y68 ff9 fs3 fc0 sc0 ls22 ws1e">\u201cSOMBRA<span class="blank _5"></span>S\u201d si deben termina<span class="blank _5"></span>r con la letra<span class="blank _5"></span> \u201cO\u201d?<span class="ff3"> </span></div><div class="t m0 x1 h4 y38 ff3 fs2 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h4 y69 ff3 fs2 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 hf y6a ffa fs3 fc0 sc0 ls22 ws1e">Buscamos <span class="blank _2"> </span>utilizar <span class="blank _2"> </span>las <span class="blank _2"> </span>7 <span class="blank _e"> </span>letras de <span class="blank _e"> </span>la <span class="blank _2"> </span>palabra <span class="blank _2"> </span>\u201cSOMBRAS\u201d <span class="blank _2"> </span>para <span class="blank _2"> </span>armar <span class="blank _2"> </span>los <span class="blank _2"> </span>nuevos <span class="blank _2"> </span>vocablos <span class="blank _2"> </span>(independientemen<span class="blank _5"></span>te <span class="blank _2"> </span>de <span class="blank _e"> </span>si <span class="blank _2"> </span>éstos </div><div class="t m0 x1 hf y6b ff4 fs3 fc0 sc0 ls22 ws1e">tienen <span class="blank _e"> </span>o <span class="blank _f"> </span>no <span class="blank _e"> </span>sentido <span class="blank _e"> </span>en <span class="blank _f"> </span>nuestr<span class="blank _5"></span>o <span class="blank _e"> </span>idioma). <span class="blank _e"> </span>Po<span class="blank _2"> </span>r <span class="blank _e"> </span>otra <span class="blank _f"> </span>par<span class="blank _5"></span>te, <span class="blank _e"> </span>importa <span class="blank _e"> </span>el <span class="blank _f"> </span>orden <span class="blank _e"> </span>en <span class="blank _e"> </span>que <span class="blank _f"> </span>se <span class="blank _e"> </span>eligen <span class="blank _e"> </span>las <span class="blank _e"> </span>letras <span class="blank _f"> </span>para <span class="blank _e"> </span>formar <span class="blank _e"> </span>dichos </div><div class="t m0 x1 hf y6c ff4 fs3 fc0 sc0 ls22 ws1e">términos. Lueg<span class="blank _5"></span>o, estamos ante un cas<span class="blank _5"></span>o de permutaci<span class="blank _5"></span>ón o reordena<span class="blank _5"></span>miento de el<span class="blank _5"></span>ementos. </div><div class="t m0 x1 hf y6d ffa fs3 fc0 sc0 ls22 ws1e">Siendo <span class="blank _e"> </span>además <span class="blank _2"> </span>que <span class="blank _e"> </span>buscamos <span class="blank _e"> </span>palabras <span class="blank _2"> </span>que <span class="blank _e"> </span>finalizan <span class="blank _e"> </span>con <span class="blank _e"> </span>la <span class="blank _e"> </span>letra <span class="blank _2"> </span>\u201cO\u201d, <span class="blank _e"> </span>en <span class="blank _e"> </span>lugar <span class="blank _2"> </span>de <span class="blank _f"> </span>per<span class="blank _5"></span>mutar <span class="blank _e"> </span>los <span class="blank _2"> </span>7 <span class="blank _e"> </span>caracteres <span class="blank _e"> </span>disponibles<span class="blank _5"></span>, </div><div class="t m0 x1 hf y6e ff4 fs3 fc0 sc0 ls22 ws1e">debemos reordenar<span class="blank _5"></span> solo 6 de ellos, aqu<span class="blank _5"></span>ellos que justa<span class="blank _5"></span>mente ocupan<span class="blank _5"></span> las posiciones 1 a 6 dentro de<span class="blank _5"></span> cada nueva palabra.<span class="blank _5"></span> </div><div class="t m0 x1 hf y6f ff4 fs3 fc0 sc0 ls22 ws1e">Por otra parte, re<span class="blank _5"></span>cordemos qu<span class="blank _5"></span>e: </div><div class="t m0 x25 hf y70 ff4 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 hf y71 ffa fs3 fc0 sc0 ls22 ws1e">Luego,como hay 2 l<span class="blank _5"></span>etras \u201cS\u201d disponibles<span class="blank _5"></span> entre las <span class="blank _5"></span>6 a reordenar,<span class="blank _5"></span> tendremos: <span class="ff4"> </span></div><div class="t m0 x26 h12 y72 ff7 fs3 fc0 sc0 ls22">\ued32</div><div class="t m0 x27 h2b y73 ff7 fs0 fc0 sc0 ls22">\uf13a</div><div class="t m0 x28 h2c y74 ff7 fs0 fc0 sc0 ls22 ws33">\uf136\ue7e1\uf135\ue7e1\uf135\ue7e1\uf135\ue7e1\uf135<span class="blank"> </span><span class="fs3 ls39 v13">\uf34c</span><span class="fs3 ws6 v14">\ue978\ue7e8</span></div><div class="t m0 x1e h27 y75 ff7 fs3 fc0 sc0 ls22 ws34">\ue974\ue7e8<span class="blank"> </span>\ue973\ue7e8<span class="blank"> </span>\ue973\ue7e8<span class="blank"> </span>\ue973\ue7e8<span class="blank"> </span>\ue973\ue7e8<span class="blank _6"> </span><span class="ls3a v2">\uf34c</span><span class="ws6 ve">\ue978\ue7e4\ue977\ue7e4\ue976\ue7e4\ue975\ue7e4\ue974\ue7e8</span></div><div class="t m0 x29 h20 y75 ff7 fs3 fc0 sc0 ls22 ws35">\ue974\ue7e8<span class="blank"> </span><span class="ws7 v2">\uf34c<span class="blank"> </span>\ue978\ue7e4\ue977\ue7e4\ue976\ue7e4\ue975<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="ls13 wsa">\ue975\ue978\ue972<span class="ff4 ls22 ws1e"> </span></span></span></div><div class="t m0 x1 h21 y76 ff4 fs3 fc0 sc0 ls22 ws1e">palabras distin<span class="blank _5"></span>tas que p<span class="blank _5"></span>ueden <span class="blank _5"></span>formarse <span class="blank _5"></span>con las <span class="blank _5"></span>7 letr<span class="blank _5"></span>as de la <span class="blank _5"></span>palabra <span class="ffb ws36">\u201cS<span class="blank _5"></span>OMBRAS<span class="blank _5"></span>\u201d<span class="ff4 ws1e"> y que <span class="blank _5"></span>además <span class="blank _5"></span>terminan<span class="blank _5"></span> con <span class="blank _5"></span>la l<span class="blank _5"></span>etra <span class="ffb ws36">\u201cO\u201d.<span class="blank _5"></span><span class="ff8 ws1e"> </span></span></span></span></div><div class="t m0 x1 h6 y77 ff3 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h4 y78 ff3 fs2 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h4 y79 ff3 fs2 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h4 y7a ff3 fs2 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h2d y7b ff8 fs2 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x13 hf y7c ff4 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x13 hf y7d ff4 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x13 hf y7e ff4 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h17 y7f ff5 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x13 hf y80 ff4 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h17 y81 ff5 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h17 y82 ff5 fs3 fc0 sc0 ls22 ws1e"> <span class="blank _8"> </span> </div></div><div class="c x0 y3f wa h1d"><div class="t m0 x11 hf y40 ff4 fs3 fc1 sc0 ls22 ws1e"><span class="fc2 sc0"> </span></div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y83 wb h2e" alt="" src="https://files.passeidireto.com/46e9e1ad-a4aa-4675-b347-4f90f436463f/bg4.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h17 y84 ff5 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h2 y85 ff1 fs0 fc0 sc0 ls22 ws1e">MATEMÁTICA (6<span class="blank _5"></span><span class="ls23 ws0">1)<span class="ff2 ls22 ws1e"> Cátedra A: <span class="blank _5"></span>NUÑEZ, <span class="blank _5"></span>MYRIAM<span class="ff1"> FI<span class="blank _5"></span>N<span class="ls3f ws37">AL</span> </span></span></span></div><div class="t m0 x1 h2 y86 ff2 fs0 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h2 y87 ff2 fs0 fc0 sc0 ls22 ws1e">APELLIDO Y NOMB<span class="blank _5"></span>RE: <span class="blank _5"></span> <span class="blank _5"></span> <span class="blank _5"></span> <span class="blank _5"></span> DNI<span class="blank _5"></span>:<span class="ff1"> <span class="blank _9"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span> <span class="blank _1"> </span>TEMA 2 </span></div><div class="t m0 x3 h2 y88 ff2 fs0 fc0 sc0 ls22 ws1e">Hoja 4 de 4 </div><div class="t m0 x3 h2 y89 ff2 fs0 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h2f y8a ff3 fs2 fc0 sc0 ls7">4<span class="ls38 ws1e">. <span class="fs3 ls22">Encontrar e<span class="blank _5"></span>l/los v<span class="blank _5"></span>alores de <span class="ff7 ws38">\uee91<span class="blank"> </span>\uebd0<span class="blank"> </span>\uee7e</span> para que e<span class="blank _5"></span>l <span class="ff7 ws6 v3">\ue801</span><span class="ff7 ls3b">\uee6d<span class="ls3c v3">\ue801</span><span class="ls22 ws39">\uf34c<span class="blank"> </span>\uf0e0</span></span> si <span class="ff7 ws3a">\uee6d<span class="blank"> </span>\uf34c<span class="blank"> </span>\udb80\udde1<span class="ws3b v15">\uee91<span class="blank"> </span>\uf0dc</span></span></span></span></div><div class="t m0 x2a h30 y8b ff7 fs3 fc0 sc0 ls22 ws23">\uf0da<span class="blank _10"> </span>\uee91<span class="blank"> </span>\uf345<span class="blank"> </span>\uf0dc<span class="ws6 v5">\udb80\udde2<span class="ff3 ws1e"> </span></span></div><div class="t m0 x1 h2d y8c ff8 fs2 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h4 y8d ff3 fs2 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x13 h10 y8e ff5 fs3 fc0 sc0 ls22 ws1e">Hallamos el dete<span class="blank _5"></span>rminante de <span class="ff7 ws3c">\ued23<span class="blank _3"> </span>\uf34c<span class="blank _6"> </span>\ued47<span class="ws6 v3">\udb80\udddb</span><span class="ws3d">\ued47<span class="blank _3"> </span>\uf345<span class="blank"> </span>\ue975<span class="ls3d v3">\udb80\udddc</span><span class="ws3e">\uf346<span class="blank _4"> </span>\ue975<span class="blank _6"> </span>\uf34c<span class="blank _3"> </span>\ued47<span class="blank"> </span><span class="fs0 ls3e v4">\uf136</span><span class="ws23">\uf345<span class="blank"> </span>\ue975\ued47<span class="blank _3"> </span>\uf346<span class="blank"> </span>\ue975</span></span></span></span> </div><div class="t m0 x26 h13 y8f ff7 fs3 fc0 sc0 ls22 ws3e">\udb80\udddb\ued47<span class="blank"> </span><span class="fs0 ls15 v4">\uf136</span><span class="ws23">\uf345<span class="blank"> </span>\ue975\ued47<span class="blank"> </span>\uf346<span class="blank"> </span>\ue975<span class="blank _6"> </span>\uf34c<span class="blank _3"> </span>\ue979\udb80\udddc<span class="blank _6"> </span>\ueb5c<span class="blank _3"> </span>\udb80\udddb\ued47<span class="blank _e"> </span><span class="fs0 ls2f v4">\uf136</span>\uf345<span class="blank"> </span>\ue975\ued47<span class="blank _3"> </span>\uf346<span class="blank"> </span><span class="ls13 ws11">\ue973\ue972<span class="blank"> </span></span><span class="ws3f">\uf34c<span class="blank"> </span>\ue972\udb80\udddc<span class="blank"> </span>\ueb5c<span class="blank"> </span><span class="fc3 ws40">\ued47<span class="blank"> </span>\uf34c<span class="blank _3"> </span>\ue974\ue7e1<span class="blank _c"> </span>\ued47<span class="blank"> </span>\uf34c<span class="blank _3"> </span>\uf346\ue977<span class="ff5 ws1e"> </span></span></span></span></div><div class="t m0 x13 h17 y90 ff5 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h6 y91 ff3 fs3 fc0 sc0 ls22 ws1e">Referencia: Un<span class="blank _5"></span>idad 9: Sistema<span class="blank _5"></span> de ecuaciones<span class="blank _5"></span> y<span class="blank _5"></span> matrices </div><div class="t m0 x1 h6 y92 ff3 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h6 y93 ff3 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h6 y94 ff3 fs3 fc0 sc0 ls22 ws1e"> </div><div class="t m0 x1 h17 y95 ff5 fs3 fc0 sc0 ls22 ws1e"> </div></div><div class="c x0 y96 wa h31"><div class="t m0 x11 hf y40 ff4 fs3 fc1 sc0 ls22 ws1e"><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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