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la cuevadel empollón
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4

2,5 puntos
Análisis

Responda al apartado 4.1 o al apartado 4.2

Consideremos la función real de variable real f(x)=x+1x2+1f(x)=\frac{x+1}{x^2+1}. Se pide:
4.1.1
Hallar el dominio y estudiar la continuidad de la función ff.0,5 pts
4.1.2
Hallar las asíntotas y los intervalos de crecimiento y decrecimiento de la función ff.0,5 pts
4.1.3
Calcular, si existen, los valores máximos y mínimos relativos y absolutos de la función ff.1 pt
4.1.4
Representar la función ff.0,5 pts
Un decorador desea pintar una pared rectangular de 1212 metros de largo por 33 de alto. Para ello supone que la esquina inferior izquierda de la pared corresponde al origen de coordenadas de un plano y pinta en la pared la curva de ecuación f(x)=cos⁡(πx9)+2.f(x)=\cos\left(\frac{\pi x}{9}\right)+2. A continuación, el decorador colorea en rojo la parte de la pared que queda por encima de la curva y en verde la que queda por debajo. Se pide:
4.2.1
Dibujar la parte de la curva anterior que corresponde a la pared, detallando los cortes con los ejes, los extremos absolutos, y la monotonía de la función en el intervalo [0,12][0, 12].1,25 pts
4.2.2
Calcular el área de la pared que tiene color verde y la que tiene color rojo.1 pt
4.2.3
La parte verde se pinta usando botes de pintura capaces de cubrir 33 metros cuadrados cada uno. ¿Cuál es el mínimo número de botes que vamos a necesitar para pintar la parte verde?0,25 pts

Formulario

Mostrar
Tabla de la distribución binomial (Bin⁡(n,p)\operatorname{Bin}(n,p))F(x)=P(X≤x)=∑k=0x(nk)pkqn−k\begin{aligned}&F(x)=P(X\leq x)=\\&\sum_{k=0}^{x}\binom{n}{k}p^kq^{n-k}\end{aligned}
nnkkpp
0,010,050,100,200,250,301/31/30,350,400,450,50
100,99000,95000,90000,80000,75000,70000,66670,65000,60000,55000,5000
11,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,0000
200,98010,90250,81000,64000,56250,49000,44440,42250,36000,30250,2500
10,99990,99750,99000,96000,93750,91000,88890,87750,84000,79750,7500
21,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,0000
300,97030,85740,72900,51200,42190,34300,29630,27460,21600,16640,1250
10,99970,99280,97200,89600,84380,78400,74070,71830,64800,57480,5000
21,00000,99990,99900,99200,98440,97300,96300,95710,93600,90890,8750
31,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,0000
400,96060,81450,65610,40960,31640,24010,19750,17850,12960,09150,0625
10,99940,98600,94770,81920,73830,65170,59260,56300,47520,39100,3125
21,00000,99950,99630,97280,94920,91630,88890,87350,82080,75850,6875
31,00001,00000,99990,99840,99610,99190,98770,98500,97440,95900,9375
41,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,0000
500,95100,77380,59050,32770,23730,16810,13170,11600,07780,05030,0313
10,99900,97740,91850,73730,63280,52820,46090,42840,33700,25620,1875
21,00000,99880,99140,94210,89650,83690,79010,76480,68260,59310,5000
31,00001,00000,99950,99330,98440,96920,95470,94600,91300,86880,8125
41,00001,00001,00000,99970,99900,99760,99590,99470,98980,98150,9688
51,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,0000
600,94150,73510,53140,26210,17800,11760,08780,07540,04670,02770,0156
10,99850,96720,88570,65540,53390,42020,35120,31910,23330,16360,1094
21,00000,99780,98420,90110,83060,74430,68040,64710,54430,44150,3438
31,00000,99990,99870,98300,96240,92950,89990,88260,82080,74470,6563
41,00001,00000,99990,99840,99540,98910,98220,97770,95900,93080,8906
51,00001,00001,00000,99990,99980,99930,99860,99820,99590,99170,9844
61,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,0000
700,93210,69830,47830,20970,13350,08240,05850,04900,02800,01520,0078
10,99800,95560,85030,57670,44490,32940,26340,23380,15860,10240,0625
21,00000,99620,97430,85200,75640,64710,57060,53230,41990,31640,2266
31,00000,99980,99730,96670,92940,87400,82670,80020,71020,60830,5000
41,00001,00000,99980,99530,98710,97120,95470,94440,90370,84710,7734
51,00001,00001,00000,99960,99870,99620,99310,99100,98120,96430,9375
61,00001,00001,00001,00000,99990,99980,99950,99940,99840,99630,9922
71,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,0000
800,92270,66340,43050,16780,10010,05760,03900,03190,01680,00840,0039
10,99730,94280,81310,50330,36710,25530,19510,16910,10640,06320,0352
20,99990,99420,96190,79690,67850,55180,46820,42780,31540,22010,1445
31,00000,99960,99500,94370,88620,80590,74140,70640,59410,47700,3633
41,00001,00000,99960,98960,97270,94200,91210,89390,82630,73960,6367
51,00001,00001,00000,99880,99580,98870,98030,97470,95020,91150,8555
61,00001,00001,00000,99990,99960,99870,99740,99640,99150,98190,9648
71,00001,00001,00001,00001,00000,99990,99980,99980,99930,99830,9961
81,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,0000
900,91350,63020,38740,13420,07510,04040,02600,02070,01010,00460,0020
10,99660,92880,77480,43620,30030,19600,14310,12110,07050,03850,0195
20,99990,99160,94700,73820,60070,46280,37720,33730,23180,14950,0898
31,00000,99940,99170,91440,83430,72970,65030,60890,48260,36140,2539
41,00001,00000,99910,98040,95110,90120,85520,82830,73340,62140,5000
51,00001,00000,99990,99690,99000,97470,95760,94640,90060,83420,7461
61,00001,00001,00000,99970,99870,99570,99170,98880,97500,95020,9102
71,00001,00001,00001,00000,99990,99960,99900,99860,99620,99090,9805
81,00001,00001,00001,00001,00001,00000,99990,99990,99970,99920,9980
91,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,0000
1000,90440,59870,34870,10740,05630,02820,01730,01350,00600,00250,0010
10,99570,91390,73610,37580,24400,14930,10400,08600,04640,02330,0107
20,99990,98850,92980,67780,52560,38280,29910,26160,16730,09960,0547
31,00000,99900,98720,87910,77590,64960,55930,51380,38230,26600,1719
41,00000,99990,99840,96720,92190,84970,78690,75150,63310,50440,3770
51,00001,00000,99990,99360,98030,95270,92340,90510,83380,73840,6230
61,00001,00001,00000,99910,99650,98940,98030,97400,94520,89800,8281
71,00001,00001,00000,99990,99960,99840,99660,99520,98770,97260,9453
81,00001,00001,00001,00001,00000,99990,99960,99950,99830,99550,9893
91,00001,00001,00001,00001,00001,00001,00001,00000,99990,99970,9990
101,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,0000
1100,89530,56880,31380,08590,04220,01980,01160,00880,00360,00140,0005
10,99480,89810,69740,32210,19710,11300,07510,06060,03020,01390,0059
20,99980,98480,91040,61740,45520,31270,23410,20010,11890,06520,0327
31,00000,99840,98150,83890,71330,56960,47260,42560,29630,19110,1133
41,00000,99990,99720,94960,88540,78970,71100,66830,53280,39710,2744
51,00001,00000,99970,98830,96570,92180,87790,85130,75350,63310,5000
61,00001,00001,00000,99800,99240,97840,96140,94990,90060,82620,7256
71,00001,00001,00000,99980,99880,99570,99120,98780,97070,93900,8867
81,00001,00001,00001,00000,99990,99940,99860,99800,99410,98520,9673
91,00001,00001,00001,00001,00001,00000,99990,99980,99930,99780,9941
101,00001,00001,00001,00001,00001,00001,00001,00001,00000,99980,9995
111,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,0000
1200,88640,54040,28240,06870,03170,01380,00770,00570,00220,00080,0002
10,99380,88160,65900,27490,15840,08500,05400,04240,01960,00830,0032
20,99980,98040,88910,55830,39070,25280,18110,15130,08340,04210,0193
31,00000,99780,97440,79460,64880,49250,39310,34670,22530,13450,0730
41,00000,99980,99570,92740,84240,72370,63150,58330,43820,30440,1938
51,00001,00000,99950,98060,94560,88220,82230,78730,66520,52690,3872
61,00001,00000,99990,99610,98570,96140,93360,91540,84180,73930,6128
71,00001,00001,00000,99940,99720,99050,98120,97450,94270,88830,8062
81,00001,00001,00000,99990,99960,99830,99610,99440,98470,96440,9270
91,00001,00001,00001,00001,00000,99980,99950,99920,99720,99210,9807
101,00001,00001,00001,00001,00001,00001,00000,99990,99970,99890,9968
111,00001,00001,00001,00001,00001,00001,00001,00001,00000,99990,9998
121,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,0000
1300,87750,51330,25420,05500,02380,00970,00510,00370,00130,00040,0001
10,99280,86460,62130,23360,12670,06370,03850,02960,01260,00490,0017
20,99970,97550,86610,50170,33260,20250,13870,11320,05790,02690,0112
31,00000,99690,96580,74730,58430,42060,32240,27830,16860,09290,0461
41,00000,99970,99350,90090,79400,65430,55200,50050,35300,22790,1334
51,00001,00000,99910,97000,91980,83460,75870,71590,57440,42680,2905
61,00001,00000,99990,99300,97570,93760,89650,87050,77120,64370,5000
71,00001,00001,00000,99880,99440,98180,96530,95380,90230,82120,7095
81,00001,00001,00000,99980,99900,99600,99120,98740,96790,93020,8666
91,00001,00001,00001,00000,99990,99930,99840,99750,99220,97970,9539
101,00001,00001,00001,00001,00000,99990,99980,99970,99870,99590,9888
111,00001,00001,00001,00001,00001,00001,00001,00000,99990,99950,9983
121,00001,00001,00001,00001,00001,00001,00001,00001,00001,00000,9999
131,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,0000