Saltar al contenido
la cuevadel empollón
Volver al examen completo

1

2,5 puntos
Parte obligatoria
La potencia de pérdida P(t)P(t) (en vatios) en una máquina, debido a la fricción, depende del tiempo de uso tt (en años) según la función P(t)=4t1+t2P(t)=\dfrac{4t}{1+t^2} siendo t≥0t\geq 0.
a
Calcula en qué momento la potencia de pérdida es máxima.1,25 pts
b
La energía total perdida en los tt primeros años viene dada por la expresión E(t)=∫0tP(x) dxE(t)=\displaystyle\int_0^t P(x)\,dx (vatios por año). Calcula la energía total perdida en los tres primeros años.1,25 pts

Formulario

Mostrar
FUNCIÓN DE DISTRIBUCIÓN NORMAL N(0,1)\mathrm{N}(0,1)
Distribución normal N(0,1) Área P(Z ≤ z) bajo la curva normal desde menos infinito hasta z. N(0,1) P(Z ≤ z) −∞ 0 z +∞
zz0,000,01
0,00,50000,5040
0,10,53980,5438
0,20,57930,5832
0,30,61790,6217
0,40,65540,6591
0,50,69150,6950
0,60,72570,7291
0,70,75800,7611
0,80,78810,7910
0,90,81590,8186
1,00,84130,8438
1,10,86430,8665
1,20,88490,8869
1,30,90320,9049
1,40,91920,9207
1,50,93320,9345
1,60,94520,9463
1,70,95540,9564
1,80,96410,9649
1,90,97130,9719
2,00,97720,9778
2,10,98210,9826
2,20,98610,9864
2,30,98930,9896
2,40,99180,9920
2,50,99380,9940
2,60,99530,9955
2,70,996530,99664
2,80,997440,99752
2,90,998130,99819
3,00,998650,99869
3,10,999030,99906
3,20,999310,99934
3,30,999520,99953
3,40,999660,99968
3,50,999770,99978
3,60,999840,99985
3,70,999890,99990
3,80,999930,99993
3,90,999950,99995
4,00,999970,99997
zz0,020,03
0,00,50800,5120
0,10,54780,5517
0,20,58710,5910
0,30,62550,6293
0,40,66280,6664
0,50,69850,7019
0,60,73240,7357
0,70,76420,7673
0,80,79390,7967
0,90,82120,8238
1,00,84610,8485
1,10,86860,8708
1,20,88880,8907
1,30,90660,9082
1,40,92220,9236
1,50,93570,9370
1,60,94740,9484
1,70,95730,9582
1,80,96560,9664
1,90,97260,9732
2,00,97830,9788
2,10,98300,9834
2,20,98680,9871
2,30,98980,9901
2,40,99220,9925
2,50,99410,9943
2,60,99560,9957
2,70,996740,99683
2,80,997600,99767
2,90,998250,99831
3,00,998740,99878
3,10,999100,99913
3,20,999360,99938
3,30,999550,99957
3,40,999690,99970
3,50,999780,99979
3,60,999850,99986
3,70,999900,99990
3,80,999930,99994
3,90,999960,99996
4,00,999970,99997
zz0,040,05
0,00,51600,5199
0,10,55570,5596
0,20,59480,5987
0,30,63310,6368
0,40,67000,6736
0,50,70540,7088
0,60,73890,7422
0,70,77040,7734
0,80,79950,8023
0,90,82640,8289
1,00,85080,8531
1,10,87290,8749
1,20,89250,8944
1,30,90990,9115
1,40,92510,9265
1,50,93820,9394
1,60,94950,9505
1,70,95910,9599
1,80,96710,9678
1,90,97380,9744
2,00,97930,9798
2,10,98380,9842
2,20,98750,9878
2,30,99040,9906
2,40,99270,9929
2,50,99450,9946
2,60,99590,9960
2,70,996930,99702
2,80,997740,99781
2,90,998360,99841
3,00,998820,99886
3,10,999160,99918
3,20,999400,99942
3,30,999580,99960
3,40,999710,99972
3,50,999800,99981
3,60,999860,99987
3,70,999910,99991
3,80,999940,99994
3,90,999960,99996
4,00,999970,99997
zz0,060,07
0,00,52390,5279
0,10,56360,5675
0,20,60260,6064
0,30,64060,6443
0,40,67720,6808
0,50,71230,7157
0,60,74540,7486
0,70,77640,7794
0,80,80510,8078
0,90,83150,8340
1,00,85540,8577
1,10,87700,8790
1,20,89620,8980
1,30,91310,9147
1,40,92790,9292
1,50,94060,9418
1,60,95150,9525
1,70,96080,9616
1,80,96860,9693
1,90,97500,9756
2,00,98030,9808
2,10,98460,9850
2,20,98810,9884
2,30,99090,9911
2,40,99310,9932
2,50,99480,9949
2,60,99610,9962
2,70,997110,99720
2,80,997880,99795
2,90,998460,99851
3,00,998890,99893
3,10,999210,99924
3,20,999440,99946
3,30,999610,99962
3,40,999730,99974
3,50,999810,99982
3,60,999870,99988
3,70,999920,99992
3,80,999940,99995
3,90,999960,99996
4,00,999980,99998
zz0,080,09
0,00,53190,5359
0,10,57140,5753
0,20,61030,6141
0,30,64800,6517
0,40,68440,6879
0,50,71900,7224
0,60,75170,7549
0,70,78230,7852
0,80,81060,8133
0,90,83650,8389
1,00,85990,8621
1,10,88100,8830
1,20,89970,9015
1,30,91620,9177
1,40,93060,9319
1,50,94290,9441
1,60,95350,9545
1,70,96250,9633
1,80,96990,9706
1,90,97610,9767
2,00,98120,9817
2,10,98540,9857
2,20,98870,9890
2,30,99130,9916
2,40,99340,9936
2,50,99510,9952
2,60,99630,9964
2,70,997280,99736
2,80,998010,99807
2,90,998560,99861
3,00,998960,99900
3,10,999260,99929
3,20,999480,99950
3,30,999640,99965
3,40,999750,99976
3,50,999830,99983
3,60,999880,99989
3,70,999920,99992
3,80,999950,99995
3,90,999970,99997
4,00,999980,99998
Nota: En el interior de la tabla se da la probabilidad de que la variable aleatoria ZZ, con distribución N(0,1)\mathrm{N}(0,1), esté por debajo del valor zz.