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C2

3 puntos
Apartado C

Elige uno de los siguientes problemas y resuélvelo, justificando las respuestas:

En una empresa de mensajería, el coste de envío de un paquete, C(x)C(x) en euros, depende de su peso, xx en kilogramos, y se determina de la siguiente manera:C(x)={x2+Ax−Bsi0≤x<55Ax+4Bsi5≤x≤10C(x)=\begin{cases}x^2+Ax-B&\text{si}\quad 0\leq x<5\\[6pt]5Ax+4B&\text{si}\quad 5\leq x\leq 10\end{cases}
a
Calcular los valores de AA y BB para que C(x)C(x) sea una función continua y el coste de un paquete de 55 kilogramos sea de 3838 euros.1,5 pts
b
Para A=−8A=-8 y B=−15B=-15, determinar el área encerrada por la función C(x)C(x) y el eje OX\mathrm{OX} entre x=2x=2 y x=4x=4.1,5 pts

Formulario

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ANEXO TABLA DISTRIBUCIÓN NORMAL Tabla de distribución normal N(0,1)N(0,1) F(z)=P(Z≤z)F(z)=P(Z\leq z)
Curva normal con el área F(z) sombreada a la izquierda de z, situado a la derecha de 0, y los extremos del eje señalados con menos infinito y más infinito.
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
2,70,99650,9966
2,80,99740,9975
2,90,99810,9982
3,00,99870,9987
3,10,99900,9991
3,20,99930,9993
3,30,99950,9995
3,40,99970,9997
3,50,99980,9998
3,60,99980,9998
3,70,99990,9999
3,80,99990,9999
3,91,00001,0000
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
2,70,99670,9968
2,80,99760,9977
2,90,99820,9983
3,00,99870,9988
3,10,99910,9991
3,20,99940,9994
3,30,99950,9996
3,40,99970,9997
3,50,99980,9998
3,60,99990,9999
3,70,99990,9999
3,80,99990,9999
3,91,00001,0000
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
2,70,99690,9970
2,80,99770,9978
2,90,99840,9984
3,00,99880,9989
3,10,99920,9992
3,20,99940,9994
3,30,99960,9996
3,40,99970,9997
3,50,99980,9998
3,60,99990,9999
3,70,99990,9999
3,80,99990,9999
3,91,00001,0000
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
2,70,99710,9972
2,80,99790,9979
2,90,99850,9985
3,00,99890,9989
3,10,99920,9992
3,20,99940,9995
3,30,99960,9996
3,40,99970,9997
3,50,99980,9998
3,60,99990,9999
3,70,99990,9999
3,80,99990,9999
3,91,00001,0000
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
2,70,99730,9974
2,80,99800,9981
2,90,99860,9986
3,00,99900,9990
3,10,99930,9993
3,20,99950,9995
3,30,99960,9997
3,40,99970,9998
3,50,99980,9998
3,60,99990,9999
3,70,99990,9999
3,80,99990,9999
3,91,00001,0000