Taller funciones

1.

Escriba una función que permita calcular las siguientes sumatoria y productorias

1.1

\[ \sum_{i = 1}^{100}\frac{1}{2^{i}} \]

mi.sum_1.1 = function(x){
  sumatoria = 0
for (i in seq(x)) {
  s_i = 1/2^i
 sumatoria <- sumatoria+s_i
}
  return(sumatoria)
}

mi.sum_1.1(100)

## [1] 1

mi.sum_1.1v = function(x){
  sumatoria_1.2 = NULL
  sum = 0
for (i in seq(x)) {
  s_i <- 1/2^i
  sum = sum + s_i
 sumatoria_1.2[i] = sum
 
}
  print(sumatoria_1.2)
}

mi.sum_1.1v(10)

##  [1] 0.5000000 0.7500000 0.8750000 0.9375000 0.9687500 0.9843750 0.9921875
##  [8] 0.9960938 0.9980469 0.9990234

1.2

\[\sum_{i = 0}^{\infty}\frac{1}{n!}\]

mi.sum_1.2 = function(x){
  suma = 0
  for (i in seq(x)) { 
    s_i = 1/(factorial(i))
    suma = suma + s_i
  }
  return(suma)
}
mi.sum_1.2(5)

## [1] 1.716667

mi.sum_1.2v = function(x){
  sumatoria = NULL
  suma = 0
  for (i in seq(x)) { 
    s_i = 1/(factorial(i))
    suma = suma + s_i
    sumatoria[i] = suma
  }
  return(sumatoria)
}
mi.sum_1.2v(5)

## [1] 1.000000 1.500000 1.666667 1.708333 1.716667

plot(mi.sum_1.2v(10))

1.3

\[\prod_{n=1}^{6}(1+x^{2^{n}})\]

mi.prod_1.3 = function(x,k){
  prod = 1
  for (n in seq(k)) {
    p_n = 1 + x^(2^n)
    #print(p_n)
    prod = prod*p_n
    #print(product)
  }
  print(prod)
}
mi.prod_1.3(2,6)

## [1] 1.134275e+38

(1 + 2^2)*(1+2^4)*(1+2^8)*(1 +2^16)*(1 + 2^32)*(1 + 2^64)

## [1] 1.134275e+38

1.4

\[\prod_{n=1}^{6}\frac{4k^{2}}{(2k^{2}-1)}\]

mi.prod_1.4 = function(k){
  productoria = 1
  for (i in seq(k)) { 
    p_i = (4*i^2)/((2*i^2)-1)
    productoria = productoria * p_i
  }
  return(productoria)
}
mi.prod_1.4(5)

## [1] 81.57512

1.5

\[\prod_{n = 0}^{\infty}\frac{x^{2^{n}}}{(2n)!}\]

mi.prod_1.5 = function(x,n){
  prod = 1
  for (i in seq(n)){
    p_i = x^(2^(i))/(factorial(2*i))
    #print(p_i)
    prod = prod * p_i
  }
  return(prod)
}
mi.prod_1.5(1,4)

## [1] 7.176385e-10

0.5*0.041666*0.0013888*0.0000248

## [1] 7.175352e-10

1.6

\[ \sum_{n = 0}^{\infty}\frac{(-1)^nx^{2^{n+1}}}{(2n+1)!} \]

mi.sum_1.6 = function(k,x){
  suma = 0
  for (i in seq(x)) { 
    s_i = (((-1)^i)*k^(2^(i+1)))/(factorial(2*i + 1))
    #print(s_i)
    suma = suma + s_i
  }
  return(suma)
}
mi.sum_1.6(1,4)

## [1] -0.158529

mi.sum_1.6v = function(k,x){
  sumatoria = NULL
  suma = 0
  for (i in seq(x)) { 
    s_i = (((-1)^i)*k^(2^(i+1)))/(factorial(2*i + 1))
    suma = suma + s_i
    sumatoria[i] = suma
  }
  return(sumatoria)
  
}
mi.sum_1.6v(1,4)

## [1] -0.1666667 -0.1583333 -0.1585317 -0.1585290

2

Evalue las siguientes funciones definiendo un dominio para esto, luego grafique la función

2.1

\[ y = x^5-7x^4-162x^3+878x^2+3937x-15015 \]

mi.poli_2.1 = function(x){
  y = x^5-7*x^4-162*x^3+878*x^2+3937*x-15015 
  return(y)
}
rango <- c(seq(-10,10,0.5))
rango_1 <- mi.poli_2.1(rango)
rango_1

##  [1]  25415.000  31324.219  33792.000  33533.281  31185.000  27309.844
##  [7]  22400.000  16880.906  11115.000   5405.469      0.000  -4905.469
## [13]  -9163.000 -12668.906 -15360.000 -17209.844 -18225.000 -18441.281
## [19] -17920.000 -16744.219 -15015.000 -12847.656 -10368.000  -7708.594
## [25]  -5005.000  -2392.031      0.000   2049.031   3645.000   4693.594
## [31]   5120.000   4872.656   3927.000   2289.219      0.000  -2861.719
## [37]  -6175.000  -9773.156 -13440.000 -16906.094 -19845.000

plot(rango , rango_1, type = "l")

2.2

\[ y = \frac{sen(x)}{x}\]

mi.función_2.2 = function(x){
  y = sin(x)/x
  return(y)
}
función_2.2 = mi.función_2.2(seq(-5,5,0.5))
graf_2.2 = plot(seq(-5,5,0.2), mi.función_2.2(seq(-5,5,0.2)), xlab = "x", ylab = "y")
points(0,1, pch = 20)

#### 2.3

\[y = \frac{cos(x)-1}{x}\]

mi.función_2.3 = function(x){
  for (i in seq(x)) {
    y  = (cos(x)-1)/x
  }
  
  return(y)
}

función_2.3.2 = mi.función_2.3(seq(-6*pi, 6*pi, pi/32))
#función_2.3.2
graf_2.3 = plot(seq(-6*pi, 6*pi, pi/32),función_2.3.2, type = "l")
points(0,0, pch = 20)

#### 2.4

\[y=x^5-3x^4+x^2-x-5\]

mi.poli_2.4 = function(x){
  y = x^5-3*x^4+x^2-x-5 
  return(y)
}
rango <- c(seq(-10,10,0.5))
rango_2.4 <- mi.poli_2.4(rango)
rango_2.4

##  [1] -129895.00000 -101718.53125  -78647.00000  -59954.96875  -44989.00000
##  [6]  -33163.90625  -23959.00000  -16914.34375  -11627.00000   -7747.28125
## [11]   -4975.00000   -3055.71875   -1777.00000    -964.65625    -479.00000
## [16]    -211.09375     -79.00000     -24.03125      -7.00000      -4.46875
## [21]      -5.00000      -5.40625      -7.00000     -11.84375     -19.00000
## [26]     -20.78125       1.00000      78.78125     263.00000     625.84375
## [31]    1265.00000    2307.40625    3913.00000    6278.46875    9641.00000
## [36]   14282.03125   20531.00000   28769.09375   39433.00000   53018.65625
## [41]   70085.00000

plot(rango , rango_2.4, type = "l")

### 3 Calcule para qué valor de n las sumatorias convergen a pi y coincide con los primeros valores (3.141593)

3.1

\[\sum_{k = 0}^{\infty}\frac{8}{(4k+1)(4k+3)}\]

 k = 0
 sumatoria = 0
while (round(sumatoria, 4) != 3.141) {
  s_k = (8/((4*k+1)*(4*k+3)))
   sumatoria = sumatoria+s_k
   k = k+1
   print(sumatoria)
}

## [1] 2.666667
## [1] 2.895238
## [1] 2.976046
## [1] 3.017072
## [1] 3.04184
## [1] 3.058403
## [1] 3.070255
## [1] 3.079153
## [1] 3.08608
## [1] 3.091624
## [1] 3.096162
## [1] 3.099944
## [1] 3.103145
## [1] 3.10589
## [1] 3.108269
## [1] 3.11035
## [1] 3.112187
## [1] 3.11382
## [1] 3.115281
## [1] 3.116597
## [1] 3.117787
## [1] 3.118868
## [1] 3.119856
## [1] 3.120762
## [1] 3.121595
## [1] 3.122364
## [1] 3.123076
## [1] 3.123737
## [1] 3.124353
## [1] 3.124927
## [1] 3.125465
## [1] 3.125969
## [1] 3.126442
## [1] 3.126888
## [1] 3.127308
## [1] 3.127704
## [1] 3.12808
## [1] 3.128435
## [1] 3.128773
## [1] 3.129093
## [1] 3.129398
## [1] 3.129688
## [1] 3.129965
## [1] 3.130229
## [1] 3.130482
## [1] 3.130723
## [1] 3.130955
## [1] 3.131176
## [1] 3.131389
## [1] 3.131593
## [1] 3.131789
## [1] 3.131977
## [1] 3.132159
## [1] 3.132334
## [1] 3.132502
## [1] 3.132664
## [1] 3.132821
## [1] 3.132972
## [1] 3.133118
## [1] 3.133259
## [1] 3.133396
## [1] 3.133528
## [1] 3.133656
## [1] 3.13378
## [1] 3.1339
## [1] 3.134017
## [1] 3.13413
## [1] 3.13424
## [1] 3.134346
## [1] 3.13445
## [1] 3.13455
## [1] 3.134648
## [1] 3.134743
## [1] 3.134836
## [1] 3.134926
## [1] 3.135014
## [1] 3.135099
## [1] 3.135182
## [1] 3.135264
## [1] 3.135343
## [1] 3.13542
## [1] 3.135495
## [1] 3.135569
## [1] 3.13564
## [1] 3.13571
## [1] 3.135779
## [1] 3.135846
## [1] 3.135911
## [1] 3.135975
## [1] 3.136037
## [1] 3.136098
## [1] 3.136158
## [1] 3.136216
## [1] 3.136274
## [1] 3.13633
## [1] 3.136384
## [1] 3.136438
## [1] 3.136491
## [1] 3.136542
## [1] 3.136593
## [1] 3.136642
## [1] 3.136691
## [1] 3.136738
## [1] 3.136785
## [1] 3.136831
## [1] 3.136876
## [1] 3.13692
## [1] 3.136963
## [1] 3.137006
## [1] 3.137047
## [1] 3.137088
## [1] 3.137128
## [1] 3.137168
## [1] 3.137207
## [1] 3.137245
## [1] 3.137282
## [1] 3.137319
## [1] 3.137355
## [1] 3.137391
## [1] 3.137426
## [1] 3.13746
## [1] 3.137494
## [1] 3.137528
## [1] 3.13756
## [1] 3.137593
## [1] 3.137624
## [1] 3.137656
## [1] 3.137686
## [1] 3.137717
## [1] 3.137747
## [1] 3.137776
## [1] 3.137805
## [1] 3.137833
## [1] 3.137861
## [1] 3.137889
## [1] 3.137916
## [1] 3.137943
## [1] 3.137969
## [1] 3.137996
## [1] 3.138021
## [1] 3.138047
## [1] 3.138072
## [1] 3.138096
## [1] 3.13812
## [1] 3.138144
## [1] 3.138168
## [1] 3.138191
## [1] 3.138214
## [1] 3.138237
## [1] 3.138259
## [1] 3.138281
## [1] 3.138303
## [1] 3.138325
## [1] 3.138346
## [1] 3.138367
## [1] 3.138388
## [1] 3.138408
## [1] 3.138428
## [1] 3.138448
## [1] 3.138468
## [1] 3.138487
## [1] 3.138506
## [1] 3.138525
## [1] 3.138544
## [1] 3.138562
## [1] 3.138581
## [1] 3.138599
## [1] 3.138616
## [1] 3.138634
## [1] 3.138651
## [1] 3.138669
## [1] 3.138686
## [1] 3.138702
## [1] 3.138719
## [1] 3.138736
## [1] 3.138752
## [1] 3.138768
## [1] 3.138784
## [1] 3.138799
## [1] 3.138815
## [1] 3.13883
## [1] 3.138845
## [1] 3.13886
## [1] 3.138875
## [1] 3.13889
## [1] 3.138904
## [1] 3.138919
## [1] 3.138933
## [1] 3.138947
## [1] 3.138961
## [1] 3.138975
## [1] 3.138988
## [1] 3.139002
## [1] 3.139015
## [1] 3.139029
## [1] 3.139042
## [1] 3.139055
## [1] 3.139067
## [1] 3.13908
## [1] 3.139093
## [1] 3.139105
## [1] 3.139117
## [1] 3.13913
## [1] 3.139142
## [1] 3.139154
## [1] 3.139165
## [1] 3.139177
## [1] 3.139189
## [1] 3.1392
## [1] 3.139212
## [1] 3.139223
## [1] 3.139234
## [1] 3.139245
## [1] 3.139256
## [1] 3.139267
## [1] 3.139278
## [1] 3.139289
## [1] 3.139299
## [1] 3.13931
## [1] 3.13932
## [1] 3.13933
## [1] 3.13934
## [1] 3.139351
## [1] 3.139361
## [1] 3.13937
## [1] 3.13938
## [1] 3.13939
## [1] 3.1394
## [1] 3.139409
## [1] 3.139419
## [1] 3.139428
## [1] 3.139437
## [1] 3.139447
## [1] 3.139456
## [1] 3.139465
## [1] 3.139474
## [1] 3.139483
## [1] 3.139492
## [1] 3.139501
## [1] 3.139509
## [1] 3.139518
## [1] 3.139527
## [1] 3.139535
## [1] 3.139543
## [1] 3.139552
## [1] 3.13956
## [1] 3.139568
## [1] 3.139577
## [1] 3.139585
## [1] 3.139593
## [1] 3.139601
## [1] 3.139609
## [1] 3.139616
## [1] 3.139624
## [1] 3.139632
## [1] 3.13964
## [1] 3.139647
## [1] 3.139655
## [1] 3.139662
## [1] 3.13967
## [1] 3.139677
## [1] 3.139684
## [1] 3.139692
## [1] 3.139699
## [1] 3.139706
## [1] 3.139713
## [1] 3.13972
## [1] 3.139727
## [1] 3.139734
## [1] 3.139741
## [1] 3.139748
## [1] 3.139754
## [1] 3.139761
## [1] 3.139768
## [1] 3.139774
## [1] 3.139781
## [1] 3.139788
## [1] 3.139794
## [1] 3.139801
## [1] 3.139807
## [1] 3.139813
## [1] 3.13982
## [1] 3.139826
## [1] 3.139832
## [1] 3.139838
## [1] 3.139844
## [1] 3.13985
## [1] 3.139857
## [1] 3.139863
## [1] 3.139869
## [1] 3.139874
## [1] 3.13988
## [1] 3.139886
## [1] 3.139892
## [1] 3.139898
## [1] 3.139903
## [1] 3.139909
## [1] 3.139915
## [1] 3.13992
## [1] 3.139926
## [1] 3.139932
## [1] 3.139937
## [1] 3.139942
## [1] 3.139948
## [1] 3.139953
## [1] 3.139959
## [1] 3.139964
## [1] 3.139969
## [1] 3.139975
## [1] 3.13998
## [1] 3.139985
## [1] 3.13999
## [1] 3.139995
## [1] 3.14
## [1] 3.140005
## [1] 3.14001
## [1] 3.140015
## [1] 3.14002
## [1] 3.140025
## [1] 3.14003
## [1] 3.140035
## [1] 3.14004
## [1] 3.140045
## [1] 3.140049
## [1] 3.140054
## [1] 3.140059
## [1] 3.140064
## [1] 3.140068
## [1] 3.140073
## [1] 3.140078
## [1] 3.140082
## [1] 3.140087
## [1] 3.140091
## [1] 3.140096
## [1] 3.1401
## [1] 3.140105
## [1] 3.140109
## [1] 3.140113
## [1] 3.140118
## [1] 3.140122
## [1] 3.140126
## [1] 3.140131
## [1] 3.140135
## [1] 3.140139
## [1] 3.140143
## [1] 3.140148
## [1] 3.140152
## [1] 3.140156
## [1] 3.14016
## [1] 3.140164
## [1] 3.140168
## [1] 3.140172
## [1] 3.140176
## [1] 3.14018
## [1] 3.140184
## [1] 3.140188
## [1] 3.140192
## [1] 3.140196
## [1] 3.1402
## [1] 3.140204
## [1] 3.140208
## [1] 3.140211
## [1] 3.140215
## [1] 3.140219
## [1] 3.140223
## [1] 3.140227
## [1] 3.14023
## [1] 3.140234
## [1] 3.140238
## [1] 3.140241
## [1] 3.140245
## [1] 3.140249
## [1] 3.140252
## [1] 3.140256
## [1] 3.140259
## [1] 3.140263
## [1] 3.140266
## [1] 3.14027
## [1] 3.140273
## [1] 3.140277
## [1] 3.14028
## [1] 3.140284
## [1] 3.140287
## [1] 3.140291
## [1] 3.140294
## [1] 3.140297
## [1] 3.140301
## [1] 3.140304
## [1] 3.140307
## [1] 3.140311
## [1] 3.140314
## [1] 3.140317
## [1] 3.14032
## [1] 3.140324
## [1] 3.140327
## [1] 3.14033
## [1] 3.140333
## [1] 3.140336
## [1] 3.14034
## [1] 3.140343
## [1] 3.140346
## [1] 3.140349
## [1] 3.140352
## [1] 3.140355
## [1] 3.140358
## [1] 3.140361
## [1] 3.140364
## [1] 3.140367
## [1] 3.14037
## [1] 3.140373
## [1] 3.140376
## [1] 3.140379
## [1] 3.140382
## [1] 3.140385
## [1] 3.140388
## [1] 3.140391
## [1] 3.140394
## [1] 3.140396
## [1] 3.140399
## [1] 3.140402
## [1] 3.140405
## [1] 3.140408
## [1] 3.140411
## [1] 3.140413
## [1] 3.140416
## [1] 3.140419
## [1] 3.140422
## [1] 3.140424
## [1] 3.140427
## [1] 3.14043
## [1] 3.140433
## [1] 3.140435
## [1] 3.140438
## [1] 3.140441
## [1] 3.140443
## [1] 3.140446
## [1] 3.140448
## [1] 3.140451
## [1] 3.140454
## [1] 3.140456
## [1] 3.140459
## [1] 3.140461
## [1] 3.140464
## [1] 3.140467
## [1] 3.140469
## [1] 3.140472
## [1] 3.140474
## [1] 3.140477
## [1] 3.140479
## [1] 3.140482
## [1] 3.140484
## [1] 3.140486
## [1] 3.140489
## [1] 3.140491
## [1] 3.140494
## [1] 3.140496
## [1] 3.140499
## [1] 3.140501
## [1] 3.140503
## [1] 3.140506
## [1] 3.140508
## [1] 3.14051
## [1] 3.140513
## [1] 3.140515
## [1] 3.140517
## [1] 3.14052
## [1] 3.140522
## [1] 3.140524
## [1] 3.140527
## [1] 3.140529
## [1] 3.140531
## [1] 3.140533
## [1] 3.140536
## [1] 3.140538
## [1] 3.14054
## [1] 3.140542
## [1] 3.140544
## [1] 3.140547
## [1] 3.140549
## [1] 3.140551
## [1] 3.140553
## [1] 3.140555
## [1] 3.140557
## [1] 3.14056
## [1] 3.140562
## [1] 3.140564
## [1] 3.140566
## [1] 3.140568
## [1] 3.14057
## [1] 3.140572
## [1] 3.140574
## [1] 3.140576
## [1] 3.140578
## [1] 3.140581
## [1] 3.140583
## [1] 3.140585
## [1] 3.140587
## [1] 3.140589
## [1] 3.140591
## [1] 3.140593
## [1] 3.140595
## [1] 3.140597
## [1] 3.140599
## [1] 3.140601
## [1] 3.140603
## [1] 3.140605
## [1] 3.140606
## [1] 3.140608
## [1] 3.14061
## [1] 3.140612
## [1] 3.140614
## [1] 3.140616
## [1] 3.140618
## [1] 3.14062
## [1] 3.140622
## [1] 3.140624
## [1] 3.140626
## [1] 3.140627
## [1] 3.140629
## [1] 3.140631
## [1] 3.140633
## [1] 3.140635
## [1] 3.140637
## [1] 3.140638
## [1] 3.14064
## [1] 3.140642
## [1] 3.140644
## [1] 3.140646
## [1] 3.140647
## [1] 3.140649
## [1] 3.140651
## [1] 3.140653
## [1] 3.140655
## [1] 3.140656
## [1] 3.140658
## [1] 3.14066
## [1] 3.140662
## [1] 3.140663
## [1] 3.140665
## [1] 3.140667
## [1] 3.140668
## [1] 3.14067
## [1] 3.140672
## [1] 3.140674
## [1] 3.140675
## [1] 3.140677
## [1] 3.140679
## [1] 3.14068
## [1] 3.140682
## [1] 3.140684
## [1] 3.140685
## [1] 3.140687
## [1] 3.140688
## [1] 3.14069
## [1] 3.140692
## [1] 3.140693
## [1] 3.140695
## [1] 3.140697
## [1] 3.140698
## [1] 3.1407
## [1] 3.140701
## [1] 3.140703
## [1] 3.140705
## [1] 3.140706
## [1] 3.140708
## [1] 3.140709
## [1] 3.140711
## [1] 3.140712
## [1] 3.140714
## [1] 3.140715
## [1] 3.140717
## [1] 3.140719
## [1] 3.14072
## [1] 3.140722
## [1] 3.140723
## [1] 3.140725
## [1] 3.140726
## [1] 3.140728
## [1] 3.140729
## [1] 3.140731
## [1] 3.140732
## [1] 3.140734
## [1] 3.140735
## [1] 3.140736
## [1] 3.140738
## [1] 3.140739
## [1] 3.140741
## [1] 3.140742
## [1] 3.140744
## [1] 3.140745
## [1] 3.140747
## [1] 3.140748
## [1] 3.140749
## [1] 3.140751
## [1] 3.140752
## [1] 3.140754
## [1] 3.140755
## [1] 3.140757
## [1] 3.140758
## [1] 3.140759
## [1] 3.140761
## [1] 3.140762
## [1] 3.140763
## [1] 3.140765
## [1] 3.140766
## [1] 3.140768
## [1] 3.140769
## [1] 3.14077
## [1] 3.140772
## [1] 3.140773
## [1] 3.140774
## [1] 3.140776
## [1] 3.140777
## [1] 3.140778
## [1] 3.14078
## [1] 3.140781
## [1] 3.140782
## [1] 3.140784
## [1] 3.140785
## [1] 3.140786
## [1] 3.140788
## [1] 3.140789
## [1] 3.14079
## [1] 3.140791
## [1] 3.140793
## [1] 3.140794
## [1] 3.140795
## [1] 3.140796
## [1] 3.140798
## [1] 3.140799
## [1] 3.1408
## [1] 3.140802
## [1] 3.140803
## [1] 3.140804
## [1] 3.140805
## [1] 3.140806
## [1] 3.140808
## [1] 3.140809
## [1] 3.14081
## [1] 3.140811
## [1] 3.140813
## [1] 3.140814
## [1] 3.140815
## [1] 3.140816
## [1] 3.140817
## [1] 3.140819
## [1] 3.14082
## [1] 3.140821
## [1] 3.140822
## [1] 3.140823
## [1] 3.140825
## [1] 3.140826
## [1] 3.140827
## [1] 3.140828
## [1] 3.140829
## [1] 3.14083
## [1] 3.140832
## [1] 3.140833
## [1] 3.140834
## [1] 3.140835
## [1] 3.140836
## [1] 3.140837
## [1] 3.140839
## [1] 3.14084
## [1] 3.140841
## [1] 3.140842
## [1] 3.140843
## [1] 3.140844
## [1] 3.140845
## [1] 3.140846
## [1] 3.140847
## [1] 3.140849
## [1] 3.14085
## [1] 3.140851
## [1] 3.140852
## [1] 3.140853
## [1] 3.140854
## [1] 3.140855
## [1] 3.140856
## [1] 3.140857
## [1] 3.140858
## [1] 3.14086
## [1] 3.140861
## [1] 3.140862
## [1] 3.140863
## [1] 3.140864
## [1] 3.140865
## [1] 3.140866
## [1] 3.140867
## [1] 3.140868
## [1] 3.140869
## [1] 3.14087
## [1] 3.140871
## [1] 3.140872
## [1] 3.140873
## [1] 3.140874
## [1] 3.140875
## [1] 3.140876
## [1] 3.140877
## [1] 3.140878
## [1] 3.140879
## [1] 3.14088
## [1] 3.140881
## [1] 3.140882
## [1] 3.140883
## [1] 3.140884
## [1] 3.140885
## [1] 3.140886
## [1] 3.140887
## [1] 3.140888
## [1] 3.140889
## [1] 3.14089
## [1] 3.140891
## [1] 3.140892
## [1] 3.140893
## [1] 3.140894
## [1] 3.140895
## [1] 3.140896
## [1] 3.140897
## [1] 3.140898
## [1] 3.140899
## [1] 3.1409
## [1] 3.140901
## [1] 3.140902
## [1] 3.140903
## [1] 3.140904
## [1] 3.140905
## [1] 3.140906
## [1] 3.140907
## [1] 3.140908
## [1] 3.140909
## [1] 3.14091
## [1] 3.140911
## [1] 3.140911
## [1] 3.140912
## [1] 3.140913
## [1] 3.140914
## [1] 3.140915
## [1] 3.140916
## [1] 3.140917
## [1] 3.140918
## [1] 3.140919
## [1] 3.14092
## [1] 3.140921
## [1] 3.140922
## [1] 3.140922
## [1] 3.140923
## [1] 3.140924
## [1] 3.140925
## [1] 3.140926
## [1] 3.140927
## [1] 3.140928
## [1] 3.140929
## [1] 3.14093
## [1] 3.14093
## [1] 3.140931
## [1] 3.140932
## [1] 3.140933
## [1] 3.140934
## [1] 3.140935
## [1] 3.140936
## [1] 3.140936
## [1] 3.140937
## [1] 3.140938
## [1] 3.140939
## [1] 3.14094
## [1] 3.140941
## [1] 3.140942
## [1] 3.140942
## [1] 3.140943
## [1] 3.140944
## [1] 3.140945
## [1] 3.140946
## [1] 3.140947
## [1] 3.140947
## [1] 3.140948
## [1] 3.140949
## [1] 3.14095
## [1] 3.140951

 k = 1
 sumatoria = 0
 sr = 0
while (round(sr, 3) != 3.14
       ) {
  
  s_k = (1/(k^2))
   sumatoria = sumatoria + s_k
  sr = sqrt(6*sumatoria)
   k = k+1
  m = c(k,sr)
  print(m)
}

## [1] 2.00000 2.44949
## [1] 3.000000 2.738613
## [1] 4.000000 2.857738
## [1] 5.000000 2.922613
## [1] 6.000000 2.963388
## [1] 7.000000 2.991376
## [1] 8.000000 3.011774
## [1] 9.000000 3.027298
## [1] 10.000000  3.039508
## [1] 11.000000  3.049362
## [1] 12.000000  3.057482
## [1] 13.000000  3.064288
## [1] 14.000000  3.070075
## [1] 15.000000  3.075057
## [1] 16.00000  3.07939
## [1] 17.000000  3.083193
## [1] 18.000000  3.086558
## [1] 19.000000  3.089556
## [1] 20.000000  3.092245
## [1] 21.00000  3.09467
## [1] 22.000000  3.096867
## [1] 23.000000  3.098868
## [1] 24.000000  3.100697
## [1] 25.000000  3.102377
## [1] 26.000000  3.103923
## [1] 27.000000  3.105353
## [1] 28.000000  3.106678
## [1] 29.000000  3.107909
## [1] 30.000000  3.109057
## [1] 31.000000  3.110129
## [1] 32.000000  3.111132
## [1] 33.000000  3.112074
## [1] 34.000000  3.112959
## [1] 35.000000  3.113792
## [1] 36.000000  3.114579
## [1] 37.000000  3.115322
## [1] 38.000000  3.116025
## [1] 39.000000  3.116692
## [1] 40.000000  3.117325
## [1] 41.000000  3.117926
## [1] 42.000000  3.118499
## [1] 43.000000  3.119044
## [1] 44.000000  3.119564
## [1] 45.000000  3.120061
## [1] 46.000000  3.120535
## [1] 47.00000  3.12099
## [1] 48.000000  3.121425
## [1] 49.000000  3.121842
## [1] 50.000000  3.122242
## [1] 51.000000  3.122627
## [1] 52.000000  3.122996
## [1] 53.000000  3.123351
## [1] 54.000000  3.123693
## [1] 55.000000  3.124022
## [1] 56.00000  3.12434
## [1] 57.000000  3.124646
## [1] 58.000000  3.124941
## [1] 59.000000  3.125227
## [1] 60.000000  3.125503
## [1] 61.000000  3.125769
## [1] 62.000000  3.126027
## [1] 63.000000  3.126277
## [1] 64.000000  3.126519
## [1] 65.000000  3.126753
## [1] 66.00000  3.12698
## [1] 67.0000  3.1272
## [1] 68.000000  3.127414
## [1] 69.000000  3.127621
## [1] 70.000000  3.127823
## [1] 71.000000  3.128018
## [1] 72.000000  3.128209
## [1] 73.000000  3.128394
## [1] 74.000000  3.128574
## [1] 75.000000  3.128749
## [1] 76.000000  3.128919
## [1] 77.000000  3.129085
## [1] 78.000000  3.129247
## [1] 79.000000  3.129404
## [1] 80.000000  3.129558
## [1] 81.000000  3.129708
## [1] 82.000000  3.129854
## [1] 83.000000  3.129996
## [1] 84.000000  3.130136
## [1] 85.000000  3.130271
## [1] 86.000000  3.130404
## [1] 87.000000  3.130534
## [1] 88.00000  3.13066
## [1] 89.000000  3.130784
## [1] 90.000000  3.130905
## [1] 91.000000  3.131023
## [1] 92.000000  3.131139
## [1] 93.000000  3.131252
## [1] 94.000000  3.131363
## [1] 95.000000  3.131471
## [1] 96.000000  3.131578
## [1] 97.000000  3.131681
## [1] 98.000000  3.131783
## [1] 99.000000  3.131883
## [1] 100.000000   3.131981
## [1] 101.000000   3.132077
## [1] 102.00000   3.13217
## [1] 103.000000   3.132262
## [1] 104.000000   3.132353
## [1] 105.000000   3.132441
## [1] 106.000000   3.132528
## [1] 107.000000   3.132613
## [1] 108.000000   3.132697
## [1] 109.000000   3.132779
## [1] 110.00000   3.13286
## [1] 111.000000   3.132939
## [1] 112.000000   3.133017
## [1] 113.000000   3.133093
## [1] 114.000000   3.133168
## [1] 115.000000   3.133242
## [1] 116.000000   3.133314
## [1] 117.000000   3.133385
## [1] 118.000000   3.133455
## [1] 119.000000   3.133524
## [1] 120.000000   3.133591
## [1] 121.000000   3.133658
## [1] 122.000000   3.133723
## [1] 123.000000   3.133788
## [1] 124.000000   3.133851
## [1] 125.000000   3.133913
## [1] 126.000000   3.133974
## [1] 127.000000   3.134035
## [1] 128.000000   3.134094
## [1] 129.000000   3.134153
## [1] 130.00000   3.13421
## [1] 131.000000   3.134267
## [1] 132.000000   3.134322
## [1] 133.000000   3.134377
## [1] 134.000000   3.134431
## [1] 135.000000   3.134485
## [1] 136.000000   3.134537
## [1] 137.000000   3.134589
## [1] 138.00000   3.13464
## [1] 139.00000   3.13469
## [1] 140.00000   3.13474
## [1] 141.000000   3.134789
## [1] 142.000000   3.134837
## [1] 143.000000   3.134884
## [1] 144.000000   3.134931
## [1] 145.000000   3.134977
## [1] 146.000000   3.135023
## [1] 147.000000   3.135068
## [1] 148.000000   3.135112
## [1] 149.000000   3.135156
## [1] 150.000000   3.135199
## [1] 151.000000   3.135241
## [1] 152.000000   3.135283
## [1] 153.000000   3.135325
## [1] 154.000000   3.135365
## [1] 155.000000   3.135406
## [1] 156.000000   3.135446
## [1] 157.000000   3.135485
## [1] 158.000000   3.135524
## [1] 159.000000   3.135562
## [1] 160.0000   3.1356
## [1] 161.000000   3.135637
## [1] 162.000000   3.135674
## [1] 163.000000   3.135711
## [1] 164.000000   3.135747
## [1] 165.000000   3.135782
## [1] 166.000000   3.135817
## [1] 167.000000   3.135852
## [1] 168.000000   3.135886
## [1] 169.00000   3.13592
## [1] 170.000000   3.135954
## [1] 171.000000   3.135987
## [1] 172.00000   3.13602
## [1] 173.000000   3.136052
## [1] 174.000000   3.136084
## [1] 175.000000   3.136116
## [1] 176.000000   3.136147
## [1] 177.000000   3.136178
## [1] 178.000000   3.136208
## [1] 179.000000   3.136238
## [1] 180.000000   3.136268
## [1] 181.000000   3.136298
## [1] 182.000000   3.136327
## [1] 183.000000   3.136356
## [1] 184.000000   3.136384
## [1] 185.000000   3.136413
## [1] 186.000000   3.136441
## [1] 187.000000   3.136468
## [1] 188.000000   3.136496
## [1] 189.000000   3.136523
## [1] 190.000000   3.136549
## [1] 191.000000   3.136576
## [1] 192.000000   3.136602
## [1] 193.000000   3.136628
## [1] 194.000000   3.136654
## [1] 195.000000   3.136679
## [1] 196.000000   3.136704
## [1] 197.000000   3.136729
## [1] 198.000000   3.136754
## [1] 199.000000   3.136778
## [1] 200.000000   3.136802
## [1] 201.000000   3.136826
## [1] 202.00000   3.13685
## [1] 203.000000   3.136873
## [1] 204.000000   3.136897
## [1] 205.00000   3.13692
## [1] 206.000000   3.136942
## [1] 207.000000   3.136965
## [1] 208.000000   3.136987
## [1] 209.000000   3.137009
## [1] 210.000000   3.137031
## [1] 211.000000   3.137053
## [1] 212.000000   3.137074
## [1] 213.000000   3.137096
## [1] 214.000000   3.137117
## [1] 215.000000   3.137138
## [1] 216.000000   3.137158
## [1] 217.000000   3.137179
## [1] 218.000000   3.137199
## [1] 219.000000   3.137219
## [1] 220.000000   3.137239
## [1] 221.000000   3.137259
## [1] 222.000000   3.137279
## [1] 223.000000   3.137298
## [1] 224.000000   3.137317
## [1] 225.000000   3.137336
## [1] 226.000000   3.137355
## [1] 227.000000   3.137374
## [1] 228.000000   3.137392
## [1] 229.000000   3.137411
## [1] 230.000000   3.137429
## [1] 231.000000   3.137447
## [1] 232.000000   3.137465
## [1] 233.000000   3.137483
## [1] 234.0000   3.1375
## [1] 235.000000   3.137518
## [1] 236.000000   3.137535
## [1] 237.000000   3.137552
## [1] 238.000000   3.137569
## [1] 239.000000   3.137586
## [1] 240.000000   3.137603
## [1] 241.00000   3.13762
## [1] 242.000000   3.137636
## [1] 243.000000   3.137652
## [1] 244.000000   3.137669
## [1] 245.000000   3.137685
## [1] 246.000000   3.137701
## [1] 247.000000   3.137716
## [1] 248.000000   3.137732
## [1] 249.000000   3.137748
## [1] 250.000000   3.137763
## [1] 251.000000   3.137778
## [1] 252.000000   3.137793
## [1] 253.000000   3.137808
## [1] 254.000000   3.137823
## [1] 255.000000   3.137838
## [1] 256.000000   3.137853
## [1] 257.000000   3.137868
## [1] 258.000000   3.137882
## [1] 259.000000   3.137896
## [1] 260.000000   3.137911
## [1] 261.000000   3.137925
## [1] 262.000000   3.137939
## [1] 263.000000   3.137953
## [1] 264.000000   3.137967
## [1] 265.00000   3.13798
## [1] 266.000000   3.137994
## [1] 267.000000   3.138007
## [1] 268.000000   3.138021
## [1] 269.000000   3.138034
## [1] 270.000000   3.138047
## [1] 271.00000   3.13806
## [1] 272.000000   3.138073
## [1] 273.000000   3.138086
## [1] 274.000000   3.138099
## [1] 275.000000   3.138112
## [1] 276.000000   3.138125
## [1] 277.000000   3.138137
## [1] 278.00000   3.13815
## [1] 279.000000   3.138162
## [1] 280.000000   3.138174
## [1] 281.000000   3.138186
## [1] 282.000000   3.138199
## [1] 283.000000   3.138211
## [1] 284.000000   3.138222
## [1] 285.000000   3.138234
## [1] 286.000000   3.138246
## [1] 287.000000   3.138258
## [1] 288.000000   3.138269
## [1] 289.000000   3.138281
## [1] 290.000000   3.138292
## [1] 291.000000   3.138304
## [1] 292.000000   3.138315
## [1] 293.000000   3.138326
## [1] 294.000000   3.138337
## [1] 295.000000   3.138348
## [1] 296.000000   3.138359
## [1] 297.00000   3.13837
## [1] 298.000000   3.138381
## [1] 299.000000   3.138392
## [1] 300.000000   3.138403
## [1] 301.000000   3.138413
## [1] 302.000000   3.138424
## [1] 303.000000   3.138434
## [1] 304.000000   3.138445
## [1] 305.000000   3.138455
## [1] 306.000000   3.138465
## [1] 307.000000   3.138476
## [1] 308.000000   3.138486
## [1] 309.000000   3.138496
## [1] 310.000000   3.138506
## [1] 311.000000   3.138516
## [1] 312.000000   3.138526
## [1] 313.000000   3.138535
## [1] 314.000000   3.138545
## [1] 315.000000   3.138555
## [1] 316.000000   3.138564
## [1] 317.000000   3.138574
## [1] 318.000000   3.138584
## [1] 319.000000   3.138593
## [1] 320.000000   3.138602
## [1] 321.000000   3.138612
## [1] 322.000000   3.138621
## [1] 323.00000   3.13863
## [1] 324.000000   3.138639
## [1] 325.000000   3.138649
## [1] 326.000000   3.138658
## [1] 327.000000   3.138667
## [1] 328.000000   3.138675
## [1] 329.000000   3.138684
## [1] 330.000000   3.138693
## [1] 331.000000   3.138702
## [1] 332.000000   3.138711
## [1] 333.000000   3.138719
## [1] 334.000000   3.138728
## [1] 335.000000   3.138737
## [1] 336.000000   3.138745
## [1] 337.000000   3.138754
## [1] 338.000000   3.138762
## [1] 339.00000   3.13877
## [1] 340.000000   3.138779
## [1] 341.000000   3.138787
## [1] 342.000000   3.138795
## [1] 343.000000   3.138803
## [1] 344.000000   3.138811
## [1] 345.00000   3.13882
## [1] 346.000000   3.138828
## [1] 347.000000   3.138836
## [1] 348.000000   3.138843
## [1] 349.000000   3.138851
## [1] 350.000000   3.138859
## [1] 351.000000   3.138867
## [1] 352.000000   3.138875
## [1] 353.000000   3.138882
## [1] 354.00000   3.13889
## [1] 355.000000   3.138898
## [1] 356.000000   3.138905
## [1] 357.000000   3.138913
## [1] 358.00000   3.13892
## [1] 359.000000   3.138928
## [1] 360.000000   3.138935
## [1] 361.000000   3.138943
## [1] 362.00000   3.13895
## [1] 363.000000   3.138957
## [1] 364.000000   3.138965
## [1] 365.000000   3.138972
## [1] 366.000000   3.138979
## [1] 367.000000   3.138986
## [1] 368.000000   3.138993
## [1] 369.000   3.139
## [1] 370.000000   3.139007
## [1] 371.000000   3.139014
## [1] 372.000000   3.139021
## [1] 373.000000   3.139028
## [1] 374.000000   3.139035
## [1] 375.000000   3.139042
## [1] 376.000000   3.139049
## [1] 377.000000   3.139055
## [1] 378.000000   3.139062
## [1] 379.000000   3.139069
## [1] 380.000000   3.139075
## [1] 381.000000   3.139082
## [1] 382.000000   3.139089
## [1] 383.000000   3.139095
## [1] 384.000000   3.139102
## [1] 385.000000   3.139108
## [1] 386.000000   3.139115
## [1] 387.000000   3.139121
## [1] 388.000000   3.139127
## [1] 389.000000   3.139134
## [1] 390.00000   3.13914
## [1] 391.000000   3.139146
## [1] 392.000000   3.139153
## [1] 393.000000   3.139159
## [1] 394.000000   3.139165
## [1] 395.000000   3.139171
## [1] 396.000000   3.139177
## [1] 397.000000   3.139183
## [1] 398.000000   3.139189
## [1] 399.000000   3.139195
## [1] 400.000000   3.139201
## [1] 401.000000   3.139207
## [1] 402.000000   3.139213
## [1] 403.000000   3.139219
## [1] 404.000000   3.139225
## [1] 405.000000   3.139231
## [1] 406.000000   3.139237
## [1] 407.000000   3.139243
## [1] 408.000000   3.139248
## [1] 409.000000   3.139254
## [1] 410.00000   3.13926
## [1] 411.000000   3.139266
## [1] 412.000000   3.139271
## [1] 413.000000   3.139277
## [1] 414.000000   3.139282
## [1] 415.000000   3.139288
## [1] 416.000000   3.139294
## [1] 417.000000   3.139299
## [1] 418.000000   3.139305
## [1] 419.00000   3.13931
## [1] 420.000000   3.139315
## [1] 421.000000   3.139321
## [1] 422.000000   3.139326
## [1] 423.000000   3.139332
## [1] 424.000000   3.139337
## [1] 425.000000   3.139342
## [1] 426.000000   3.139348
## [1] 427.000000   3.139353
## [1] 428.000000   3.139358
## [1] 429.000000   3.139363
## [1] 430.000000   3.139369
## [1] 431.000000   3.139374
## [1] 432.000000   3.139379
## [1] 433.000000   3.139384
## [1] 434.000000   3.139389
## [1] 435.000000   3.139394
## [1] 436.000000   3.139399
## [1] 437.000000   3.139404
## [1] 438.000000   3.139409
## [1] 439.000000   3.139414
## [1] 440.000000   3.139419
## [1] 441.000000   3.139424
## [1] 442.000000   3.139429
## [1] 443.000000   3.139434
## [1] 444.000000   3.139439
## [1] 445.000000   3.139444
## [1] 446.000000   3.139448
## [1] 447.000000   3.139453
## [1] 448.000000   3.139458
## [1] 449.000000   3.139463
## [1] 450.000000   3.139468
## [1] 451.000000   3.139472
## [1] 452.000000   3.139477
## [1] 453.000000   3.139482
## [1] 454.000000   3.139486
## [1] 455.000000   3.139491
## [1] 456.000000   3.139496
## [1] 457.0000   3.1395

mi.suma_3.2 = function(x){
k = 0
 sumatoria = 0
 sum = 0
 for (k in seq(x)) {
  s_k = (1/(k^2))
   sumatoria = sumatoria+s_k
 }
  return(sqrt(6*sumatoria))
}
mi.suma_3.2(1000)

## [1] 3.140638

4

mi.poli_4.1 <- function(x,n){
  me=NULL
  for(i in 1:n){
  s <- 1+x
  me[i]= (x^i)/i
  sum = s+me
  }
  print(sum)
  plot(c(1:20),sum,type = "l" )
 
}
mi.poli_4.1(2,20)

##  [1]     5.000000     5.000000     5.666667     7.000000     9.400000
##  [6]    13.666667    21.285714    35.000000    59.888889   105.400000
## [11]   189.181818   344.333333   633.153846  1173.285714  2187.533333
## [16]  4099.000000  7713.117647 14566.555556 27597.105263 52431.800000

5

5.1

mi.poli_5.1 = function(x){
  y = exp(x)*cos(x) #*(180/pi)
  return(y)
}
rango <- c(seq(3,6,0.1))
mi.poli_5.1(rango)

##  [1] -19.884531 -22.178753 -24.490697 -26.773182 -28.969238 -31.011186
##  [7] -32.819775 -34.303360 -35.357194 -35.862834 -35.687732 -34.685042
## [13] -32.693695 -29.538816 -25.032529 -18.975233 -11.157417  -1.362099
## [19]  10.632038  25.046705  42.099201  61.996630  84.929067 111.061586
## [25] 140.525075 173.405776 209.733494 249.468441 292.486707 338.564378
## [31] 387.360340

5.2

mi.poli_5.2 <- function(x){
  me=NULL
  vec = NULL
  for(i in 1:x){
  vec[i] = round((2^i)/i,3)
  }
  return(vec)
}
vect = mi.poli_5.2(25)
vect

##  [1]       2.000       2.000       2.667       4.000       6.400      10.667
##  [7]      18.286      32.000      56.889     102.400     186.182     341.333
## [13]     630.154    1170.286    2184.533    4096.000    7710.118   14563.556
## [19]   27594.105   52428.800   99864.381  190650.182  364722.087  699050.667
## [25] 1342177.280

5.3

vector_5.3 = paste(rep("trat"), 1:30)
vector_5.3

##  [1] "trat 1"  "trat 2"  "trat 3"  "trat 4"  "trat 5"  "trat 6"  "trat 7" 
##  [8] "trat 8"  "trat 9"  "trat 10" "trat 11" "trat 12" "trat 13" "trat 14"
## [15] "trat 15" "trat 16" "trat 17" "trat 18" "trat 19" "trat 20" "trat 21"
## [22] "trat 22" "trat 23" "trat 24" "trat 25" "trat 26" "trat 27" "trat 28"
## [29] "trat 29" "trat 30"

5.4

vector_5.3 = paste(rep("gen"), 1:10)
vector_5.3

##  [1] "gen 1"  "gen 2"  "gen 3"  "gen 4"  "gen 5"  "gen 6"  "gen 7"  "gen 8" 
##  [9] "gen 9"  "gen 10"

5.5

vec_5.5 <- replicate(20,rnorm(40,3,0.3))
vect_5.5 <- colMeans(vec_5.5)
vect_5.5

##  [1] 2.988457 3.040816 2.951497 2.938778 3.061114 3.033902 3.085661 2.998273
##  [9] 2.993491 2.991066 3.008360 2.921978 3.005830 3.033124 3.032093 3.017476
## [17] 2.968271 3.008245 2.996851 2.933366

5.6

vec_5.6 = NULL
  for(i in 1:ncol(vec_5.5)){
    vec_5.6[i] <- sd(vec_5.5[,i])}
  vec_5.6

##  [1] 0.2468044 0.3681146 0.2278619 0.3256627 0.3576524 0.3085730 0.3105537
##  [8] 0.3126417 0.2821374 0.2592634 0.3027011 0.2470736 0.3034292 0.2672211
## [15] 0.2975102 0.2772651 0.2615603 0.2653949 0.2777012 0.3248164

5.7

cfv_5.7 <- vec_5.6/vect_5.5
cfv_5.7

##  [1] 0.08258592 0.12105783 0.07720214 0.11081571 0.11683730 0.10170830
##  [7] 0.10064412 0.10427394 0.09425029 0.08667927 0.10061996 0.08455696
## [13] 0.10094690 0.08810094 0.09812042 0.09188645 0.08811873 0.08822251
## [19] 0.09266432 0.11073161

6

6.1

8

8.1

mi.resd_8.1 = function(x,N_0){
  N = NULL
  for(i in seq(1,x,8)){
  N[i] = N_0*((1/2)^(i))
  }
    return(N)
}
vect_8.1 <-(mi.resd_8.1(64, 500)[!is.na(mi.resd_8.1(64, 500))])
vect_8.1 <- round(vect_8.1,3)
vect_8.1

## [1] 250.000   0.977   0.004   0.000   0.000   0.000   0.000   0.000

8.2

 i = 1
 N = 0
while (round(N, 0) != 100) {
  N = round(500*((1/2)^(i)),0)
   i = i+0.01
  m = c(i,round(N,0))
  print(m)
}

## [1]   1.01 250.00
## [1]   1.02 248.00
## [1]   1.03 247.00
## [1]   1.04 245.00
## [1]   1.05 243.00
## [1]   1.06 241.00
## [1]   1.07 240.00
## [1]   1.08 238.00
## [1]   1.09 237.00
## [1]   1.1 235.0
## [1]   1.11 233.00
## [1]   1.12 232.00
## [1]   1.13 230.00
## [1]   1.14 228.00
## [1]   1.15 227.00
## [1]   1.16 225.00
## [1]   1.17 224.00
## [1]   1.18 222.00
## [1]   1.19 221.00
## [1]   1.2 219.0
## [1]   1.21 218.00
## [1]   1.22 216.00
## [1]   1.23 215.00
## [1]   1.24 213.00
## [1]   1.25 212.00
## [1]   1.26 210.00
## [1]   1.27 209.00
## [1]   1.28 207.00
## [1]   1.29 206.00
## [1]   1.3 204.0
## [1]   1.31 203.00
## [1]   1.32 202.00
## [1]   1.33 200.00
## [1]   1.34 199.00
## [1]   1.35 198.00
## [1]   1.36 196.00
## [1]   1.37 195.00
## [1]   1.38 193.00
## [1]   1.39 192.00
## [1]   1.4 191.0
## [1]   1.41 189.00
## [1]   1.42 188.00
## [1]   1.43 187.00
## [1]   1.44 186.00
## [1]   1.45 184.00
## [1]   1.46 183.00
## [1]   1.47 182.00
## [1]   1.48 180.00
## [1]   1.49 179.00
## [1]   1.5 178.0
## [1]   1.51 177.00
## [1]   1.52 176.00
## [1]   1.53 174.00
## [1]   1.54 173.00
## [1]   1.55 172.00
## [1]   1.56 171.00
## [1]   1.57 170.00
## [1]   1.58 168.00
## [1]   1.59 167.00
## [1]   1.6 166.0
## [1]   1.61 165.00
## [1]   1.62 164.00
## [1]   1.63 163.00
## [1]   1.64 162.00
## [1]   1.65 160.00
## [1]   1.66 159.00
## [1]   1.67 158.00
## [1]   1.68 157.00
## [1]   1.69 156.00
## [1]   1.7 155.0
## [1]   1.71 154.00
## [1]   1.72 153.00
## [1]   1.73 152.00
## [1]   1.74 151.00
## [1]   1.75 150.00
## [1]   1.76 149.00
## [1]   1.77 148.00
## [1]   1.78 147.00
## [1]   1.79 146.00
## [1]   1.8 145.0
## [1]   1.81 144.00
## [1]   1.82 143.00
## [1]   1.83 142.00
## [1]   1.84 141.00
## [1]   1.85 140.00
## [1]   1.86 139.00
## [1]   1.87 138.00
## [1]   1.88 137.00
## [1]   1.89 136.00
## [1]   1.9 135.0
## [1]   1.91 134.00
## [1]   1.92 133.00
## [1]   1.93 132.00
## [1]   1.94 131.00
## [1]   1.95 130.00
## [1]   1.96 129.00
## [1]   1.97 129.00
## [1]   1.98 128.00
## [1]   1.99 127.00
## [1]   2 126
## [1]   2.01 125.00
## [1]   2.02 124.00
## [1]   2.03 123.00
## [1]   2.04 122.00
## [1]   2.05 122.00
## [1]   2.06 121.00
## [1]   2.07 120.00
## [1]   2.08 119.00
## [1]   2.09 118.00
## [1]   2.1 117.0
## [1]   2.11 117.00
## [1]   2.12 116.00
## [1]   2.13 115.00
## [1]   2.14 114.00
## [1]   2.15 113.00
## [1]   2.16 113.00
## [1]   2.17 112.00
## [1]   2.18 111.00
## [1]   2.19 110.00
## [1]   2.2 110.0
## [1]   2.21 109.00
## [1]   2.22 108.00
## [1]   2.23 107.00
## [1]   2.24 107.00
## [1]   2.25 106.00
## [1]   2.26 105.00
## [1]   2.27 104.00
## [1]   2.28 104.00
## [1]   2.29 103.00
## [1]   2.3 102.0
## [1]   2.31 102.00
## [1]   2.32 101.00
## [1]   2.33 100.00

8.3

mi.resd_8.3 = function(x,N_0){
  N = NULL
  Nn = NULL
  for(i in 1:(x/8)){
  N[i] = N_0*((1/2)^(i*8))
  
  }
  plot(seq(1,x,8),N, pch = 16)

  
}
mi.resd_8.3(64, 500)

9

9.1

pH <- c(6.12, 5.13, 5.84, 6.53, 6.12, 6.30, 6.04, 5.79, 5.94, 6.03, 6.12)
t <- seq(0,300,30)
t

##  [1]   0  30  60  90 120 150 180 210 240 270 300

plot(t, pH, type= "b", pch = 16, col = "purple" )

10

10.1

mi.nor_10.1 = function(x){
  T
  dt<- rnorm(x,25,2)
  media <- mean(dt)
  mediat <- mean(dt,trim = 0.05)
  med <- median(dt)
  Q <- quantile(dt,c(0.10,0.25,0.75,0.90))
  Q1 <- Q[2]
  Q3 <- Q[3]
  P10 <- Q[1]
  P90 <- Q[4]
  dv1 <- dt>(media-sd(dt)) & dt<(media+sd(dt))
  DV1 <- 100*(sum(dv1))/x
  dv2 <- dt>(media-2*sd(dt)) & dt<(media+2*sd(dt))
  DV2 <- 100*(sum(dv2))/x
  
  print(list(media,mediat,med,Q1,Q3,P10,P90,DV1,DV2))
}
mi.nor_10.1(50)

## [[1]]
## [1] 25.35181
## 
## [[2]]
## [1] 25.36005
## 
## [[3]]
## [1] 25.30838
## 
## [[4]]
##     25% 
## 23.8011 
## 
## [[5]]
##      75% 
## 27.12511 
## 
## [[6]]
##      10% 
## 22.58801 
## 
## [[7]]
##      90% 
## 28.15354 
## 
## [[8]]
## [1] 62
## 
## [[9]]
## [1] 96

11

11.1

mi.T_11.1 <- function(x){
  T <- runif(x,18,24)
  media <- mean(T)
  mediat <- mean(T,trim = 0.05)
  med <- median(T)
  sd <- sd(T)
  Q <- quantile(T,c(0.10,0.25,0.75,0.90))
  Q1 <- Q[2]
  Q3 <- Q[3]
  P10 <- Q[1]
  P90 <- Q[4]
  dv1 <- T>(media-sd(T)) & T<(media+sd(T))
  DV1 <- 100*(sum(dv1))/x
  dv2 <- T>(media-2*sd(T)) & T<(media+2*sd(T))
  DV2 <- 100*(sum(dv2))/x
  CV <- sd/media
  
  print(list(media,mediat,med,Q1,Q3,P10,P90,DV1,DV2))
}
mi.T_11.1(40)

## [[1]]
## [1] 21.51507
## 
## [[2]]
## [1] 21.55121
## 
## [[3]]
## [1] 21.83636
## 
## [[4]]
##      25% 
## 20.10197 
## 
## [[5]]
##     75% 
## 22.7395 
## 
## [[6]]
##      10% 
## 19.33791 
## 
## [[7]]
##      90% 
## 23.71236 
## 
## [[8]]
## [1] 57.5
## 
## [[9]]
## [1] 100

12

12.1

pp <- rbeta(30, 0.8, 0.5)
pp <- pp*100
media <- mean(pp); media

## [1] 65.02446

dv2 <- pp>(media-2*sd(pp)) & pp<(media+2*sd(pp))
DV2 <- 100*(sum(dv2))/30; DV2

## [1] 96.66667

sc <- cumsum(pp); sc

##  [1]   84.81471  131.30961  219.86246  315.37980  379.96957  446.69699
##  [7]  544.59641  551.09460  592.16106  687.18667  716.32029  724.64444
## [13]  766.21843  815.28929  888.73432  950.42335 1021.57467 1118.34354
## [19] 1145.18372 1224.20775 1318.08118 1338.34939 1403.15117 1500.18346
## [25] 1543.65694 1580.66826 1680.64625 1779.92478 1856.38981 1950.73385

max(pp)

## [1] 99.97799

min(pp)

## [1] 6.498187

13

13.1

x <- c(1, 2, 5, 9, 11)
y <- c(2, 5, 1, 0, 23)
intersect(x, y)

## [1] 1 2 5

setdiff(x, y)

## [1]  9 11

setdiff(y, x)

## [1]  0 23

union(x, y)

## [1]  1  2  5  9 11  0 23

14

14.1

Td <- rbeta(30,2,1)
Td <- Td*25
Td[Td > 20]

##  [1] 24.41385 22.80428 23.99924 24.24419 21.15532 23.20651 21.88302 22.58439
##  [9] 21.36725 20.17872 24.34523

mean(Td[Td >= 4])

## [1] 17.46545

Td[Td == 0|Td == 1 ]

## numeric(0)

Td[Td %in% c(0, 0.6)]

## numeric(0)

15

15.1

\[ P = \frac{exitos}{total}\]

Pas <- 4/52
Pp <- (13/52)

15.2

Pcara <- 2/4
Psumocara <- 4/4 - 1/4
Palmenoscara <- 1/2 + 1/4
P2caras <- 1/4