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1 Xt = −1/2Xt−1 + 1 con X1 = 1

X<-numeric(10)
X [1]<-1
for (t in 2:10)     
X[t]<-(-0.5)*(X[t-1])+1
X
##  [1] 1.0000000 0.5000000 0.7500000 0.6250000 0.6875000 0.6562500 0.6718750
##  [8] 0.6640625 0.6679688 0.6660156
plot(X,type='l')

X<-numeric(100)
X [1]<-1
for (t in 2:100)     
X[t]<-(-0.5)*(X[t-1])+1
X
##   [1] 1.0000000 0.5000000 0.7500000 0.6250000 0.6875000 0.6562500 0.6718750
##   [8] 0.6640625 0.6679688 0.6660156 0.6669922 0.6665039 0.6667480 0.6666260
##  [15] 0.6666870 0.6666565 0.6666718 0.6666641 0.6666679 0.6666660 0.6666670
##  [22] 0.6666665 0.6666667 0.6666666 0.6666667 0.6666667 0.6666667 0.6666667
##  [29] 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667
##  [36] 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667
##  [43] 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667
##  [50] 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667
##  [57] 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667
##  [64] 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667
##  [71] 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667
##  [78] 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667
##  [85] 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667
##  [92] 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667
##  [99] 0.6666667 0.6666667
plot(X,type='l')

2 Xt =1/4Xt−1 con X1 = 1

X<-numeric(10)
X [1]<-1
for (t in 2:10)     
X[t]<-(1/4)*(X[t-1])
X
##  [1] 1.000000e+00 2.500000e-01 6.250000e-02 1.562500e-02 3.906250e-03
##  [6] 9.765625e-04 2.441406e-04 6.103516e-05 1.525879e-05 3.814697e-06
plot(X,type='l')

X<-numeric(100)
X [1]<-1
for (t in 2:100)     
X[t]<-(1/4)*(X[t-1])
X
##   [1] 1.000000e+00 2.500000e-01 6.250000e-02 1.562500e-02 3.906250e-03
##   [6] 9.765625e-04 2.441406e-04 6.103516e-05 1.525879e-05 3.814697e-06
##  [11] 9.536743e-07 2.384186e-07 5.960464e-08 1.490116e-08 3.725290e-09
##  [16] 9.313226e-10 2.328306e-10 5.820766e-11 1.455192e-11 3.637979e-12
##  [21] 9.094947e-13 2.273737e-13 5.684342e-14 1.421085e-14 3.552714e-15
##  [26] 8.881784e-16 2.220446e-16 5.551115e-17 1.387779e-17 3.469447e-18
##  [31] 8.673617e-19 2.168404e-19 5.421011e-20 1.355253e-20 3.388132e-21
##  [36] 8.470329e-22 2.117582e-22 5.293956e-23 1.323489e-23 3.308722e-24
##  [41] 8.271806e-25 2.067952e-25 5.169879e-26 1.292470e-26 3.231174e-27
##  [46] 8.077936e-28 2.019484e-28 5.048710e-29 1.262177e-29 3.155444e-30
##  [51] 7.888609e-31 1.972152e-31 4.930381e-32 1.232595e-32 3.081488e-33
##  [56] 7.703720e-34 1.925930e-34 4.814825e-35 1.203706e-35 3.009266e-36
##  [61] 7.523164e-37 1.880791e-37 4.701977e-38 1.175494e-38 2.938736e-39
##  [66] 7.346840e-40 1.836710e-40 4.591775e-41 1.147944e-41 2.869859e-42
##  [71] 7.174648e-43 1.793662e-43 4.484155e-44 1.121039e-44 2.802597e-45
##  [76] 7.006492e-46 1.751623e-46 4.379058e-47 1.094764e-47 2.736911e-48
##  [81] 6.842278e-49 1.710569e-49 4.276424e-50 1.069106e-50 2.672765e-51
##  [86] 6.681912e-52 1.670478e-52 4.176195e-53 1.044049e-53 2.610122e-54
##  [91] 6.525304e-55 1.631326e-55 4.078315e-56 1.019579e-56 2.548947e-57
##  [96] 6.372368e-58 1.593092e-58 3.982730e-59 9.956824e-60 2.489206e-60
plot(X,type='l')

3 Xt = −1/3Xt−1 con X1 = 2

X<-numeric(10)
X [1]<-1
for (t in 2:10)     
X[t]<-(-1/3)*(X[t-1])
X
##  [1]  1.000000e+00 -3.333333e-01  1.111111e-01 -3.703704e-02  1.234568e-02
##  [6] -4.115226e-03  1.371742e-03 -4.572474e-04  1.524158e-04 -5.080526e-05
plot(X,type='l')

X<-numeric(100)
X [1]<-1
for (t in 2:100)     
X[t]<-(-1/3)*(X[t-1])
X
##   [1]  1.000000e+00 -3.333333e-01  1.111111e-01 -3.703704e-02  1.234568e-02
##   [6] -4.115226e-03  1.371742e-03 -4.572474e-04  1.524158e-04 -5.080526e-05
##  [11]  1.693509e-05 -5.645029e-06  1.881676e-06 -6.272255e-07  2.090752e-07
##  [16] -6.969172e-08  2.323057e-08 -7.743524e-09  2.581175e-09 -8.603916e-10
##  [21]  2.867972e-10 -9.559907e-11  3.186636e-11 -1.062212e-11  3.540706e-12
##  [26] -1.180235e-12  3.934118e-13 -1.311373e-13  4.371242e-14 -1.457081e-14
##  [31]  4.856936e-15 -1.618979e-15  5.396595e-16 -1.798865e-16  5.996217e-17
##  [36] -1.998739e-17  6.662463e-18 -2.220821e-18  7.402737e-19 -2.467579e-19
##  [41]  8.225263e-20 -2.741754e-20  9.139181e-21 -3.046394e-21  1.015465e-21
##  [46] -3.384882e-22  1.128294e-22 -3.760980e-23  1.253660e-23 -4.178867e-24
##  [51]  1.392956e-24 -4.643185e-25  1.547728e-25 -5.159095e-26  1.719698e-26
##  [56] -5.732327e-27  1.910776e-27 -6.369253e-28  2.123084e-28 -7.076947e-29
##  [61]  2.358982e-29 -7.863275e-30  2.621092e-30 -8.736972e-31  2.912324e-31
##  [66] -9.707747e-32  3.235916e-32 -1.078639e-32  3.595462e-33 -1.198487e-33
##  [71]  3.994958e-34 -1.331653e-34  4.438842e-35 -1.479614e-35  4.932046e-36
##  [76] -1.644015e-36  5.480052e-37 -1.826684e-37  6.088946e-38 -2.029649e-38
##  [81]  6.765496e-39 -2.255165e-39  7.517217e-40 -2.505739e-40  8.352464e-41
##  [86] -2.784155e-41  9.280515e-42 -3.093505e-42  1.031168e-42 -3.437228e-43
##  [91]  1.145743e-43 -3.819142e-44  1.273047e-44 -4.243491e-45  1.414497e-45
##  [96] -4.714990e-46  1.571663e-46 -5.238878e-47  1.746293e-47 -5.820976e-48
plot(X,type='l')

4 Xt = 2Xt−1 con X1 = 2

X<-numeric(10)
X [1]<-1
for (t in 2:10)     
X[t]<-(2)*(X[t-1])
X
##  [1]   1   2   4   8  16  32  64 128 256 512
plot(X,type='l')

X<-numeric(100)
X [1]<-1
for (t in 2:100)     
X[t]<-(2)*(X[t-1])
X
##   [1] 1.000000e+00 2.000000e+00 4.000000e+00 8.000000e+00 1.600000e+01
##   [6] 3.200000e+01 6.400000e+01 1.280000e+02 2.560000e+02 5.120000e+02
##  [11] 1.024000e+03 2.048000e+03 4.096000e+03 8.192000e+03 1.638400e+04
##  [16] 3.276800e+04 6.553600e+04 1.310720e+05 2.621440e+05 5.242880e+05
##  [21] 1.048576e+06 2.097152e+06 4.194304e+06 8.388608e+06 1.677722e+07
##  [26] 3.355443e+07 6.710886e+07 1.342177e+08 2.684355e+08 5.368709e+08
##  [31] 1.073742e+09 2.147484e+09 4.294967e+09 8.589935e+09 1.717987e+10
##  [36] 3.435974e+10 6.871948e+10 1.374390e+11 2.748779e+11 5.497558e+11
##  [41] 1.099512e+12 2.199023e+12 4.398047e+12 8.796093e+12 1.759219e+13
##  [46] 3.518437e+13 7.036874e+13 1.407375e+14 2.814750e+14 5.629500e+14
##  [51] 1.125900e+15 2.251800e+15 4.503600e+15 9.007199e+15 1.801440e+16
##  [56] 3.602880e+16 7.205759e+16 1.441152e+17 2.882304e+17 5.764608e+17
##  [61] 1.152922e+18 2.305843e+18 4.611686e+18 9.223372e+18 1.844674e+19
##  [66] 3.689349e+19 7.378698e+19 1.475740e+20 2.951479e+20 5.902958e+20
##  [71] 1.180592e+21 2.361183e+21 4.722366e+21 9.444733e+21 1.888947e+22
##  [76] 3.777893e+22 7.555786e+22 1.511157e+23 3.022315e+23 6.044629e+23
##  [81] 1.208926e+24 2.417852e+24 4.835703e+24 9.671407e+24 1.934281e+25
##  [86] 3.868563e+25 7.737125e+25 1.547425e+26 3.094850e+26 6.189700e+26
##  [91] 1.237940e+27 2.475880e+27 4.951760e+27 9.903520e+27 1.980704e+28
##  [96] 3.961408e+28 7.922816e+28 1.584563e+29 3.169127e+29 6.338253e+29
plot(X,type='l')

5 Xt = −1/4Xt−1 + 3 con X1 = 1

X<-numeric(10)
X [1]<-1
for (t in 2:10)     
X[t]<-(-1/4)*(X[t-1])+3
X
##  [1] 1.000000 2.750000 2.312500 2.421875 2.394531 2.401367 2.399658 2.400085
##  [9] 2.399979 2.400005
plot(X,type='l')

X<-numeric(100)
X [1]<-1
for (t in 2:100)     
X[t]<-(-1/4)*(X[t-1])+3
X
##   [1] 1.000000 2.750000 2.312500 2.421875 2.394531 2.401367 2.399658 2.400085
##   [9] 2.399979 2.400005 2.399999 2.400000 2.400000 2.400000 2.400000 2.400000
##  [17] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [25] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [33] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [41] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [49] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [57] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [65] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [73] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [81] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [89] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [97] 2.400000 2.400000 2.400000 2.400000
plot(X,type='l')

PARTE 2

1

Y<-numeric(10)
for (t in 2:100)
Y[t]<-(-2/3)*(-1/2)^(t)+(2/3)
T<-sequence(10)
Y<-(-2/3)*(-1/2)^(t)+(2/3)
plot(X,type ='l' )

2

Y<-numeric(10)
for (t in 2:10)
Y[t]<-((4)*(1/4)^(t))
T<-sequence(10)
Y<-((4)*(1/4)^(t))
plot(X,type ='l' )

3

Y<-numeric(10)
for (t in 2:10)
Y[t]<-((-6)*(-1/3)^(t))
T<-sequence(10)
Y<-((-6)*(-1/3)^(t))
plot(X,type ='l' )

4

Y<-numeric(10)
for (t in 2:10)
Y[t]<-((1)*2^(t))
T<-sequence(10)
Y<-((1)*2^(t))
plot(X,type ='l' )

Y<-numeric(10)
for (t in 2:10)
Y[t]<-((28/5)*(-1/4)^(t))+12/5
T<-sequence(10)
Y<-((28/5)*(-1/4)^(t))+12/5
plot(X,type ='l' )