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Trazado el gráfico de la función/ x*sin(x-1)

Gráfico de la función y = x*sin(x-1)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = x*sin(x - 1)
f(x)=xsin⁡(x−1)f{\left(x \right)} = x \sin{\left(x - 1 \right)} 
f = x*sin(x - 1)
Gráfico de la función
02468-8-6-4-2-1010-2020
Puntos de cruce con el eje de coordenadas X
El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
xsin⁡(x−1)=0x \sin{\left(x - 1 \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=1x_{2} = 1
x3=−ilog⁡(−ei)x_{3} = - i \log{\left(- e^{i} \right)}
Solución numérica
x1=−74.398223686155x_{1} = -74.398223686155
x2=−55.5486677646163x_{2} = -55.5486677646163
x3=−8.42477796076938x_{3} = -8.42477796076938
x4=−96.3893722612836x_{4} = -96.3893722612836
x5=−42.9822971502571x_{5} = -42.9822971502571
x6=79.5398163397448x_{6} = 79.5398163397448
x7=1x_{7} = 1
x8=44.9822971502571x_{8} = 44.9822971502571
x9=−71.2566310325652x_{9} = -71.2566310325652
x10=−64.9734457253857x_{10} = -64.9734457253857
x11=−46.1238898038469x_{11} = -46.1238898038469
x12=−83.8230016469244x_{12} = -83.8230016469244
x13=92.106186954104x_{13} = 92.106186954104
x14=82.6814089933346x_{14} = 82.6814089933346
x15=4.14159265358979x_{15} = 4.14159265358979
x16=29.2743338823081x_{16} = 29.2743338823081
x17=48.1238898038469x_{17} = 48.1238898038469
x18=−77.5398163397448x_{18} = -77.5398163397448
x19=−80.6814089933346x_{19} = -80.6814089933346
x20=88.9645943005142x_{20} = 88.9645943005142
x21=−93.2477796076938x_{21} = -93.2477796076938
x22=−14.707963267949x_{22} = -14.707963267949
x23=54.4070751110265x_{23} = 54.4070751110265
x24=−11.5663706143592x_{24} = -11.5663706143592
x25=63.8318530717959x_{25} = 63.8318530717959
x26=98.3893722612836x_{26} = 98.3893722612836
x27=66.9734457253857x_{27} = 66.9734457253857
x28=−52.4070751110265x_{28} = -52.4070751110265
x29=95.2477796076938x_{29} = 95.2477796076938
x30=10.4247779607694x_{30} = 10.4247779607694
x31=−86.9645943005142x_{31} = -86.9645943005142
x32=−5.28318530717959x_{32} = -5.28318530717959
x33=−2.14159265358979x_{33} = -2.14159265358979
x34=−58.6902604182061x_{34} = -58.6902604182061
x35=35.5575191894877x_{35} = 35.5575191894877
x36=51.2654824574367x_{36} = 51.2654824574367
x37=76.398223686155x_{37} = 76.398223686155
x38=73.2566310325652x_{38} = 73.2566310325652
x39=32.4159265358979x_{39} = 32.4159265358979
x40=−49.2654824574367x_{40} = -49.2654824574367
x41=−30.4159265358979x_{41} = -30.4159265358979
x42=−27.2743338823081x_{42} = -27.2743338823081
x43=−17.8495559215388x_{43} = -17.8495559215388
x44=−68.1150383789755x_{44} = -68.1150383789755
x45=−99.5309649148734x_{45} = -99.5309649148734
x46=70.1150383789755x_{46} = 70.1150383789755
x47=−24.1327412287183x_{47} = -24.1327412287183
x48=38.6991118430775x_{48} = 38.6991118430775
x49=−36.6991118430775x_{49} = -36.6991118430775
x50=26.1327412287183x_{50} = 26.1327412287183
x51=60.6902604182061x_{51} = 60.6902604182061
x52=19.8495559215388x_{52} = 19.8495559215388
x53=0x_{53} = 0
x54=−33.5575191894877x_{54} = -33.5575191894877
x55=−90.106186954104x_{55} = -90.106186954104
x56=−39.8407044966673x_{56} = -39.8407044966673
x57=57.5486677646163x_{57} = 57.5486677646163
x58=−61.8318530717959x_{58} = -61.8318530717959
x59=41.8407044966673x_{59} = 41.8407044966673
x60=13.5663706143592x_{60} = 13.5663706143592
x61=16.707963267949x_{61} = 16.707963267949
x62=−20.9911485751286x_{62} = -20.9911485751286
x63=22.9911485751286x_{63} = 22.9911485751286
x64=85.8230016469244x_{64} = 85.8230016469244
x65=164.362817986669x_{65} = 164.362817986669
x66=7.28318530717959x_{66} = 7.28318530717959
Puntos de cruce con el eje de coordenadas Y
El gráfico cruce el eje Y cuando x es igual a 0:
sustituimos x = 0 en x*sin(x - 1).
0sin⁡(−1)0 \sin{\left(-1 \right)}
Resultado:
f(0)=0f{\left(0 \right)} = 0
Punto:
(0, 0)
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
ddxf(x)=0\frac{d}{d x} f{\left(x \right)} = 0
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
primera derivada
xcos⁡(x−1)+sin⁡(x−1)=0x \cos{\left(x - 1 \right)} + \sin{\left(x - 1 \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−91.6878894142842x_{1} = -91.6878894142842
x2=2.9025816596713x_{2} = 2.9025816596713
x3=−35.1567518873749x_{3} = -35.1567518873749
x4=77.9818428080439x_{4} = 77.9818428080439
x5=81.1229390117807x_{5} = 81.1229390117807
x6=−47.7156405519083x_{6} = -47.7156405519083
x7=−69.7001808865412x_{7} = -69.7001808865412
x8=99.9701712382329x_{8} = 99.9701712382329
x9=43.4345199190886x_{9} = 43.4345199190886
x10=−88.5466836249472x_{10} = -88.5466836249472
x11=8.96506651296683x_{11} = 8.96506651296683
x12=15.2028494649391x_{12} = 15.2028494649391
x13=−22.6061518286588x_{13} = -22.6061518286588
x14=52.8551961430023x_{14} = 52.8551961430023
x15=−53.9963890778611x_{15} = -53.9963890778611
x16=87.4052384364358x_{16} = 87.4052384364358
x17=40.2947202239912x_{17} = 40.2947202239912
x18=65.417934536029x_{18} = 65.417934536029
x19=55.9957280448611x_{19} = 55.9957280448611
x20=74.8407882621237x_{20} = 74.8407882621237
x21=−85.4055062856094x_{21} = -85.4055062856094
x22=−97.9703754007943x_{22} = -97.9703754007943
x23=46.5745611270113x_{23} = 46.5745611270113
x24=34.0161122316173x_{24} = 34.0161122316173
x25=−60.2776451215302x_{25} = -60.2776451215302
x26=12.0781798144108x_{26} = 12.0781798144108
x27=−3.95975747525199x_{27} = -3.95975747525199
x28=24.6025687023826x_{28} = 24.6025687023826
x29=−25.74236450316x_{29} = -25.74236450316
x30=71.6997808455739x_{30} = 71.6997808455739
x31=−6.99595954344623x_{31} = -6.99595954344623
x32=−72.8411549997741x_{32} = -72.8411549997741
x33=−32.0179451984154x_{33} = -32.0179451984154
x34=62.2771126285488x_{34} = 62.2771126285488
x35=27.7395715348192x_{35} = 27.7395715348192
x36=−16.3398833066804x_{36} = -16.3398833066804
x37=−113.676928488903x_{37} = -113.676928488903
x38=−79.1232505037716x_{38} = -79.1232505037716
x39=−57.1369641096559x_{39} = -57.1369641096559
x40=90.5464342355346x_{40} = 90.5464342355346
x41=21.4669019371238x_{41} = 21.4669019371238
x42=18.3332512943446x_{42} = 18.3332512943446
x43=96.8289030622188x_{43} = 96.8289030622188
x44=−94.8291208275139x_{44} = -94.8291208275139
x45=−10.0943177411687x_{45} = -10.0943177411687
x46=−66.5592651262192x_{46} = -66.5592651262192
x47=−41.4356299587436x_{47} = -41.4356299587436
x48=84.2640722170426x_{48} = 84.2640722170426
x49=68.5588270317532x_{49} = 68.5588270317532
x50=49.7147981536679x_{50} = 49.7147981536679
x51=0.52026899271959x_{51} = 0.52026899271959
x52=30.8775049299126x_{52} = 30.8775049299126
x53=−50.8559396371055x_{53} = -50.8559396371055
x54=−101.111650976312x_{54} = -101.111650976312
x55=−82.2643606537498x_{55} = -82.2643606537498
x56=−1.24679137687774x_{56} = -1.24679137687774
x57=−75.9821802337515x_{57} = -75.9821802337515
x58=−44.5755235510474x_{58} = -44.5755235510474
x59=59.1363725465042x_{59} = 59.1363725465042
x60=−63.418416382217x_{60} = -63.418416382217
x61=−13.2127076381121x_{61} = -13.2127076381121
x62=93.687656640251x_{62} = 93.687656640251
x63=−38.2960146150878x_{63} = -38.2960146150878
x64=−19.4716638479466x_{64} = -19.4716638479466
x65=−28.8797427274828x_{65} = -28.8797427274828
x66=5.88082214577343x_{66} = 5.88082214577343
x67=37.1552231369057x_{67} = 37.1552231369057
Signos de extremos en los puntos:
(-91.68788941428421, -91.6824366178443)

(2.9025816596712968, 2.74428156512549)

(-35.15675188737488, -35.1425384922561)

(77.98184280804387, 77.9754318497405)

(81.12293901178074, -81.1167762293361)

(-47.71564055190829, -47.7051652580978)

(-69.70018088654118, 69.6930084112843)

(99.97017123823291, -99.9651701216543)

(43.43451991908864, -43.4230129123589)

(-88.54668362494724, 88.5410374261725)

(8.965066512966832, 8.9098095803668)

(15.202849464939055, 15.1700672327781)

(-22.606151828658817, -22.5840663628153)

(52.85519614300229, 52.8457388740002)

(-53.99638907786112, -53.9871315806976)

(87.4052384364358, -87.39951851703)

(40.29472022399124, 40.2823173792352)

(65.41793453602904, 65.4102927112959)

(55.99572804486114, -55.9868009275273)

(74.8407882621237, -74.8341083076369)

(-85.40550628560945, -85.3996524640445)

(-97.97037540079432, -97.9652722159642)

(46.57456112701128, 46.5638293631754)

(34.016112231617306, 34.0014228355276)

(-60.27764512153021, -60.2693518842382)

(12.078179814410767, -12.0369944668751)

(-3.9597574752519944, -3.83922289715174)

(24.602568702382584, -24.5822707686047)

(-25.742364503160008, 25.722963223315)

(71.69978084557387, 71.6928083407641)

(-6.995959543446228, 6.92556658903625)

(-72.84115499977409, -72.8342917185126)

(-32.01794519841537, 32.0023403713893)

(62.27711262854878, -62.2690855490764)

(27.73957153481918, 27.7215642924624)

(-16.339883306680367, -16.3093690231589)

(-113.67692848890253, 113.672530314275)

(-79.1232505037716, -79.116932005665)

(-57.13696410965594, 57.1282152170667)

(90.54643423553456, 90.5409127120238)

(21.46690193712382, 21.4436481058367)

(18.333251294344578, -18.3060391518502)

(96.82890306221881, 96.8237397278082)

(-94.82912082751392, 94.8238486252793)

(-10.09431774116865, -10.0451465534963)

(-66.55926512621922, -66.5517542955715)

(-41.43562995874359, -41.4235683178081)

(84.26407221704262, 84.2581391167382)

(68.55882703175322, -68.5515351883268)

(49.71479815366795, -49.7047438369707)

(0.5202689927195903, -0.240125244155308)

(30.877504929912625, -30.8613246386669)

(-50.85593963710546, 50.8461107939658)

(-101.1116509763116, 101.106706310507)

(-82.26436065374978, 82.2582833611003)

(-1.2467913768777432, 0.972602952761917)

(-75.98218023375154, 75.9756005981902)

(-44.57552355104743, 44.5643108650166)

(59.13637254650418, 59.1279193260472)

(-63.41841638221703, 63.4105337069909)

(-13.21270763811213, 13.1750270846423)

(93.687656640251, -93.6823202138901)

(-38.2960146150878, 38.2829650992537)

(-19.471663847946616, 19.446036191929)

(-28.879742727482828, -28.8624451069843)

(5.880822145773428, -5.79760050138202)

(37.15522313690572, -37.1417733852139)


Intervalos de crecimiento y decrecimiento de la función:
Hallemos los intervalos donde la función crece y decrece y también los puntos mínimos y máximos de la función, para lo cual miramos cómo se comporta la función en los extremos con desviación mínima del extremo:
Puntos mínimos de la función:
x1=−91.6878894142842x_{1} = -91.6878894142842
x2=−35.1567518873749x_{2} = -35.1567518873749
x3=81.1229390117807x_{3} = 81.1229390117807
x4=−47.7156405519083x_{4} = -47.7156405519083
x5=99.9701712382329x_{5} = 99.9701712382329
x6=43.4345199190886x_{6} = 43.4345199190886
x7=−22.6061518286588x_{7} = -22.6061518286588
x8=−53.9963890778611x_{8} = -53.9963890778611
x9=87.4052384364358x_{9} = 87.4052384364358
x10=55.9957280448611x_{10} = 55.9957280448611
x11=74.8407882621237x_{11} = 74.8407882621237
x12=−85.4055062856094x_{12} = -85.4055062856094
x13=−97.9703754007943x_{13} = -97.9703754007943
x14=−60.2776451215302x_{14} = -60.2776451215302
x15=12.0781798144108x_{15} = 12.0781798144108
x16=−3.95975747525199x_{16} = -3.95975747525199
x17=24.6025687023826x_{17} = 24.6025687023826
x18=−72.8411549997741x_{18} = -72.8411549997741
x19=62.2771126285488x_{19} = 62.2771126285488
x20=−16.3398833066804x_{20} = -16.3398833066804
x21=−79.1232505037716x_{21} = -79.1232505037716
x22=18.3332512943446x_{22} = 18.3332512943446
x23=−10.0943177411687x_{23} = -10.0943177411687
x24=−66.5592651262192x_{24} = -66.5592651262192
x25=−41.4356299587436x_{25} = -41.4356299587436
x26=68.5588270317532x_{26} = 68.5588270317532
x27=49.7147981536679x_{27} = 49.7147981536679
x28=0.52026899271959x_{28} = 0.52026899271959
x29=30.8775049299126x_{29} = 30.8775049299126
x30=93.687656640251x_{30} = 93.687656640251
x31=−28.8797427274828x_{31} = -28.8797427274828
x32=5.88082214577343x_{32} = 5.88082214577343
x33=37.1552231369057x_{33} = 37.1552231369057
Puntos máximos de la función:
x33=2.9025816596713x_{33} = 2.9025816596713
x33=77.9818428080439x_{33} = 77.9818428080439
x33=−69.7001808865412x_{33} = -69.7001808865412
x33=−88.5466836249472x_{33} = -88.5466836249472
x33=8.96506651296683x_{33} = 8.96506651296683
x33=15.2028494649391x_{33} = 15.2028494649391
x33=52.8551961430023x_{33} = 52.8551961430023
x33=40.2947202239912x_{33} = 40.2947202239912
x33=65.417934536029x_{33} = 65.417934536029
x33=46.5745611270113x_{33} = 46.5745611270113
x33=34.0161122316173x_{33} = 34.0161122316173
x33=−25.74236450316x_{33} = -25.74236450316
x33=71.6997808455739x_{33} = 71.6997808455739
x33=−6.99595954344623x_{33} = -6.99595954344623
x33=−32.0179451984154x_{33} = -32.0179451984154
x33=27.7395715348192x_{33} = 27.7395715348192
x33=−113.676928488903x_{33} = -113.676928488903
x33=−57.1369641096559x_{33} = -57.1369641096559
x33=90.5464342355346x_{33} = 90.5464342355346
x33=21.4669019371238x_{33} = 21.4669019371238
x33=96.8289030622188x_{33} = 96.8289030622188
x33=−94.8291208275139x_{33} = -94.8291208275139
x33=84.2640722170426x_{33} = 84.2640722170426
x33=−50.8559396371055x_{33} = -50.8559396371055
x33=−101.111650976312x_{33} = -101.111650976312
x33=−82.2643606537498x_{33} = -82.2643606537498
x33=−1.24679137687774x_{33} = -1.24679137687774
x33=−75.9821802337515x_{33} = -75.9821802337515
x33=−44.5755235510474x_{33} = -44.5755235510474
x33=59.1363725465042x_{33} = 59.1363725465042
x33=−63.418416382217x_{33} = -63.418416382217
x33=−13.2127076381121x_{33} = -13.2127076381121
x33=−38.2960146150878x_{33} = -38.2960146150878
x33=−19.4716638479466x_{33} = -19.4716638479466
Decrece en los intervalos
[99.9701712382329,∞)\left[99.9701712382329, \infty\right)
Crece en los intervalos
(−∞,−97.9703754007943]\left(-\infty, -97.9703754007943\right]
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(la segunda derivada es igual a cero),
las raíces de la ecuación obtenida serán los puntos de flexión para el gráfico de la función indicado:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
segunda derivada
−xsin⁡(x−1)+2cos⁡(x−1)=0- x \sin{\left(x - 1 \right)} + 2 \cos{\left(x - 1 \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−43.0287442777039x_{1} = -43.0287442777039
x2=19.9494753233659x_{2} = 19.9494753233659
x3=1.82980778511476x_{3} = 1.82980778511476
x4=−93.26921962348x_{4} = -93.26921962348
x5=57.5833860488256x_{5} = 57.5833860488256
x6=−21.0857165904375x_{6} = -21.0857165904375
x7=−80.7061851705226x_{7} = -80.7061851705226
x8=82.7055864445969x_{8} = 82.7055864445969
x9=−99.5510524070647x_{9} = -99.5510524070647
x10=−83.8468501375396x_{10} = -83.8468501375396
x11=76.4243873714523x_{11} = 76.4243873714523
x12=32.4774300959393x_{12} = 32.4774300959393
x13=23.0775967158608x_{13} = 23.0775967158608
x14=67.0032861473391x_{14} = 67.0032861473391
x15=85.8462948859968x_{15} = 85.8462948859968
x16=−46.1671835489837x_{16} = -46.1671835489837
x17=−55.5846334164642x_{17} = -55.5846334164642
x18=−71.2846801935272x_{18} = -71.2846801935272
x19=10.6110747018983x_{19} = 10.6110747018983
x20=−17.9604547964261x_{20} = -17.9604547964261
x21=−90.1283738829242x_{21} = -90.1283738829242
x22=−39.8907994245121x_{22} = -39.8907994245121
x23=54.4437937330033x_{23} = 54.4437937330033
x24=−0.382046815813819x_{24} = -0.382046815813819
x25=26.2089035666106x_{25} = 26.2089035666106
x26=−86.9875820379593x_{26} = -86.9875820379593
x27=−36.7534748494487x_{27} = -36.7534748494487
x28=4.55530232809579x_{28} = 4.55530232809579
x29=13.7112150916678x_{29} = 13.7112150916678
x30=−8.65194947351645x_{30} = -8.65194947351645
x31=−11.7351764999819x_{31} = -11.7351764999819
x32=73.2839153783142x_{32} = 73.2839153783142
x33=−52.4451916906271x_{33} = -52.4451916906271
x34=45.0266860764045x_{34} = 45.0266860764045
x35=51.3044457047797x_{35} = 51.3044457047797
x36=−61.8641707064194x_{36} = -61.8641707064194
x37=−96.410113997765x_{37} = -96.410113997765
x38=95.268769762935x_{38} = 95.268769762935
x39=92.1278924967891x_{39} = 92.1278924967891
x40=38.7506780882588x_{40} = 38.7506780882588
x41=−74.4250898785271x_{41} = -74.4250898785271
x42=−77.5655952554972x_{42} = -77.5655952554972
x43=7.5423880142908x_{43} = 7.5423880142908
x44=−24.2151471205849x_{44} = -24.2151471205849
x45=−5.62481138255003x_{45} = -5.62481138255003
x46=−68.1443794053954x_{46} = -68.1443794053954
x47=−2.76739284990934x_{47} = -2.76739284990934
x48=98.4096926652911x_{48} = 98.4096926652911
x49=−30.481446303805x_{49} = -30.481446303805
x50=48.1653895557155x_{50} = 48.1653895557155
x51=29.3423893946758x_{51} = 29.3423893946758
x52=35.6136185567512x_{52} = 35.6136185567512
x53=−65.0042032637559x_{53} = -65.0042032637559
x54=−14.8419099455851x_{54} = -14.8419099455851
x55=−58.7243047082906x_{55} = -58.7243047082906
x56=−27.3473371782595x_{56} = -27.3473371782595
x57=63.8631597994322x_{57} = 63.8631597994322
x58=−33.6169429546333x_{58} = -33.6169429546333
x59=41.8884141637599x_{59} = 41.8884141637599
x60=70.1435436150758x_{60} = 70.1435436150758
x61=104.691658963662x_{61} = 104.691658963662
x62=16.8262699577122x_{62} = 16.8262699577122
x63=−49.3060232280431x_{63} = -49.3060232280431
x64=79.5649477447241x_{64} = 79.5649477447241
x65=88.9870656937525x_{65} = 88.9870656937525
x66=60.7231848649845x_{66} = 60.7231848649845

Intervalos de convexidad y concavidad:
Hallemos los intervales donde la función es convexa o cóncava, para eso veamos cómo se comporta la función en los puntos de flexiones:
Cóncava en los intervalos
[104.691658963662,∞)\left[104.691658963662, \infty\right)
Convexa en los intervalos
(−∞,−99.5510524070647]\left(-\infty, -99.5510524070647\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(xsin⁡(x−1))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x \sin{\left(x - 1 \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−∞,∞⟩y = \left\langle -\infty, \infty\right\rangle
lim⁡x→∞(xsin⁡(x−1))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x \sin{\left(x - 1 \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−∞,∞⟩y = \left\langle -\infty, \infty\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función x*sin(x - 1), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞sin⁡(x−1)=⟨−1,1⟩\lim_{x \to -\infty} \sin{\left(x - 1 \right)} = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−1,1⟩xy = \left\langle -1, 1\right\rangle x
lim⁡x→∞sin⁡(x−1)=⟨−1,1⟩\lim_{x \to \infty} \sin{\left(x - 1 \right)} = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−1,1⟩xy = \left\langle -1, 1\right\rangle x
Paridad e imparidad de la función
Comprobemos si la función es par o impar mediante las relaciones f = f(-x) и f = -f(-x).
Pues, comprobamos:
xsin⁡(x−1)=xsin⁡(x+1)x \sin{\left(x - 1 \right)} = x \sin{\left(x + 1 \right)}
- No
xsin⁡(x−1)=−xsin⁡(x+1)x \sin{\left(x - 1 \right)} = - x \sin{\left(x + 1 \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор