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x^3*sin(2*x)
Trazado el gráfico de la función/ x^3*sin(2*x)

Gráfico de la función y = x^3*sin(2*x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
        3         
f(x) = x *sin(2*x)
f(x)=x3sin⁡(2x)f{\left(x \right)} = x^{3} \sin{\left(2 x \right)} 
f = x^3*sin(2*x)
Gráfico de la función
02468-8-6-4-2-1010-20002000
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:
x3sin⁡(2x)=0x^{3} \sin{\left(2 x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=−π2x_{2} = - \frac{\pi}{2}
x3=π2x_{3} = \frac{\pi}{2}
x4=πx_{4} = \pi
Solución numérica
x1=69.1150383789755x_{1} = 69.1150383789755
x2=73.8274273593601x_{2} = 73.8274273593601
x3=70.6858347057703x_{3} = 70.6858347057703
x4=−89.5353906273091x_{4} = -89.5353906273091
x5=42.4115008234622x_{5} = 42.4115008234622
x6=−64.4026493985908x_{6} = -64.4026493985908
x7=14.1371669411541x_{7} = 14.1371669411541
x8=−1.5707963267949x_{8} = -1.5707963267949
x9=−53.4070751110265x_{9} = -53.4070751110265
x10=−67.5442420521806x_{10} = -67.5442420521806
x11=89.5353906273091x_{11} = 89.5353906273091
x12=−9.42477796076938x_{12} = -9.42477796076938
x13=−20.4203522483337x_{13} = -20.4203522483337
x14=28.2743338823081x_{14} = 28.2743338823081
x15=9.42477796076938x_{15} = 9.42477796076938
x16=−80.1106126665397x_{16} = -80.1106126665397
x17=50.2654824574367x_{17} = 50.2654824574367
x18=36.1283155162826x_{18} = 36.1283155162826
x19=−97.3893722612836x_{19} = -97.3893722612836
x20=95.8185759344887x_{20} = 95.8185759344887
x21=45.553093477052x_{21} = 45.553093477052
x22=92.6769832808989x_{22} = 92.6769832808989
x23=34.5575191894877x_{23} = 34.5575191894877
x24=1.5707963267949x_{24} = 1.5707963267949
x25=−29.845130209103x_{25} = -29.845130209103
x26=65.9734457253857x_{26} = 65.9734457253857
x27=0x_{27} = 0
x28=23.5619449019235x_{28} = 23.5619449019235
x29=20.4203522483337x_{29} = 20.4203522483337
x30=78.5398163397448x_{30} = 78.5398163397448
x31=59.6902604182061x_{31} = 59.6902604182061
x32=100.530964914873x_{32} = 100.530964914873
x33=−72.2566310325652x_{33} = -72.2566310325652
x34=21.9911485751286x_{34} = 21.9911485751286
x35=7.85398163397448x_{35} = 7.85398163397448
x36=−17.2787595947439x_{36} = -17.2787595947439
x37=4.71238898038469x_{37} = 4.71238898038469
x38=−37.6991118430775x_{38} = -37.6991118430775
x39=−81.6814089933346x_{39} = -81.6814089933346
x40=−21.9911485751286x_{40} = -21.9911485751286
x41=26.7035375555132x_{41} = 26.7035375555132
x42=−58.1194640914112x_{42} = -58.1194640914112
x43=12.5663706143592x_{43} = 12.5663706143592
x44=−87.9645943005142x_{44} = -87.9645943005142
x45=−42.4115008234622x_{45} = -42.4115008234622
x46=−3.14159265358979x_{46} = -3.14159265358979
x47=−14.1371669411541x_{47} = -14.1371669411541
x48=−94.2477796076938x_{48} = -94.2477796076938
x49=−51.8362787842316x_{49} = -51.8362787842316
x50=15.707963267949x_{50} = 15.707963267949
x51=40.8407044966673x_{51} = 40.8407044966673
x52=−102.101761241668x_{52} = -102.101761241668
x53=−43.9822971502571x_{53} = -43.9822971502571
x54=−6.28318530717959x_{54} = -6.28318530717959
x55=58.1194640914112x_{55} = 58.1194640914112
x56=−28.2743338823081x_{56} = -28.2743338823081
x57=48.6946861306418x_{57} = 48.6946861306418
x58=−83.2522053201295x_{58} = -83.2522053201295
x59=−95.8185759344887x_{59} = -95.8185759344887
x60=81.6814089933346x_{60} = 81.6814089933346
x61=−75.398223686155x_{61} = -75.398223686155
x62=−36.1283155162826x_{62} = -36.1283155162826
x63=94.2477796076938x_{63} = 94.2477796076938
x64=86.3937979737193x_{64} = 86.3937979737193
x65=−59.6902604182061x_{65} = -59.6902604182061
x66=87.9645943005142x_{66} = 87.9645943005142
x67=−15.707963267949x_{67} = -15.707963267949
x68=−23.5619449019235x_{68} = -23.5619449019235
x69=−61.261056745001x_{69} = -61.261056745001
x70=−7.85398163397448x_{70} = -7.85398163397448
x71=67.5442420521806x_{71} = 67.5442420521806
x72=80.1106126665397x_{72} = 80.1106126665397
x73=6.28318530717959x_{73} = 6.28318530717959
x74=29.845130209103x_{74} = 29.845130209103
x75=−50.2654824574367x_{75} = -50.2654824574367
x76=−18.8495559215388x_{76} = -18.8495559215388
x77=−73.8274273593601x_{77} = -73.8274273593601
x78=37.6991118430775x_{78} = 37.6991118430775
x79=−86.3937979737193x_{79} = -86.3937979737193
x80=51.8362787842316x_{80} = 51.8362787842316
x81=43.9822971502571x_{81} = 43.9822971502571
x82=56.5486677646163x_{82} = 56.5486677646163
x83=−45.553093477052x_{83} = -45.553093477052
x84=−65.9734457253857x_{84} = -65.9734457253857
x85=−39.2699081698724x_{85} = -39.2699081698724
x86=−31.4159265358979x_{86} = -31.4159265358979
x87=72.2566310325652x_{87} = 72.2566310325652
x88=64.4026493985908x_{88} = 64.4026493985908
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^3*sin(2*x).
03sin⁡(0⋅2)0^{3} \sin{\left(0 \cdot 2 \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
2x3cos⁡(2x)+3x2sin⁡(2x)=02 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=47.9249323344094x_{1} = 47.9249323344094
x2=−10.2826039699167x_{2} = -10.2826039699167
x3=11.8439605280008x_{3} = 11.8439605280008
x4=−1.22782193143972x_{4} = -1.22782193143972
x5=54.2063057730885x_{5} = 54.2063057730885
x6=−40.0740129706512x_{6} = -40.0740129706512
x7=5.62802150717675x_{7} = 5.62802150717675
x8=−44.7844359449587x_{8} = -44.7844359449587
x9=−33.7942995608669x_{9} = -33.7942995608669
x10=−55.7767128328603x_{10} = -55.7767128328603
x11=−32.2245820689369x_{11} = -32.2245820689369
x12=−76.1934639421929x_{12} = -76.1934639421929
x13=−49.4952326320496x_{13} = -49.4952326320496
x14=−63.6290361239317x_{14} = -63.6290361239317
x15=76.1934639421929x_{15} = 76.1934639421929
x16=−19.6730037732597x_{16} = -19.6730037732597
x17=−62.0585379193797x_{17} = -62.0585379193797
x18=−85.6171588404973x_{18} = -85.6171588404973
x19=−98.1824086733896x_{19} = -98.1824086733896
x20=62.0585379193797x_{20} = 62.0585379193797
x21=49.4952326320496x_{21} = 49.4952326320496
x22=2.6164692267562x_{22} = 2.6164692267562
x23=−41.6441046295573x_{23} = -41.6441046295573
x24=−60.4880551831425x_{24} = -60.4880551831425
x25=29.085495270014x_{25} = 29.085495270014
x26=−13.4074760654875x_{26} = -13.4074760654875
x27=−57.3471411923439x_{27} = -57.3471411923439
x28=−24.37806968342x_{28} = -24.37806968342
x29=−11.8439605280008x_{29} = -11.8439605280008
x30=84.0465261650259x_{30} = 84.0465261650259
x31=−84.0465261650259x_{31} = -84.0465261650259
x32=24.37806968342x_{32} = 24.37806968342
x33=4.10226568129063x_{33} = 4.10226568129063
x34=98.1824086733896x_{34} = 98.1824086733896
x35=10.2826039699167x_{35} = 10.2826039699167
x36=32.2245820689369x_{36} = 32.2245820689369
x37=0x_{37} = 0
x38=38.5039786681257x_{38} = 38.5039786681257
x39=−82.4758997198447x_{39} = -82.4758997198447
x40=−74.622874706927x_{40} = -74.622874706927
x41=52.635921916513x_{41} = 52.635921916513
x42=77.7640615384407x_{42} = 77.7640615384407
x43=16.5385861921536x_{43} = 16.5385861921536
x44=30.6549747237827x_{44} = 30.6549747237827
x45=−1.27381931903792⋅10−5x_{45} = -1.27381931903792 \cdot 10^{-5}
x46=−4.10226568129063x_{46} = -4.10226568129063
x47=−99.7530847493478x_{47} = -99.7530847493478
x48=−90.3290910005897x_{48} = -90.3290910005897
x49=−91.8997454600995x_{49} = -91.8997454600995
x50=−77.7640615384407x_{50} = -77.7640615384407
x51=−68.3406128944097x_{51} = -68.3406128944097
x52=−7.17167539419575x_{52} = -7.17167539419575
x53=85.6171588404973x_{53} = 85.6171588404973
x54=96.6117365061729x_{54} = 96.6117365061729
x55=14.9724903867582x_{55} = 14.9724903867582
x56=69.91116279715x_{56} = 69.91116279715
x57=41.6441046295573x_{57} = 41.6441046295573
x58=68.3406128944097x_{58} = 68.3406128944097
x59=−38.5039786681257x_{59} = -38.5039786681257
x60=−71.4817235219672x_{60} = -71.4817235219672
x61=99.7530847493478x_{61} = 99.7530847493478
x62=18.1054872777926x_{62} = 18.1054872777926
x63=−25.9470123181995x_{63} = -25.9470123181995
x64=−69.91116279715x_{64} = -69.91116279715
x65=−35.3641125887692x_{65} = -35.3641125887692
x66=88.7584415601129x_{66} = 88.7584415601129
x67=46.3546655978102x_{67} = 46.3546655978102
x68=91.8997454600995x_{68} = 91.8997454600995
x69=−46.3546655978102x_{69} = -46.3546655978102
x70=55.7767128328603x_{70} = 55.7767128328603
x71=−79.3346669994664x_{71} = -79.3346669994664
x72=40.0740129706512x_{72} = 40.0740129706512
x73=−8.72451217135942x_{73} = -8.72451217135942
x74=74.622874706927x_{74} = 74.622874706927
x75=71.4817235219672x_{75} = 71.4817235219672
x76=21.2410009626834x_{76} = 21.2410009626834
x77=82.4758997198447x_{77} = 82.4758997198447
x78=−18.1054872777926x_{78} = -18.1054872777926
x79=63.6290361239317x_{79} = 63.6290361239317
x80=27.5161654720774x_{80} = 27.5161654720774
x81=90.3290910005897x_{81} = 90.3290910005897
x82=−27.5161654720774x_{82} = -27.5161654720774
x83=−21.2410009626834x_{83} = -21.2410009626834
x84=−5.62802150717675x_{84} = -5.62802150717675
x85=60.4880551831425x_{85} = 60.4880551831425
x86=33.7942995608669x_{86} = 33.7942995608669
x87=−93.4704046857599x_{87} = -93.4704046857599
x88=−54.2063057730885x_{88} = -54.2063057730885
x89=93.4704046857599x_{89} = 93.4704046857599
x90=19.6730037732597x_{90} = 19.6730037732597
x91=−47.9249323344094x_{91} = -47.9249323344094
x92=25.9470123181995x_{92} = 25.9470123181995
Signos de extremos en los puntos:
(47.92493233440943, 110020.067366202)

(-10.28260396991667, 1075.81319367875)

(11.843960528000844, -1648.2974072075)

(-1.22782193143972, 1.17243656093029)

(54.206305773088495, 159214.719645564)

(-40.07401297065124, -64310.8840683886)

(5.628021507176746, -172.252470254656)

(-44.78443594495867, 89771.3713707053)

(-33.7942995608669, -38556.9755629467)

(-55.77671283286032, -173460.964415744)

(-32.22458206893689, 33426.5755569007)

(-76.19346394219286, 442251.191344079)

(-49.495232632049614, -121196.690834931)

(-63.62903612393173, 257540.413923442)

(76.19346394219286, 442251.191344079)

(-19.67300377325972, 7591.94906051947)

(-62.05853791937968, -238933.911571878)

(-85.61715884049732, 627502.981482316)

(-98.18240867338956, 946346.911128967)

(62.05853791937968, -238933.911571878)

(49.495232632049614, -121196.690834931)

(2.616469226756203, -15.5395850793378)

(-41.64410462955729, 72173.7118924681)

(-60.488055183142485, 221245.970153935)

(29.08549527001398, 24572.6850569784)

(-13.40747606548751, 2395.19017816037)

(-57.34714119234387, 188532.751284596)

(-24.378069683419987, -14460.3021958633)

(-11.843960528000844, -1648.2974072075)

(84.04652616502592, -593594.881702365)

(-84.04652616502592, -593594.881702365)

(24.378069683419987, -14460.3021958633)

(4.102265681290634, 64.8368741941138)

(98.18240867338956, 946346.911128967)

(10.28260396991667, 1075.81319367875)

(32.22458206893689, 33426.5755569007)

(0, 0)

(38.50397866812573, 57041.0512375873)

(-82.4758997198447, 560930.908768958)

(-74.62287470692696, -415459.032025635)

(52.63592191651302, -145770.762264945)

(77.76406153844069, -470171.203969721)

(16.538586192153595, 4505.22212782221)

(30.654974723782733, -28772.8969623597)

(-1.2738193190379192e-05, 5.26576314371066e-20)

(-4.102265681290634, 64.8368741941138)

(-99.75308474934779, -992498.614376456)

(-90.32909100058974, -736924.588979275)

(-91.89974546009948, 776041.743223149)

(-77.76406153844069, -470171.203969721)

(-68.34061289440973, -319103.833663929)

(-7.171675394195755, 361.047547551862)

(85.61715884049732, 627502.981482316)

(96.61173650617286, -901648.627097571)

(14.972490386758171, -3339.74673736232)

(69.91116279715004, 341617.126833644)

(41.64410462955729, 72173.7118924681)

(68.34061289440973, -319103.833663929)

(-38.50397866812573, 57041.0512375873)

(-71.48172352196723, -365165.254478444)

(99.75308474934779, -992498.614376456)

(18.105487277792616, -5914.87128129151)

(-25.9470123181995, 17439.6424066069)

(-69.91116279715004, 341617.126833644)

(-35.36411258876923, 44187.3517002339)

(88.75844156011291, 699144.580413006)

(46.35466559781024, -99552.7124482832)

(91.89974546009948, 776041.743223149)

(-46.35466559781024, -99552.7124482832)

(55.77671283286032, -173460.964415744)

(-79.33466699946635, 499242.324610489)

(40.07401297065124, -64310.8840683886)

(-8.724512171359422, -654.481972438707)

(74.62287470692696, -415459.032025635)

(71.48172352196723, -365165.254478444)

(21.24100096268344, -9559.71028374067)

(82.4758997198447, 560930.908768958)

(-18.105487277792616, -5914.87128129151)

(63.62903612393173, 257540.413923442)

(27.516165472077358, -20802.6851150688)

(90.32909100058974, -736924.588979275)

(-27.516165472077358, -20802.6851150688)

(-21.24100096268344, -9559.71028374067)

(-5.628021507176746, -172.252470254656)

(60.488055183142485, 221245.970153935)

(33.7942995608669, -38556.9755629467)

(-93.47040468575992, -816519.297852352)

(-54.206305773088495, 159214.719645564)

(93.47040468575992, -816519.297852352)

(19.67300377325972, 7591.94906051947)

(-47.92493233440943, 110020.067366202)

(25.9470123181995, 17439.6424066069)


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=11.8439605280008x_{1} = 11.8439605280008
x2=−40.0740129706512x_{2} = -40.0740129706512
x3=5.62802150717675x_{3} = 5.62802150717675
x4=−33.7942995608669x_{4} = -33.7942995608669
x5=−55.7767128328603x_{5} = -55.7767128328603
x6=−49.4952326320496x_{6} = -49.4952326320496
x7=−62.0585379193797x_{7} = -62.0585379193797
x8=62.0585379193797x_{8} = 62.0585379193797
x9=49.4952326320496x_{9} = 49.4952326320496
x10=2.6164692267562x_{10} = 2.6164692267562
x11=−24.37806968342x_{11} = -24.37806968342
x12=−11.8439605280008x_{12} = -11.8439605280008
x13=84.0465261650259x_{13} = 84.0465261650259
x14=−84.0465261650259x_{14} = -84.0465261650259
x15=24.37806968342x_{15} = 24.37806968342
x16=0x_{16} = 0
x17=−74.622874706927x_{17} = -74.622874706927
x18=52.635921916513x_{18} = 52.635921916513
x19=77.7640615384407x_{19} = 77.7640615384407
x20=30.6549747237827x_{20} = 30.6549747237827
x21=−99.7530847493478x_{21} = -99.7530847493478
x22=−90.3290910005897x_{22} = -90.3290910005897
x23=−77.7640615384407x_{23} = -77.7640615384407
x24=−68.3406128944097x_{24} = -68.3406128944097
x25=96.6117365061729x_{25} = 96.6117365061729
x26=14.9724903867582x_{26} = 14.9724903867582
x27=68.3406128944097x_{27} = 68.3406128944097
x28=−71.4817235219672x_{28} = -71.4817235219672
x29=99.7530847493478x_{29} = 99.7530847493478
x30=18.1054872777926x_{30} = 18.1054872777926
x31=46.3546655978102x_{31} = 46.3546655978102
x32=−46.3546655978102x_{32} = -46.3546655978102
x33=55.7767128328603x_{33} = 55.7767128328603
x34=40.0740129706512x_{34} = 40.0740129706512
x35=−8.72451217135942x_{35} = -8.72451217135942
x36=74.622874706927x_{36} = 74.622874706927
x37=71.4817235219672x_{37} = 71.4817235219672
x38=21.2410009626834x_{38} = 21.2410009626834
x39=−18.1054872777926x_{39} = -18.1054872777926
x40=27.5161654720774x_{40} = 27.5161654720774
x41=90.3290910005897x_{41} = 90.3290910005897
x42=−27.5161654720774x_{42} = -27.5161654720774
x43=−21.2410009626834x_{43} = -21.2410009626834
x44=−5.62802150717675x_{44} = -5.62802150717675
x45=33.7942995608669x_{45} = 33.7942995608669
x46=−93.4704046857599x_{46} = -93.4704046857599
x47=93.4704046857599x_{47} = 93.4704046857599
Puntos máximos de la función:
x47=47.9249323344094x_{47} = 47.9249323344094
x47=−10.2826039699167x_{47} = -10.2826039699167
x47=−1.22782193143972x_{47} = -1.22782193143972
x47=54.2063057730885x_{47} = 54.2063057730885
x47=−44.7844359449587x_{47} = -44.7844359449587
x47=−32.2245820689369x_{47} = -32.2245820689369
x47=−76.1934639421929x_{47} = -76.1934639421929
x47=−63.6290361239317x_{47} = -63.6290361239317
x47=76.1934639421929x_{47} = 76.1934639421929
x47=−19.6730037732597x_{47} = -19.6730037732597
x47=−85.6171588404973x_{47} = -85.6171588404973
x47=−98.1824086733896x_{47} = -98.1824086733896
x47=−41.6441046295573x_{47} = -41.6441046295573
x47=−60.4880551831425x_{47} = -60.4880551831425
x47=29.085495270014x_{47} = 29.085495270014
x47=−13.4074760654875x_{47} = -13.4074760654875
x47=−57.3471411923439x_{47} = -57.3471411923439
x47=4.10226568129063x_{47} = 4.10226568129063
x47=98.1824086733896x_{47} = 98.1824086733896
x47=10.2826039699167x_{47} = 10.2826039699167
x47=32.2245820689369x_{47} = 32.2245820689369
x47=38.5039786681257x_{47} = 38.5039786681257
x47=−82.4758997198447x_{47} = -82.4758997198447
x47=16.5385861921536x_{47} = 16.5385861921536
x47=−4.10226568129063x_{47} = -4.10226568129063
x47=−91.8997454600995x_{47} = -91.8997454600995
x47=−7.17167539419575x_{47} = -7.17167539419575
x47=85.6171588404973x_{47} = 85.6171588404973
x47=69.91116279715x_{47} = 69.91116279715
x47=41.6441046295573x_{47} = 41.6441046295573
x47=−38.5039786681257x_{47} = -38.5039786681257
x47=−25.9470123181995x_{47} = -25.9470123181995
x47=−69.91116279715x_{47} = -69.91116279715
x47=−35.3641125887692x_{47} = -35.3641125887692
x47=88.7584415601129x_{47} = 88.7584415601129
x47=91.8997454600995x_{47} = 91.8997454600995
x47=−79.3346669994664x_{47} = -79.3346669994664
x47=82.4758997198447x_{47} = 82.4758997198447
x47=63.6290361239317x_{47} = 63.6290361239317
x47=60.4880551831425x_{47} = 60.4880551831425
x47=−54.2063057730885x_{47} = -54.2063057730885
x47=19.6730037732597x_{47} = 19.6730037732597
x47=−47.9249323344094x_{47} = -47.9249323344094
x47=25.9470123181995x_{47} = 25.9470123181995
Decrece en los intervalos
[99.7530847493478,∞)\left[99.7530847493478, \infty\right)
Crece en los intervalos
(−∞,−99.7530847493478]\left(-\infty, -99.7530847493478\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
2x(−2x2sin⁡(2x)+6xcos⁡(2x)+3sin⁡(2x))=02 x \left(- 2 x^{2} \sin{\left(2 x \right)} + 6 x \cos{\left(2 x \right)} + 3 \sin{\left(2 x \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−42.446809801701x_{1} = -42.446809801701
x2=50.2952886626566x_{2} = 50.2952886626566
x3=51.865183812274x_{3} = 51.865183812274
x4=78.558905653723x_{4} = 78.558905653723
x5=−89.5521375145848x_{5} = -89.5521375145848
x6=48.7254514405766x_{6} = 48.7254514405766
x7=−17.3647165828345x_{7} = -17.3647165828345
x8=−73.8477338412449x_{8} = -73.8477338412449
x9=9.57890040507837x_{9} = 9.57890040507837
x10=−9.57890040507837x_{10} = -9.57890040507837
x11=−81.6997647754416x_{11} = -81.6997647754416
x12=92.6931628801607x_{12} = 92.6931628801607
x13=−15.8023232458624x_{13} = -15.8023232458624
x14=−80.129328033163x_{14} = -80.129328033163
x15=−67.5664351351282x_{15} = -67.5664351351282
x16=44.0163490577684x_{16} = 44.0163490577684
x17=45.5859746208446x_{17} = 45.5859746208446
x18=95.8342254072697x_{18} = 95.8342254072697
x19=−58.1452501209932x_{19} = -58.1452501209932
x20=58.1452501209932x_{20} = 58.1452501209932
x21=36.1697392174966x_{21} = 36.1697392174966
x22=59.7153690231685x_{22} = 59.7153690231685
x23=−86.4111533583478x_{23} = -86.4111533583478
x24=12.6835533701953x_{24} = 12.6835533701953
x25=15.8023232458624x_{25} = 15.8023232458624
x26=−6.50614905103301x_{26} = -6.50614905103301
x27=−62.8557081999776x_{27} = -62.8557081999776
x28=0x_{28} = 0
x29=−97.4047694840374x_{29} = -97.4047694840374
x30=8.03650370467335x_{30} = 8.03650370467335
x31=72.2773784586757x_{31} = 72.2773784586757
x32=−59.7153690231685x_{32} = -59.7153690231685
x33=23.6252666217247x_{33} = 23.6252666217247
x34=70.7070426391611x_{34} = 70.7070426391611
x35=14.2417247682097x_{35} = 14.2417247682097
x36=73.8477338412449x_{36} = 73.8477338412449
x37=−36.1697392174966x_{37} = -36.1697392174966
x38=−102.116448241893x_{38} = -102.116448241893
x39=86.4111533583478x_{39} = 86.4111533583478
x40=−4.99661458367966x_{40} = -4.99661458367966
x41=67.5664351351282x_{41} = 67.5664351351282
x42=−45.5859746208446x_{42} = -45.5859746208446
x43=42.446809801701x_{43} = 42.446809801701
x44=−44.0163490577684x_{44} = -44.0163490577684
x45=−18.928472870295x_{45} = -18.928472870295
x46=28.3271879634083x_{46} = 28.3271879634083
x47=89.5521375145848x_{47} = 89.5521375145848
x48=87.9816400097655x_{48} = 87.9816400097655
x49=64.4259235446297x_{49} = 64.4259235446297
x50=−37.7388169519635x_{50} = -37.7388169519635
x51=3.52604429659053x_{51} = 3.52604429659053
x52=37.7388169519635x_{52} = 37.7388169519635
x53=−22.0589400080757x_{53} = -22.0589400080757
x54=−61.2855225797955x_{54} = -61.2855225797955
x55=22.0589400080757x_{55} = 22.0589400080757
x56=−95.8342254072697x_{56} = -95.8342254072697
x57=−28.3271879634083x_{57} = -28.3271879634083
x58=2.13369690356451x_{58} = 2.13369690356451
x59=31.4635287842855x_{59} = 31.4635287842855
x60=−2.13369690356451x_{60} = -2.13369690356451
x61=−31.4635287842855x_{61} = -31.4635287842855
x62=−23.6252666217247x_{62} = -23.6252666217247
x63=56.5751687507672x_{63} = 56.5751687507672
x64=−51.865183812274x_{64} = -51.865183812274
x65=−14.2417247682097x_{65} = -14.2417247682097
x66=−3.52604429659053x_{66} = -3.52604429659053
x67=6.50614905103301x_{67} = 6.50614905103301
x68=−64.4259235446297x_{68} = -64.4259235446297
x69=−65.996166496632x_{69} = -65.996166496632
x70=84.8406781623214x_{70} = 84.8406781623214
x71=34.6008166012508x_{71} = 34.6008166012508
x72=−50.2952886626566x_{72} = -50.2952886626566
x73=81.6997647754416x_{73} = 81.6997647754416
x74=−83.2702150690143x_{74} = -83.2702150690143
x75=−33.032071036794x_{75} = -33.032071036794
x76=−20.4932875561866x_{76} = -20.4932875561866
x77=−8.03650370467335x_{77} = -8.03650370467335
x78=29.8952215488538x_{78} = 29.8952215488538
x79=65.996166496632x_{79} = 65.996166496632
x80=−87.9816400097655x_{80} = -87.9816400097655
x81=94.2636897304656x_{81} = 94.2636897304656
x82=100.545881264407x_{82} = 100.545881264407
x83=−29.8952215488538x_{83} = -29.8952215488538
x84=−72.2773784586757x_{84} = -72.2773784586757
x85=80.129328033163x_{85} = 80.129328033163
x86=20.4932875561866x_{86} = 20.4932875561866
x87=−39.3080313435475x_{87} = -39.3080313435475
x88=−69.1367277133119x_{88} = -69.1367277133119
x89=−75.4181075668373x_{89} = -75.4181075668373
x90=−94.2636897304656x_{90} = -94.2636897304656
x91=−53.4351318005928x_{91} = -53.4351318005928

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
[95.8342254072697,∞)\left[95.8342254072697, \infty\right)
Convexa en los intervalos
(−∞,−97.4047694840374]\left(-\infty, -97.4047694840374\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(x3sin⁡(2x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x^{3} \sin{\left(2 x \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→∞(x3sin⁡(2x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x^{3} \sin{\left(2 x \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^3*sin(2*x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(x2sin⁡(2x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x^{2} \sin{\left(2 x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−∞,∞⟩xy = \left\langle -\infty, \infty\right\rangle x
lim⁡x→∞(x2sin⁡(2x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x^{2} \sin{\left(2 x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−∞,∞⟩xy = \left\langle -\infty, \infty\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:
x3sin⁡(2x)=x3sin⁡(2x)x^{3} \sin{\left(2 x \right)} = x^{3} \sin{\left(2 x \right)}
- Sí
x3sin⁡(2x)=−x3sin⁡(2x)x^{3} \sin{\left(2 x \right)} = - x^{3} \sin{\left(2 x \right)}
- No
es decir, función
es
par
Gráfico
Gráfico de la función y = x^3*sin(2*x)
    © Sr Examen – Калькулятор