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

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

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
          2       
f(x) = 2*x *sin(x)
f(x)=2x2sin⁡(x)f{\left(x \right)} = 2 x^{2} \sin{\left(x \right)} 
f = (2*x^2)*sin(x)
Gráfico de la función
02468-8-6-4-2-1010-250250
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:
2x2sin⁡(x)=02 x^{2} \sin{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=πx_{2} = \pi
Solución numérica
x1=−75.398223686155x_{1} = -75.398223686155
x2=47.1238898038469x_{2} = 47.1238898038469
x3=−31.4159265358979x_{3} = -31.4159265358979
x4=9.42477796076938x_{4} = 9.42477796076938
x5=−34.5575191894877x_{5} = -34.5575191894877
x6=−97.3893722612836x_{6} = -97.3893722612836
x7=−62.8318530717959x_{7} = -62.8318530717959
x8=87.9645943005142x_{8} = 87.9645943005142
x9=−87.9645943005142x_{9} = -87.9645943005142
x10=−3.14159265358979x_{10} = -3.14159265358979
x11=6.28318530717959x_{11} = 6.28318530717959
x12=59.6902604182061x_{12} = 59.6902604182061
x13=−47.1238898038469x_{13} = -47.1238898038469
x14=−40.8407044966673x_{14} = -40.8407044966673
x15=100.530964914873x_{15} = 100.530964914873
x16=62.8318530717959x_{16} = 62.8318530717959
x17=−106.814150222053x_{17} = -106.814150222053
x18=3.14159265358979x_{18} = 3.14159265358979
x19=28.2743338823081x_{19} = 28.2743338823081
x20=−69.1150383789755x_{20} = -69.1150383789755
x21=97.3893722612836x_{21} = 97.3893722612836
x22=12.5663706143592x_{22} = 12.5663706143592
x23=94.2477796076938x_{23} = 94.2477796076938
x24=31.4159265358979x_{24} = 31.4159265358979
x25=25.1327412287183x_{25} = 25.1327412287183
x26=−37.6991118430775x_{26} = -37.6991118430775
x27=−94.2477796076938x_{27} = -94.2477796076938
x28=−59.6902604182061x_{28} = -59.6902604182061
x29=−56.5486677646163x_{29} = -56.5486677646163
x30=81.6814089933346x_{30} = 81.6814089933346
x31=43.9822971502571x_{31} = 43.9822971502571
x32=−91.106186954104x_{32} = -91.106186954104
x33=15.707963267949x_{33} = 15.707963267949
x34=34.5575191894877x_{34} = 34.5575191894877
x35=21.9911485751286x_{35} = 21.9911485751286
x36=40.8407044966673x_{36} = 40.8407044966673
x37=69.1150383789755x_{37} = 69.1150383789755
x38=65.9734457253857x_{38} = 65.9734457253857
x39=−72.2566310325652x_{39} = -72.2566310325652
x40=−21.9911485751286x_{40} = -21.9911485751286
x41=91.106186954104x_{41} = 91.106186954104
x42=53.4070751110265x_{42} = 53.4070751110265
x43=−28.2743338823081x_{43} = -28.2743338823081
x44=56.5486677646163x_{44} = 56.5486677646163
x45=−65.9734457253857x_{45} = -65.9734457253857
x46=−18.8495559215388x_{46} = -18.8495559215388
x47=−100.530964914873x_{47} = -100.530964914873
x48=−53.4070751110265x_{48} = -53.4070751110265
x49=−15.707963267949x_{49} = -15.707963267949
x50=84.8230016469244x_{50} = 84.8230016469244
x51=72.2566310325652x_{51} = 72.2566310325652
x52=18.8495559215388x_{52} = 18.8495559215388
x53=0x_{53} = 0
x54=−43.9822971502571x_{54} = -43.9822971502571
x55=−84.8230016469244x_{55} = -84.8230016469244
x56=−78.5398163397448x_{56} = -78.5398163397448
x57=−12.5663706143592x_{57} = -12.5663706143592
x58=75.398223686155x_{58} = 75.398223686155
x59=−6.28318530717959x_{59} = -6.28318530717959
x60=78.5398163397448x_{60} = 78.5398163397448
x61=−50.2654824574367x_{61} = -50.2654824574367
x62=−81.6814089933346x_{62} = -81.6814089933346
x63=50.2654824574367x_{63} = 50.2654824574367
x64=−9.42477796076938x_{64} = -9.42477796076938
x65=37.6991118430775x_{65} = 37.6991118430775
x66=−25.1327412287183x_{66} = -25.1327412287183
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 (2*x^2)*sin(x).
2⋅02sin⁡(0)2 \cdot 0^{2} \sin{\left(0 \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
2x2cos⁡(x)+4xsin⁡(x)=02 x^{2} \cos{\left(x \right)} + 4 x \sin{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=29.9118938695518x_{1} = 29.9118938695518
x2=48.7357007949054x_{2} = 48.7357007949054
x3=86.4169374541167x_{3} = 86.4169374541167
x4=95.839441141233x_{4} = 95.839441141233
x5=83.2762171649775x_{5} = 83.2762171649775
x6=−51.8748140534268x_{6} = -51.8748140534268
x7=36.1835330907526x_{7} = 36.1835330907526
x8=0x_{8} = 0
x9=51.8748140534268x_{9} = 51.8748140534268
x10=67.573830670859x_{10} = 67.573830670859
x11=33.0471686947054x_{11} = 33.0471686947054
x12=8.09616360322292x_{12} = 8.09616360322292
x13=−26.7780870755585x_{13} = -26.7780870755585
x14=5.08698509410227x_{14} = 5.08698509410227
x15=−55.0142096788381x_{15} = -55.0142096788381
x16=−92.6985552433969x_{16} = -92.6985552433969
x17=61.2936749662429x_{17} = 61.2936749662429
x18=11.17270586833x_{18} = 11.17270586833
x19=20.5175229099417x_{19} = 20.5175229099417
x20=−36.1835330907526x_{20} = -36.1835330907526
x21=−23.6463238196036x_{21} = -23.6463238196036
x22=−58.153842078645x_{22} = -58.153842078645
x23=−20.5175229099417x_{23} = -20.5175229099417
x24=70.7141100665485x_{24} = 70.7141100665485
x25=45.5969279840735x_{25} = 45.5969279840735
x26=14.2763529183365x_{26} = 14.2763529183365
x27=42.458570771699x_{27} = 42.458570771699
x28=−5.08698509410227x_{28} = -5.08698509410227
x29=−29.9118938695518x_{29} = -29.9118938695518
x30=98.9803718651523x_{30} = 98.9803718651523
x31=−42.458570771699x_{31} = -42.458570771699
x32=−80.1355651940744x_{32} = -80.1355651940744
x33=−89.5577188827244x_{33} = -89.5577188827244
x34=−11.17270586833x_{34} = -11.17270586833
x35=2.2889297281034x_{35} = 2.2889297281034
x36=−48.7357007949054x_{36} = -48.7357007949054
x37=−17.3932439645948x_{37} = -17.3932439645948
x38=−120.967848975693x_{38} = -120.967848975693
x39=92.6985552433969x_{39} = 92.6985552433969
x40=39.3207281322521x_{40} = 39.3207281322521
x41=−39.3207281322521x_{41} = -39.3207281322521
x42=−83.2762171649775x_{42} = -83.2762171649775
x43=73.8545010149048x_{43} = 73.8545010149048
x44=58.153842078645x_{44} = 58.153842078645
x45=−8.09616360322292x_{45} = -8.09616360322292
x46=−76.9949898891676x_{46} = -76.9949898891676
x47=64.4336791037316x_{47} = 64.4336791037316
x48=−64.4336791037316x_{48} = -64.4336791037316
x49=89.5577188827244x_{49} = 89.5577188827244
x50=55.0142096788381x_{50} = 55.0142096788381
x51=−33.0471686947054x_{51} = -33.0471686947054
x52=−67.573830670859x_{52} = -67.573830670859
x53=80.1355651940744x_{53} = 80.1355651940744
x54=76.9949898891676x_{54} = 76.9949898891676
x55=−70.7141100665485x_{55} = -70.7141100665485
x56=−61.2936749662429x_{56} = -61.2936749662429
x57=17.3932439645948x_{57} = 17.3932439645948
x58=26.7780870755585x_{58} = 26.7780870755585
x59=−14.2763529183365x_{59} = -14.2763529183365
x60=−98.9803718651523x_{60} = -98.9803718651523
x61=23.6463238196036x_{61} = 23.6463238196036
x62=−86.4169374541167x_{62} = -86.4169374541167
x63=−73.8545010149048x_{63} = -73.8545010149048
x64=−45.5969279840735x_{64} = -45.5969279840735
x65=3.95930141892882⋅10−7x_{65} = 3.95930141892882 \cdot 10^{-7}
x66=−2.2889297281034x_{66} = -2.2889297281034
x67=−95.839441141233x_{67} = -95.839441141233
Signos de extremos en los puntos:
(29.911893869551772, -1785.45615195047)

(48.73570079490539, -4746.34210913418)

(86.4169374541167, -14931.7757640607)

(95.83944114123304, 18366.3982625035)

(83.27621716497754, 13865.8584201569)

(-51.874814053426775, -5377.99711995352)

(36.18353309075258, -2614.50527615227)

(0, 0)

(51.874814053426775, 5377.99711995352)

(67.573830670859, -9128.44780914367)

(33.04716869470536, 2180.24167189308)

(8.096163603222921, 127.269963903109)

(-26.778087075558506, -1430.14855229942)

(5.08698509410227, -48.1659204461367)

(-55.01420967883812, 6049.13049370577)

(-92.69855524339692, 17182.0456843666)

(61.2936749662429, -7509.83237301393)

(11.172705868329984, -245.752347027832)

(20.51752290994169, 837.965774544867)

(-36.18353309075258, 2614.50527615227)

(-23.64632381960362, 1114.31859441805)

(-58.153842078645, -6759.74224185558)

(-20.51752290994169, -837.965774544867)

(70.7141100665485, 9996.97312317635)

(45.59692798407349, 4154.16544571548)

(14.276352918336478, 403.686435763722)

(42.458570771699044, -3601.4671082363)

(-5.08698509410227, 48.1659204461367)

(-29.911893869551772, 1785.45615195047)

(98.98037186515228, -19590.2292535616)

(-42.458570771699044, 3601.4671082363)

(-80.13556519407445, 12839.4194856396)

(-89.55771888272442, -16037.1715184829)

(-11.172705868329984, 245.752347027832)

(2.2889297281034042, 7.89060325056865)

(-48.73570079490539, 4746.34210913418)

(-17.393243964594753, 601.089105315992)

(-120.96784897569329, -29262.4417914774)

(92.69855524339692, -17182.0456843666)

(39.32072813225213, 3088.24706637139)

(-39.32072813225213, -3088.24706637139)

(-83.27621716497754, -13865.8584201569)

(73.85450101490484, -10904.976839001)

(58.153842078645, 6759.74224185558)

(-8.096163603222921, -127.269963903109)

(-76.9949898891676, -11852.458959142)

(64.43367910373156, 8299.40089374957)

(-64.43367910373156, -8299.40089374957)

(89.55771888272442, 16037.1715184829)

(55.01420967883812, -6049.13049370577)

(-33.04716869470536, -2180.24167189308)

(-67.573830670859, 9128.44780914367)

(80.13556519407445, -12839.4194856396)

(76.9949898891676, 11852.458959142)

(-70.7141100665485, -9996.97312317635)

(-61.2936749662429, 7509.83237301393)

(17.393243964594753, -601.089105315992)

(26.778087075558506, 1430.14855229942)

(-14.276352918336478, -403.686435763722)

(-98.98037186515228, 19590.2292535616)

(23.64632381960362, -1114.31859441805)

(-86.4169374541167, 14931.7757640607)

(-73.85450101490484, 10904.976839001)

(-45.59692798407349, -4154.16544571548)

(3.9593014189288195e-07, 1.24132554381009e-19)

(-2.2889297281034042, -7.89060325056865)

(-95.83944114123304, -18366.3982625035)


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=29.9118938695518x_{1} = 29.9118938695518
x2=48.7357007949054x_{2} = 48.7357007949054
x3=86.4169374541167x_{3} = 86.4169374541167
x4=−51.8748140534268x_{4} = -51.8748140534268
x5=36.1835330907526x_{5} = 36.1835330907526
x6=67.573830670859x_{6} = 67.573830670859
x7=−26.7780870755585x_{7} = -26.7780870755585
x8=5.08698509410227x_{8} = 5.08698509410227
x9=61.2936749662429x_{9} = 61.2936749662429
x10=11.17270586833x_{10} = 11.17270586833
x11=−58.153842078645x_{11} = -58.153842078645
x12=−20.5175229099417x_{12} = -20.5175229099417
x13=42.458570771699x_{13} = 42.458570771699
x14=98.9803718651523x_{14} = 98.9803718651523
x15=−89.5577188827244x_{15} = -89.5577188827244
x16=−120.967848975693x_{16} = -120.967848975693
x17=92.6985552433969x_{17} = 92.6985552433969
x18=−39.3207281322521x_{18} = -39.3207281322521
x19=−83.2762171649775x_{19} = -83.2762171649775
x20=73.8545010149048x_{20} = 73.8545010149048
x21=−8.09616360322292x_{21} = -8.09616360322292
x22=−76.9949898891676x_{22} = -76.9949898891676
x23=−64.4336791037316x_{23} = -64.4336791037316
x24=55.0142096788381x_{24} = 55.0142096788381
x25=−33.0471686947054x_{25} = -33.0471686947054
x26=80.1355651940744x_{26} = 80.1355651940744
x27=−70.7141100665485x_{27} = -70.7141100665485
x28=17.3932439645948x_{28} = 17.3932439645948
x29=−14.2763529183365x_{29} = -14.2763529183365
x30=23.6463238196036x_{30} = 23.6463238196036
x31=−45.5969279840735x_{31} = -45.5969279840735
x32=−2.2889297281034x_{32} = -2.2889297281034
x33=−95.839441141233x_{33} = -95.839441141233
Puntos máximos de la función:
x33=95.839441141233x_{33} = 95.839441141233
x33=83.2762171649775x_{33} = 83.2762171649775
x33=51.8748140534268x_{33} = 51.8748140534268
x33=33.0471686947054x_{33} = 33.0471686947054
x33=8.09616360322292x_{33} = 8.09616360322292
x33=−55.0142096788381x_{33} = -55.0142096788381
x33=−92.6985552433969x_{33} = -92.6985552433969
x33=20.5175229099417x_{33} = 20.5175229099417
x33=−36.1835330907526x_{33} = -36.1835330907526
x33=−23.6463238196036x_{33} = -23.6463238196036
x33=70.7141100665485x_{33} = 70.7141100665485
x33=45.5969279840735x_{33} = 45.5969279840735
x33=14.2763529183365x_{33} = 14.2763529183365
x33=−5.08698509410227x_{33} = -5.08698509410227
x33=−29.9118938695518x_{33} = -29.9118938695518
x33=−42.458570771699x_{33} = -42.458570771699
x33=−80.1355651940744x_{33} = -80.1355651940744
x33=−11.17270586833x_{33} = -11.17270586833
x33=2.2889297281034x_{33} = 2.2889297281034
x33=−48.7357007949054x_{33} = -48.7357007949054
x33=−17.3932439645948x_{33} = -17.3932439645948
x33=39.3207281322521x_{33} = 39.3207281322521
x33=58.153842078645x_{33} = 58.153842078645
x33=64.4336791037316x_{33} = 64.4336791037316
x33=89.5577188827244x_{33} = 89.5577188827244
x33=−67.573830670859x_{33} = -67.573830670859
x33=76.9949898891676x_{33} = 76.9949898891676
x33=−61.2936749662429x_{33} = -61.2936749662429
x33=26.7780870755585x_{33} = 26.7780870755585
x33=−98.9803718651523x_{33} = -98.9803718651523
x33=−86.4169374541167x_{33} = -86.4169374541167
x33=−73.8545010149048x_{33} = -73.8545010149048
Decrece en los intervalos
[98.9803718651523,∞)\left[98.9803718651523, \infty\right)
Crece en los intervalos
(−∞,−120.967848975693]\left(-\infty, -120.967848975693\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
2(−x2sin⁡(x)+4xcos⁡(x)+2sin⁡(x))=02 \left(- x^{2} \sin{\left(x \right)} + 4 x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−62.895397234671x_{1} = -62.895397234671
x2=−1.51985529843113x_{2} = -1.51985529843113
x3=−75.4512070764701x_{3} = -75.4512070764701
x4=−100.570724821846x_{4} = -100.570724821846
x5=−56.6192418251285x_{5} = -56.6192418251285
x6=−22.1703631077661x_{6} = -22.1703631077661
x7=−40.9382191715155x_{7} = -40.9382191715155
x8=0x_{8} = 0
x9=1.51985529843113x_{9} = 1.51985529843113
x10=56.6192418251285x_{10} = 56.6192418251285
x11=−6.83214574693118x_{11} = -6.83214574693118
x12=−47.2084939833195x_{12} = -47.2084939833195
x13=97.4304127980508x_{13} = 97.4304127980508
x14=−97.4304127980508x_{14} = -97.4304127980508
x15=9.81900340196872x_{15} = 9.81900340196872
x16=−44.0729006762809x_{16} = -44.0729006762809
x17=69.1728243307457x_{17} = 69.1728243307457
x18=81.7303260381702x_{18} = 81.7303260381702
x19=47.2084939833195x_{19} = 47.2084939833195
x20=−31.5423183719258x_{20} = -31.5423183719258
x21=−3.99444471574142x_{21} = -3.99444471574142
x22=91.1500530451789x_{22} = 91.1500530451789
x23=75.4512070764701x_{23} = 75.4512070764701
x24=−59.7571356682663x_{24} = -59.7571356682663
x25=−66.0339743721325x_{25} = -66.0339743721325
x26=−84.8701107016488x_{26} = -84.8701107016488
x27=53.4817799880237x_{27} = 53.4817799880237
x28=34.6725661362236x_{28} = 34.6725661362236
x29=94.290185945407x_{29} = 94.290185945407
x30=3.99444471574142x_{30} = 3.99444471574142
x31=−53.4817799880237x_{31} = -53.4817799880237
x32=−28.4145306971625x_{32} = -28.4145306971625
x33=6.83214574693118x_{33} = 6.83214574693118
x34=−91.1500530451789x_{34} = -91.1500530451789
x35=59.7571356682663x_{35} = 59.7571356682663
x36=−69.1728243307457x_{36} = -69.1728243307457
x37=−94.290185945407x_{37} = -94.290185945407
x38=−19.0575561537385x_{38} = -19.0575561537385
x39=−72.3119117382824x_{39} = -72.3119117382824
x40=−12.8711405784383x_{40} = -12.8711405784383
x41=−50.3448303040845x_{41} = -50.3448303040845
x42=28.4145306971625x_{42} = 28.4145306971625
x43=40.9382191715155x_{43} = 40.9382191715155
x44=37.8046732869526x_{44} = 37.8046732869526
x45=−25.2900904960802x_{45} = -25.2900904960802
x46=84.8701107016488x_{46} = 84.8701107016488
x47=−37.8046732869526x_{47} = -37.8046732869526
x48=22.1703631077661x_{48} = 22.1703631077661
x49=88.0100241275575x_{49} = 88.0100241275575
x50=−9.81900340196872x_{50} = -9.81900340196872
x51=−15.9554654297511x_{51} = -15.9554654297511
x52=62.895397234671x_{52} = 62.895397234671
x53=−81.7303260381702x_{53} = -81.7303260381702
x54=−78.5906855194896x_{54} = -78.5906855194896
x55=19.0575561537385x_{55} = 19.0575561537385
x56=100.570724821846x_{56} = 100.570724821846
x57=25.2900904960802x_{57} = 25.2900904960802
x58=31.5423183719258x_{58} = 31.5423183719258
x59=−88.0100241275575x_{59} = -88.0100241275575
x60=78.5906855194896x_{60} = 78.5906855194896
x61=66.0339743721325x_{61} = 66.0339743721325
x62=50.3448303040845x_{62} = 50.3448303040845
x63=44.0729006762809x_{63} = 44.0729006762809
x64=15.9554654297511x_{64} = 15.9554654297511
x65=−34.6725661362236x_{65} = -34.6725661362236
x66=72.3119117382824x_{66} = 72.3119117382824
x67=12.8711405784383x_{67} = 12.8711405784383

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
[97.4304127980508,∞)\left[97.4304127980508, \infty\right)
Convexa en los intervalos
(−∞,−97.4304127980508]\left(-\infty, -97.4304127980508\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(2x2sin⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(2 x^{2} \sin{\left(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→∞(2x2sin⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(2 x^{2} \sin{\left(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 (2*x^2)*sin(x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(2xsin⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(2 x \sin{\left(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→∞(2xsin⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(2 x \sin{\left(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:
2x2sin⁡(x)=−2x2sin⁡(x)2 x^{2} \sin{\left(x \right)} = - 2 x^{2} \sin{\left(x \right)}
- No
2x2sin⁡(x)=2x2sin⁡(x)2 x^{2} \sin{\left(x \right)} = 2 x^{2} \sin{\left(x \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор