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Trazado el gráfico de la función/ x^3cosx

Gráfico de la función y = x^3cosx

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
        3       
f(x) = x *cos(x)
f(x)=x3cos⁡(x)f{\left(x \right)} = x^{3} \cos{\left(x \right)} 
f = x^3*cos(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:
x3cos⁡(x)=0x^{3} \cos{\left(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}
Solución numérica
x1=−1.5707963267949x_{1} = -1.5707963267949
x2=−64.4026493985908x_{2} = -64.4026493985908
x3=76.9690200129499x_{3} = 76.9690200129499
x4=−23.5619449019235x_{4} = -23.5619449019235
x5=−58.1194640914112x_{5} = -58.1194640914112
x6=61.261056745001x_{6} = 61.261056745001
x7=80.1106126665397x_{7} = 80.1106126665397
x8=−48.6946861306418x_{8} = -48.6946861306418
x9=−29.845130209103x_{9} = -29.845130209103
x10=−4.71238898038469x_{10} = -4.71238898038469
x11=−86.3937979737193x_{11} = -86.3937979737193
x12=−36.1283155162826x_{12} = -36.1283155162826
x13=−98.9601685880785x_{13} = -98.9601685880785
x14=1.5707963267949x_{14} = 1.5707963267949
x15=−39.2699081698724x_{15} = -39.2699081698724
x16=73.8274273593601x_{16} = 73.8274273593601
x17=−92.6769832808989x_{17} = -92.6769832808989
x18=42.4115008234622x_{18} = 42.4115008234622
x19=67.5442420521806x_{19} = 67.5442420521806
x20=−32.9867228626928x_{20} = -32.9867228626928
x21=14.1371669411541x_{21} = 14.1371669411541
x22=4.71238898038469x_{22} = 4.71238898038469
x23=32.9867228626928x_{23} = 32.9867228626928
x24=−10.9955742875643x_{24} = -10.9955742875643
x25=0x_{25} = 0
x26=36.1283155162826x_{26} = 36.1283155162826
x27=70.6858347057703x_{27} = 70.6858347057703
x28=20.4203522483337x_{28} = 20.4203522483337
x29=−70.6858347057703x_{29} = -70.6858347057703
x30=−26.7035375555132x_{30} = -26.7035375555132
x31=10.9955742875643x_{31} = 10.9955742875643
x32=23.5619449019235x_{32} = 23.5619449019235
x33=45.553093477052x_{33} = 45.553093477052
x34=83.2522053201295x_{34} = 83.2522053201295
x35=−67.5442420521806x_{35} = -67.5442420521806
x36=−89.5353906273091x_{36} = -89.5353906273091
x37=−54.9778714378214x_{37} = -54.9778714378214
x38=95.8185759344887x_{38} = 95.8185759344887
x39=−17.2787595947439x_{39} = -17.2787595947439
x40=26.7035375555132x_{40} = 26.7035375555132
x41=17.2787595947439x_{41} = 17.2787595947439
x42=−42.4115008234622x_{42} = -42.4115008234622
x43=54.9778714378214x_{43} = 54.9778714378214
x44=−7.85398163397448x_{44} = -7.85398163397448
x45=48.6946861306418x_{45} = 48.6946861306418
x46=−51.8362787842316x_{46} = -51.8362787842316
x47=89.5353906273091x_{47} = 89.5353906273091
x48=92.6769832808989x_{48} = 92.6769832808989
x49=58.1194640914112x_{49} = 58.1194640914112
x50=−80.1106126665397x_{50} = -80.1106126665397
x51=−73.8274273593601x_{51} = -73.8274273593601
x52=86.3937979737193x_{52} = 86.3937979737193
x53=−76.9690200129499x_{53} = -76.9690200129499
x54=51.8362787842316x_{54} = 51.8362787842316
x55=39.2699081698724x_{55} = 39.2699081698724
x56=−20.4203522483337x_{56} = -20.4203522483337
x57=64.4026493985908x_{57} = 64.4026493985908
x58=−83.2522053201295x_{58} = -83.2522053201295
x59=98.9601685880785x_{59} = 98.9601685880785
x60=7.85398163397448x_{60} = 7.85398163397448
x61=−95.8185759344887x_{61} = -95.8185759344887
x62=−14.1371669411541x_{62} = -14.1371669411541
x63=29.845130209103x_{63} = 29.845130209103
x64=−45.553093477052x_{64} = -45.553093477052
x65=−61.261056745001x_{65} = -61.261056745001
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*cos(x).
03cos⁡(0)0^{3} \cos{\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
−x3sin⁡(x)+3x2cos⁡(x)=0- x^{3} \sin{\left(x \right)} + 3 x^{2} \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−28.3796522911214x_{1} = -28.3796522911214
x2=−72.2981021067071x_{2} = -72.2981021067071
x3=−40.913898225293x_{3} = -40.913898225293
x4=−62.8795272030449x_{4} = -62.8795272030449
x5=97.4201569811411x_{5} = 97.4201569811411
x6=34.6438990396267x_{6} = 34.6438990396267
x7=−9.72402747617551x_{7} = -9.72402747617551
x8=−47.1873806732917x_{8} = -47.1873806732917
x9=78.5779764426249x_{9} = 78.5779764426249
x10=59.7404355133729x_{10} = 59.7404355133729
x11=−50.325024483292x_{11} = -50.325024483292
x12=72.2981021067071x_{12} = 72.2981021067071
x13=−91.1390917936668x_{13} = -91.1390917936668
x14=69.1583898858035x_{14} = 69.1583898858035
x15=3.80876221919969x_{15} = 3.80876221919969
x16=47.1873806732917x_{16} = 47.1873806732917
x17=−6.70395577578075x_{17} = -6.70395577578075
x18=−44.0502961191214x_{18} = -44.0502961191214
x19=100.560788770886x_{19} = 100.560788770886
x20=−19.0061082873963x_{20} = -19.0061082873963
x21=−81.7181040853573x_{21} = -81.7181040853573
x22=37.7783560989567x_{22} = 37.7783560989567
x23=66.0188560490172x_{23} = 66.0188560490172
x24=−25.2509941253717x_{24} = -25.2509941253717
x25=44.0502961191214x_{25} = 44.0502961191214
x26=56.6016202331048x_{26} = 56.6016202331048
x27=91.1390917936668x_{27} = 91.1390917936668
x28=1.19245882933643x_{28} = 1.19245882933643
x29=87.9986725257711x_{29} = 87.9986725257711
x30=−94.2795891235637x_{30} = -94.2795891235637
x31=81.7181040853573x_{31} = 81.7181040853573
x32=−12.7966483902814x_{32} = -12.7966483902814
x33=40.913898225293x_{33} = 40.913898225293
x34=31.510845756676x_{34} = 31.510845756676
x35=19.0061082873963x_{35} = 19.0061082873963
x36=−56.6016202331048x_{36} = -56.6016202331048
x37=−59.7404355133729x_{37} = -59.7404355133729
x38=−87.9986725257711x_{38} = -87.9986725257711
x39=−75.4379705139506x_{39} = -75.4379705139506
x40=28.3796522911214x_{40} = 28.3796522911214
x41=−66.0188560490172x_{41} = -66.0188560490172
x42=0x_{42} = 0
x43=−34.6438990396267x_{43} = -34.6438990396267
x44=−37.7783560989567x_{44} = -37.7783560989567
x45=−97.4201569811411x_{45} = -97.4201569811411
x46=−3.80876221919969x_{46} = -3.80876221919969
x47=25.2509941253717x_{47} = 25.2509941253717
x48=−84.8583399660622x_{48} = -84.8583399660622
x49=15.8945130636842x_{49} = 15.8945130636842
x50=−100.560788770886x_{50} = -100.560788770886
x51=75.4379705139506x_{51} = 75.4379705139506
x52=9.72402747617551x_{52} = 9.72402747617551
x53=−15.8945130636842x_{53} = -15.8945130636842
x54=−31.510845756676x_{54} = -31.510845756676
x55=6.70395577578075x_{55} = 6.70395577578075
x56=−1.19245882933643x_{56} = -1.19245882933643
x57=−22.12591435735x_{57} = -22.12591435735
x58=−69.1583898858035x_{58} = -69.1583898858035
x59=−53.4631297645908x_{59} = -53.4631297645908
x60=62.8795272030449x_{60} = 62.8795272030449
x61=22.12591435735x_{61} = 22.12591435735
x62=53.4631297645908x_{62} = 53.4631297645908
x63=12.7966483902814x_{63} = 12.7966483902814
x64=94.2795891235637x_{64} = 94.2795891235637
x65=50.325024483292x_{65} = 50.325024483292
x66=84.8583399660622x_{66} = 84.8583399660622
x67=−78.5779764426249x_{67} = -78.5779764426249
Signos de extremos en los puntos:
(-28.37965229112142, 22730.4563261038)

(-72.29810210670713, 377578.383339478)

(-40.91389822529297, 68304.326534245)

(-62.87952720304487, -248332.79602616)

(97.42015698114113, -924146.136898602)

(34.64389903962671, -41424.5724319187)

(-9.72402747617551, 878.608875900237)

(-47.18738067329166, 104858.027361626)

(78.57797644262494, -484826.373587257)

(59.74043551337287, -212940.488750329)

(-50.32502448329199, -127227.703282192)

(72.29810210670713, -377578.383339478)

(-91.13909179366682, 756621.948790976)

(69.15838988580347, 330465.705562301)

(3.808762219199689, -43.4050129540828)

(47.18738067329166, -104858.027361626)

(-6.703955775780748, -275.015342086354)

(-44.05029611912139, -85278.9144731517)

(100.56078877088648, 1016465.96298217)

(-19.006108287396344, -6781.65561120486)

(-81.71810408535728, -545333.761493627)

(37.77835609895673, 53748.2253256845)

(66.01885604901719, -287445.855707585)

(-25.25099412537165, -15987.9141234403)

(44.05029611912139, 85278.9144731517)

(56.60162023310481, 181082.896088805)

(91.13909179366682, -756621.948790976)

(1.1924588293364287, 0.626323798219316)

(87.99867252577111, 681045.511399255)

(-94.27958912356374, -837593.47806229)

(81.71810408535728, 545333.761493627)

(-12.796648390281426, -2040.19006584704)

(40.91389822529297, -68304.326534245)

(31.51084575667604, 31147.3291476214)

(19.006108287396344, 6781.65561120486)

(-56.60162023310481, -181082.896088805)

(-59.74043551337287, 212940.488750329)

(-87.99867252577111, -681045.511399255)

(-75.43797051395065, -428969.926773577)

(28.37965229112142, -22730.4563261038)

(-66.01885604901719, 287445.855707585)

(0, 0)

(-34.64389903962671, 41424.5724319187)

(-37.77835609895673, -53748.2253256845)

(-97.42015698114113, 924146.136898602)

(-3.808762219199689, 43.4050129540828)

(25.25099412537165, 15987.9141234403)

(-84.85833996606219, 610678.128197996)

(15.894513063684203, -3945.84968737938)

(-100.56078877088648, -1016465.96298217)

(75.43797051395065, 428969.926773577)

(9.72402747617551, -878.608875900237)

(-15.894513063684203, 3945.84968737938)

(-31.51084575667604, -31147.3291476214)

(6.703955775780748, 275.015342086354)

(-1.1924588293364287, -0.626323798219316)

(-22.125914357349984, 10733.6615463961)

(-69.15838988580347, -330465.705562301)

(-53.463129764590846, 152573.980219896)

(62.87952720304487, 248332.79602616)

(22.125914357349984, -10733.6615463961)

(53.463129764590846, -152573.980219896)

(12.796648390281426, 2040.19006584704)

(94.27958912356374, 837593.47806229)

(50.32502448329199, 127227.703282192)

(84.85833996606219, -610678.128197996)

(-78.57797644262494, 484826.373587257)


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=−62.8795272030449x_{1} = -62.8795272030449
x2=97.4201569811411x_{2} = 97.4201569811411
x3=34.6438990396267x_{3} = 34.6438990396267
x4=78.5779764426249x_{4} = 78.5779764426249
x5=59.7404355133729x_{5} = 59.7404355133729
x6=−50.325024483292x_{6} = -50.325024483292
x7=72.2981021067071x_{7} = 72.2981021067071
x8=3.80876221919969x_{8} = 3.80876221919969
x9=47.1873806732917x_{9} = 47.1873806732917
x10=−6.70395577578075x_{10} = -6.70395577578075
x11=−44.0502961191214x_{11} = -44.0502961191214
x12=−19.0061082873963x_{12} = -19.0061082873963
x13=−81.7181040853573x_{13} = -81.7181040853573
x14=66.0188560490172x_{14} = 66.0188560490172
x15=−25.2509941253717x_{15} = -25.2509941253717
x16=91.1390917936668x_{16} = 91.1390917936668
x17=−94.2795891235637x_{17} = -94.2795891235637
x18=−12.7966483902814x_{18} = -12.7966483902814
x19=40.913898225293x_{19} = 40.913898225293
x20=−56.6016202331048x_{20} = -56.6016202331048
x21=−87.9986725257711x_{21} = -87.9986725257711
x22=−75.4379705139506x_{22} = -75.4379705139506
x23=28.3796522911214x_{23} = 28.3796522911214
x24=−37.7783560989567x_{24} = -37.7783560989567
x25=15.8945130636842x_{25} = 15.8945130636842
x26=−100.560788770886x_{26} = -100.560788770886
x27=9.72402747617551x_{27} = 9.72402747617551
x28=−31.510845756676x_{28} = -31.510845756676
x29=−1.19245882933643x_{29} = -1.19245882933643
x30=−69.1583898858035x_{30} = -69.1583898858035
x31=22.12591435735x_{31} = 22.12591435735
x32=53.4631297645908x_{32} = 53.4631297645908
x33=84.8583399660622x_{33} = 84.8583399660622
Puntos máximos de la función:
x33=−28.3796522911214x_{33} = -28.3796522911214
x33=−72.2981021067071x_{33} = -72.2981021067071
x33=−40.913898225293x_{33} = -40.913898225293
x33=−9.72402747617551x_{33} = -9.72402747617551
x33=−47.1873806732917x_{33} = -47.1873806732917
x33=−91.1390917936668x_{33} = -91.1390917936668
x33=69.1583898858035x_{33} = 69.1583898858035
x33=100.560788770886x_{33} = 100.560788770886
x33=37.7783560989567x_{33} = 37.7783560989567
x33=44.0502961191214x_{33} = 44.0502961191214
x33=56.6016202331048x_{33} = 56.6016202331048
x33=1.19245882933643x_{33} = 1.19245882933643
x33=87.9986725257711x_{33} = 87.9986725257711
x33=81.7181040853573x_{33} = 81.7181040853573
x33=31.510845756676x_{33} = 31.510845756676
x33=19.0061082873963x_{33} = 19.0061082873963
x33=−59.7404355133729x_{33} = -59.7404355133729
x33=−66.0188560490172x_{33} = -66.0188560490172
x33=−34.6438990396267x_{33} = -34.6438990396267
x33=−97.4201569811411x_{33} = -97.4201569811411
x33=−3.80876221919969x_{33} = -3.80876221919969
x33=25.2509941253717x_{33} = 25.2509941253717
x33=−84.8583399660622x_{33} = -84.8583399660622
x33=75.4379705139506x_{33} = 75.4379705139506
x33=−15.8945130636842x_{33} = -15.8945130636842
x33=6.70395577578075x_{33} = 6.70395577578075
x33=−22.12591435735x_{33} = -22.12591435735
x33=−53.4631297645908x_{33} = -53.4631297645908
x33=62.8795272030449x_{33} = 62.8795272030449
x33=12.7966483902814x_{33} = 12.7966483902814
x33=94.2795891235637x_{33} = 94.2795891235637
x33=50.325024483292x_{33} = 50.325024483292
x33=−78.5779764426249x_{33} = -78.5779764426249
Decrece en los intervalos
[97.4201569811411,∞)\left[97.4201569811411, \infty\right)
Crece en los intervalos
(−∞,−100.560788770886]\left(-\infty, -100.560788770886\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
x(−x2cos⁡(x)−6xsin⁡(x)+6cos⁡(x))=0x \left(- x^{2} \cos{\left(x \right)} - 6 x \sin{\left(x \right)} + 6 \cos{\left(x \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−55.0865764667238x_{1} = -55.0865764667238
x2=11.495916748171x_{2} = 11.495916748171
x3=20.7061859967519x_{3} = 20.7061859967519
x4=−61.3586871153543x_{4} = -61.3586871153543
x5=23.811319714972x_{5} = 23.811319714972
x6=−48.8172856736618x_{6} = -48.8172856736618
x7=73.9085198432299x_{7} = 73.9085198432299
x8=39.4215265901233x_{8} = 39.4215265901233
x9=−67.6328403186065x_{9} = -67.6328403186065
x10=42.5520407715344x_{10} = 42.5520407715344
x11=64.495545315785x_{11} = 64.495545315785
x12=5.63254352434708x_{12} = 5.63254352434708
x13=102.160458658341x_{13} = 102.160458658341
x14=−80.185369601293x_{14} = -80.185369601293
x15=45.6840551197015x_{15} = 45.6840551197015
x16=−11.495916748171x_{16} = -11.495916748171
x17=−92.741634081119x_{17} = -92.741634081119
x18=58.2223356290493x_{18} = 58.2223356290493
x19=67.6328403186065x_{19} = 67.6328403186065
x20=30.0435319479484x_{20} = 30.0435319479484
x21=−17.6130932998928x_{21} = -17.6130932998928
x22=−64.495545315785x_{22} = -64.495545315785
x23=−70.7705144780994x_{23} = -70.7705144780994
x24=−77.0468162058446x_{24} = -77.0468162058446
x25=−73.9085198432299x_{25} = -73.9085198432299
x26=−89.6023032306285x_{26} = -89.6023032306285
x27=86.4631361132255x_{27} = 86.4631361132255
x28=55.0865764667238x_{28} = 55.0865764667238
x29=0x_{29} = 0
x30=−83.3241511438861x_{30} = -83.3241511438861
x31=−33.1666524059798x_{31} = -33.1666524059798
x32=83.3241511438861x_{32} = 83.3241511438861
x33=70.7705144780994x_{33} = 70.7705144780994
x34=−23.811319714972x_{34} = -23.811319714972
x35=−2.98146897551057x_{35} = -2.98146897551057
x36=99.0207249350603x_{36} = 99.0207249350603
x37=17.6130932998928x_{37} = 17.6130932998928
x38=61.3586871153543x_{38} = 61.3586871153543
x39=89.6023032306285x_{39} = 89.6023032306285
x40=26.924570790473x_{40} = 26.924570790473
x41=51.9515155836453x_{41} = 51.9515155836453
x42=8.50941039706366x_{42} = 8.50941039706366
x43=48.8172856736618x_{43} = 48.8172856736618
x44=95.8811126479692x_{44} = 95.8811126479692
x45=−8.50941039706366x_{45} = -8.50941039706366
x46=−20.7061859967519x_{46} = -20.7061859967519
x47=77.0468162058446x_{47} = 77.0468162058446
x48=−58.2223356290493x_{48} = -58.2223356290493
x49=−95.8811126479692x_{49} = -95.8811126479692
x50=−30.0435319479484x_{50} = -30.0435319479484
x51=36.2928915290304x_{51} = 36.2928915290304
x52=−45.6840551197015x_{52} = -45.6840551197015
x53=−86.4631361132255x_{53} = -86.4631361132255
x54=−39.4215265901233x_{54} = -39.4215265901233
x55=80.185369601293x_{55} = 80.185369601293
x56=−36.2928915290304x_{56} = -36.2928915290304
x57=92.741634081119x_{57} = 92.741634081119
x58=33.1666524059798x_{58} = 33.1666524059798
x59=2.98146897551057x_{59} = 2.98146897551057
x60=−99.0207249350603x_{60} = -99.0207249350603
x61=−51.9515155836453x_{61} = -51.9515155836453
x62=−26.924570790473x_{62} = -26.924570790473
x63=−14.538821316956x_{63} = -14.538821316956
x64=−5.63254352434708x_{64} = -5.63254352434708
x65=−0.822926400561141x_{65} = -0.822926400561141
x66=14.538821316956x_{66} = 14.538821316956
x67=−42.5520407715344x_{67} = -42.5520407715344

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
[102.160458658341,∞)\left[102.160458658341, \infty\right)
Convexa en los intervalos
(−∞,−95.8811126479692]\left(-\infty, -95.8811126479692\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(x3cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x^{3} \cos{\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→∞(x3cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x^{3} \cos{\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 x^3*cos(x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(x2cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x^{2} \cos{\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→∞(x2cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x^{2} \cos{\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:
x3cos⁡(x)=−x3cos⁡(x)x^{3} \cos{\left(x \right)} = - x^{3} \cos{\left(x \right)}
- No
x3cos⁡(x)=x3cos⁡(x)x^{3} \cos{\left(x \right)} = x^{3} \cos{\left(x \right)}
- Sí
es decir, función
es
impar
    © Sr Examen – Калькулятор