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

Gráfico de la función y = sin(x)/3*x

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       sin(x)  
f(x) = ------*x
         3
f(x)=xsin⁡(x)3f{\left(x \right)} = x \frac{\sin{\left(x \right)}}{3} 
f = x*(sin(x)/3)
Gráfico de la función
02468-8-6-4-2-10105-5
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)3=0x \frac{\sin{\left(x \right)}}{3} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=πx_{2} = \pi
Solución numérica
x1=69.1150383789755x_{1} = 69.1150383789755
x2=65.9734457253857x_{2} = 65.9734457253857
x3=−91.106186954104x_{3} = -91.106186954104
x4=697.433569096934x_{4} = 697.433569096934
x5=−59.6902604182061x_{5} = -59.6902604182061
x6=−21.9911485751286x_{6} = -21.9911485751286
x7=12.5663706143592x_{7} = 12.5663706143592
x8=21.9911485751286x_{8} = 21.9911485751286
x9=−69.1150383789755x_{9} = -69.1150383789755
x10=−100.530964914873x_{10} = -100.530964914873
x11=3.14159265358979x_{11} = 3.14159265358979
x12=−3.14159265358979x_{12} = -3.14159265358979
x13=−25.1327412287183x_{13} = -25.1327412287183
x14=−15.707963267949x_{14} = -15.707963267949
x15=−53.4070751110265x_{15} = -53.4070751110265
x16=−72.2566310325652x_{16} = -72.2566310325652
x17=84.8230016469244x_{17} = 84.8230016469244
x18=−81.6814089933346x_{18} = -81.6814089933346
x19=−94.2477796076938x_{19} = -94.2477796076938
x20=18.8495559215388x_{20} = 18.8495559215388
x21=−65.9734457253857x_{21} = -65.9734457253857
x22=94.2477796076938x_{22} = 94.2477796076938
x23=9.42477796076938x_{23} = 9.42477796076938
x24=−40.8407044966673x_{24} = -40.8407044966673
x25=34.5575191894877x_{25} = 34.5575191894877
x26=0x_{26} = 0
x27=97.3893722612836x_{27} = 97.3893722612836
x28=53.4070751110265x_{28} = 53.4070751110265
x29=−62.8318530717959x_{29} = -62.8318530717959
x30=59.6902604182061x_{30} = 59.6902604182061
x31=−28.2743338823081x_{31} = -28.2743338823081
x32=−56.5486677646163x_{32} = -56.5486677646163
x33=91.106186954104x_{33} = 91.106186954104
x34=15.707963267949x_{34} = 15.707963267949
x35=−18.8495559215388x_{35} = -18.8495559215388
x36=6.28318530717959x_{36} = 6.28318530717959
x37=56.5486677646163x_{37} = 56.5486677646163
x38=87.9645943005142x_{38} = 87.9645943005142
x39=31.4159265358979x_{39} = 31.4159265358979
x40=25.1327412287183x_{40} = 25.1327412287183
x41=43.9822971502571x_{41} = 43.9822971502571
x42=−47.1238898038469x_{42} = -47.1238898038469
x43=72.2566310325652x_{43} = 72.2566310325652
x44=−34.5575191894877x_{44} = -34.5575191894877
x45=−97.3893722612836x_{45} = -97.3893722612836
x46=−50.2654824574367x_{46} = -50.2654824574367
x47=100.530964914873x_{47} = 100.530964914873
x48=81.6814089933346x_{48} = 81.6814089933346
x49=−75.398223686155x_{49} = -75.398223686155
x50=40.8407044966673x_{50} = 40.8407044966673
x51=−9.42477796076938x_{51} = -9.42477796076938
x52=78.5398163397448x_{52} = 78.5398163397448
x53=−87.9645943005142x_{53} = -87.9645943005142
x54=37.6991118430775x_{54} = 37.6991118430775
x55=−78.5398163397448x_{55} = -78.5398163397448
x56=−6.28318530717959x_{56} = -6.28318530717959
x57=50.2654824574367x_{57} = 50.2654824574367
x58=−37.6991118430775x_{58} = -37.6991118430775
x59=−43.9822971502571x_{59} = -43.9822971502571
x60=47.1238898038469x_{60} = 47.1238898038469
x61=28.2743338823081x_{61} = 28.2743338823081
x62=62.8318530717959x_{62} = 62.8318530717959
x63=−31.4159265358979x_{63} = -31.4159265358979
x64=−12.5663706143592x_{64} = -12.5663706143592
x65=75.398223686155x_{65} = 75.398223686155
x66=−84.8230016469244x_{66} = -84.8230016469244
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 (sin(x)/3)*x.
0sin⁡(0)30 \frac{\sin{\left(0 \right)}}{3}
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)3+sin⁡(x)3=0\frac{x \cos{\left(x \right)}}{3} + \frac{\sin{\left(x \right)}}{3} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−64.4181717218392x_{1} = -64.4181717218392
x2=−45.57503179559x_{2} = -45.57503179559
x3=70.69997803861x_{3} = 70.69997803861
x4=−51.855560729152x_{4} = -51.855560729152
x5=−48.7152107175577x_{5} = -48.7152107175577
x6=−7.97866571241324x_{6} = -7.97866571241324
x7=89.5465575382492x_{7} = 89.5465575382492
x8=−42.4350618814099x_{8} = -42.4350618814099
x9=64.4181717218392x_{9} = 64.4181717218392
x10=36.1559664195367x_{10} = 36.1559664195367
x11=−29.8785865061074x_{11} = -29.8785865061074
x12=−98.9702722883957x_{12} = -98.9702722883957
x13=45.57503179559x_{13} = 45.57503179559
x14=−73.8409691490209x_{14} = -73.8409691490209
x15=98.9702722883957x_{15} = 98.9702722883957
x16=95.8290108090195x_{16} = 95.8290108090195
x17=14.2074367251912x_{17} = 14.2074367251912
x18=80.1230928148503x_{18} = 80.1230928148503
x19=−20.469167402741x_{19} = -20.469167402741
x20=73.8409691490209x_{20} = 73.8409691490209
x21=−58.1366632448992x_{21} = -58.1366632448992
x22=4.91318043943488x_{22} = 4.91318043943488
x23=−17.3363779239834x_{23} = -17.3363779239834
x24=−61.2773745335697x_{24} = -61.2773745335697
x25=23.6042847729804x_{25} = 23.6042847729804
x26=−39.295350981473x_{26} = -39.295350981473
x27=58.1366632448992x_{27} = 58.1366632448992
x28=−54.9960525574964x_{28} = -54.9960525574964
x29=83.2642147040886x_{29} = 83.2642147040886
x30=39.295350981473x_{30} = 39.295350981473
x31=20.469167402741x_{31} = 20.469167402741
x32=102.111554139654x_{32} = 102.111554139654
x33=51.855560729152x_{33} = 51.855560729152
x34=92.687771772017x_{34} = 92.687771772017
x35=17.3363779239834x_{35} = 17.3363779239834
x36=0x_{36} = 0
x37=−67.5590428388084x_{37} = -67.5590428388084
x38=−11.085538406497x_{38} = -11.085538406497
x39=7.97866571241324x_{39} = 7.97866571241324
x40=−95.8290108090195x_{40} = -95.8290108090195
x41=−14.2074367251912x_{41} = -14.2074367251912
x42=67.5590428388084x_{42} = 67.5590428388084
x43=−70.69997803861x_{43} = -70.69997803861
x44=−23.6042847729804x_{44} = -23.6042847729804
x45=11.085538406497x_{45} = 11.085538406497
x46=−4.91318043943488x_{46} = -4.91318043943488
x47=−76.9820093304187x_{47} = -76.9820093304187
x48=2.02875783811043x_{48} = 2.02875783811043
x49=−26.7409160147873x_{49} = -26.7409160147873
x50=26.7409160147873x_{50} = 26.7409160147873
x51=54.9960525574964x_{51} = 54.9960525574964
x52=−89.5465575382492x_{52} = -89.5465575382492
x53=−36.1559664195367x_{53} = -36.1559664195367
x54=−83.2642147040886x_{54} = -83.2642147040886
x55=86.4053708116885x_{55} = 86.4053708116885
x56=61.2773745335697x_{56} = 61.2773745335697
x57=76.9820093304187x_{57} = 76.9820093304187
x58=−92.687771772017x_{58} = -92.687771772017
x59=42.4350618814099x_{59} = 42.4350618814099
x60=−86.4053708116885x_{60} = -86.4053708116885
x61=48.7152107175577x_{61} = 48.7152107175577
x62=−33.0170010333572x_{62} = -33.0170010333572
x63=33.0170010333572x_{63} = 33.0170010333572
x64=−80.1230928148503x_{64} = -80.1230928148503
x65=−2.02875783811043x_{65} = -2.02875783811043
x66=29.8785865061074x_{66} = 29.8785865061074
Signos de extremos en los puntos:
(-64.41817172183916, 21.4701371131251)

(-45.57503179559002, 15.1880216120089)

(70.69997803861, 23.564302320531)

(-51.85556072915197, 17.2819737500672)

(-48.715210717557724, -16.234983408456)

(-7.978665712413241, 2.63890912386259)

(89.54655753824919, 29.8469914576284)

(-42.43506188140989, -14.1410946924197)

(64.41817172183916, 21.4701371131251)

(36.15596641953672, -12.0473817907474)

(-29.878586506107393, -9.9539553863956)

(-98.9702722883957, -32.9884068843729)

(45.57503179559002, 15.1880216120089)

(-73.8409691490209, -24.6113995905139)

(98.9702722883957, -32.9884068843729)

(95.82901080901948, 31.9412645361552)

(14.207436725191188, 4.72412470459143)

(80.12309281485025, -26.7056177152197)

(-20.46916740274095, 6.81492801941742)

(73.8409691490209, -24.6113995905139)

(-58.13666324489916, 19.3760215760286)

(4.913180439434884, -1.60482329657076)

(-17.33637792398336, -5.76920286928617)

(-61.277374533569656, -20.4230721814922)

(23.604284772980407, -7.86104354987779)

(-39.295350981472986, 13.0942110022973)

(58.13666324489916, 19.3760215760286)

(-54.99605255749639, -18.3289877498992)

(83.26421470408864, 27.7527367909844)

(39.295350981472986, 13.0942110022973)

(20.46916740274095, 6.81492801941742)

(102.11155413965392, 34.0355526287721)

(51.85556072915197, 17.2819737500672)

(92.687771772017, -30.8941259293531)

(17.33637792398336, -5.76920286928617)

(0, 0)

(-67.5590428388084, -22.5172143736575)

(-11.085538406497022, -3.68023600531)

(7.978665712413241, 2.63890912386259)

(-95.82901080901948, 31.9412645361552)

(-14.207436725191188, 4.72412470459143)

(67.5590428388084, -22.5172143736575)

(-70.69997803861, 23.564302320531)

(-23.604284772980407, -7.86104354987779)

(11.085538406497022, -3.68023600531)

(-4.913180439434884, -1.60482329657076)

(-76.98200933041872, 25.6585050427546)

(2.028757838110434, 0.606568580386551)

(-26.74091601478731, 8.90741255489913)

(26.74091601478731, 8.90741255489913)

(54.99605255749639, -18.3289877498992)

(-89.54655753824919, 29.8469914576284)

(-36.15596641953672, -12.0473817907474)

(-83.26421470408864, 27.7527367909844)

(86.40537081168854, -28.7998615718702)

(61.277374533569656, -20.4230721814922)

(76.98200933041872, 25.6585050427546)

(-92.687771772017, -30.8941259293531)

(42.43506188140989, -14.1410946924197)

(-86.40537081168854, -28.7998615718702)

(48.715210717557724, -16.234983408456)

(-33.017001033357246, 11.0006225769485)

(33.017001033357246, 11.0006225769485)

(-80.12309281485025, -26.7056177152197)

(-2.028757838110434, 0.606568580386551)

(29.878586506107393, -9.9539553863956)


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=−48.7152107175577x_{1} = -48.7152107175577
x2=−42.4350618814099x_{2} = -42.4350618814099
x3=36.1559664195367x_{3} = 36.1559664195367
x4=−29.8785865061074x_{4} = -29.8785865061074
x5=−98.9702722883957x_{5} = -98.9702722883957
x6=−73.8409691490209x_{6} = -73.8409691490209
x7=98.9702722883957x_{7} = 98.9702722883957
x8=80.1230928148503x_{8} = 80.1230928148503
x9=73.8409691490209x_{9} = 73.8409691490209
x10=4.91318043943488x_{10} = 4.91318043943488
x11=−17.3363779239834x_{11} = -17.3363779239834
x12=−61.2773745335697x_{12} = -61.2773745335697
x13=23.6042847729804x_{13} = 23.6042847729804
x14=−54.9960525574964x_{14} = -54.9960525574964
x15=92.687771772017x_{15} = 92.687771772017
x16=17.3363779239834x_{16} = 17.3363779239834
x17=0x_{17} = 0
x18=−67.5590428388084x_{18} = -67.5590428388084
x19=−11.085538406497x_{19} = -11.085538406497
x20=67.5590428388084x_{20} = 67.5590428388084
x21=−23.6042847729804x_{21} = -23.6042847729804
x22=11.085538406497x_{22} = 11.085538406497
x23=−4.91318043943488x_{23} = -4.91318043943488
x24=54.9960525574964x_{24} = 54.9960525574964
x25=−36.1559664195367x_{25} = -36.1559664195367
x26=86.4053708116885x_{26} = 86.4053708116885
x27=61.2773745335697x_{27} = 61.2773745335697
x28=−92.687771772017x_{28} = -92.687771772017
x29=42.4350618814099x_{29} = 42.4350618814099
x30=−86.4053708116885x_{30} = -86.4053708116885
x31=48.7152107175577x_{31} = 48.7152107175577
x32=−80.1230928148503x_{32} = -80.1230928148503
x33=29.8785865061074x_{33} = 29.8785865061074
Puntos máximos de la función:
x33=−64.4181717218392x_{33} = -64.4181717218392
x33=−45.57503179559x_{33} = -45.57503179559
x33=70.69997803861x_{33} = 70.69997803861
x33=−51.855560729152x_{33} = -51.855560729152
x33=−7.97866571241324x_{33} = -7.97866571241324
x33=89.5465575382492x_{33} = 89.5465575382492
x33=64.4181717218392x_{33} = 64.4181717218392
x33=45.57503179559x_{33} = 45.57503179559
x33=95.8290108090195x_{33} = 95.8290108090195
x33=14.2074367251912x_{33} = 14.2074367251912
x33=−20.469167402741x_{33} = -20.469167402741
x33=−58.1366632448992x_{33} = -58.1366632448992
x33=−39.295350981473x_{33} = -39.295350981473
x33=58.1366632448992x_{33} = 58.1366632448992
x33=83.2642147040886x_{33} = 83.2642147040886
x33=39.295350981473x_{33} = 39.295350981473
x33=20.469167402741x_{33} = 20.469167402741
x33=102.111554139654x_{33} = 102.111554139654
x33=51.855560729152x_{33} = 51.855560729152
x33=7.97866571241324x_{33} = 7.97866571241324
x33=−95.8290108090195x_{33} = -95.8290108090195
x33=−14.2074367251912x_{33} = -14.2074367251912
x33=−70.69997803861x_{33} = -70.69997803861
x33=−76.9820093304187x_{33} = -76.9820093304187
x33=2.02875783811043x_{33} = 2.02875783811043
x33=−26.7409160147873x_{33} = -26.7409160147873
x33=26.7409160147873x_{33} = 26.7409160147873
x33=−89.5465575382492x_{33} = -89.5465575382492
x33=−83.2642147040886x_{33} = -83.2642147040886
x33=76.9820093304187x_{33} = 76.9820093304187
x33=−33.0170010333572x_{33} = -33.0170010333572
x33=33.0170010333572x_{33} = 33.0170010333572
x33=−2.02875783811043x_{33} = -2.02875783811043
Decrece en los intervalos
[98.9702722883957,∞)\left[98.9702722883957, \infty\right)
Crece en los intervalos
(−∞,−98.9702722883957]\left(-\infty, -98.9702722883957\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)+2cos⁡(x)3=0\frac{- x \sin{\left(x \right)} + 2 \cos{\left(x \right)}}{3} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−44.0276918992479x_{1} = -44.0276918992479
x2=59.7237354324305x_{2} = 59.7237354324305
x3=−72.2842925036825x_{3} = -72.2842925036825
x4=−37.7520396346102x_{4} = -37.7520396346102
x5=3.6435971674254x_{5} = 3.6435971674254
x6=−28.3447768697864x_{6} = -28.3447768697864
x7=44.0276918992479x_{7} = 44.0276918992479
x8=−91.1281305511393x_{8} = -91.1281305511393
x9=−62.863657228703x_{9} = -62.863657228703
x10=−9.62956034329743x_{10} = -9.62956034329743
x11=−12.7222987717666x_{11} = -12.7222987717666
x12=84.8465692433091x_{12} = 84.8465692433091
x13=94.2689923093066x_{13} = 94.2689923093066
x14=78.5652673845995x_{14} = 78.5652673845995
x15=34.6152330552306x_{15} = 34.6152330552306
x16=53.4444796697636x_{16} = 53.4444796697636
x17=−25.2119030642106x_{17} = -25.2119030642106
x18=15.8336114149477x_{18} = 15.8336114149477
x19=72.2842925036825x_{19} = 72.2842925036825
x20=−1.0768739863118x_{20} = -1.0768739863118
x21=−47.1662676027767x_{21} = -47.1662676027767
x22=−53.4444796697636x_{22} = -53.4444796697636
x23=40.8895777660408x_{23} = 40.8895777660408
x24=28.3447768697864x_{24} = 28.3447768697864
x25=−50.3052188363296x_{25} = -50.3052188363296
x26=1.0768739863118x_{26} = 1.0768739863118
x27=−75.4247339745236x_{27} = -75.4247339745236
x28=−40.8895777660408x_{28} = -40.8895777660408
x29=81.7058821480364x_{29} = 81.7058821480364
x30=91.1281305511393x_{30} = 91.1281305511393
x31=−22.0814757672807x_{31} = -22.0814757672807
x32=37.7520396346102x_{32} = 37.7520396346102
x33=−78.5652673845995x_{33} = -78.5652673845995
x34=−100.550852725424x_{34} = -100.550852725424
x35=6.57833373272234x_{35} = 6.57833373272234
x36=−6.57833373272234x_{36} = -6.57833373272234
x37=22.0814757672807x_{37} = 22.0814757672807
x38=−97.4099011706723x_{38} = -97.4099011706723
x39=−87.9873209346887x_{39} = -87.9873209346887
x40=−15.8336114149477x_{40} = -15.8336114149477
x41=−18.954681766529x_{41} = -18.954681766529
x42=66.0037377708277x_{42} = 66.0037377708277
x43=87.9873209346887x_{43} = 87.9873209346887
x44=−84.8465692433091x_{44} = -84.8465692433091
x45=31.479374920314x_{45} = 31.479374920314
x46=62.863657228703x_{46} = 62.863657228703
x47=−94.2689923093066x_{47} = -94.2689923093066
x48=100.550852725424x_{48} = 100.550852725424
x49=69.1439554764926x_{49} = 69.1439554764926
x50=−128.820822990274x_{50} = -128.820822990274
x51=75.4247339745236x_{51} = 75.4247339745236
x52=−34.6152330552306x_{52} = -34.6152330552306
x53=12.7222987717666x_{53} = 12.7222987717666
x54=−59.7237354324305x_{54} = -59.7237354324305
x55=47.1662676027767x_{55} = 47.1662676027767
x56=97.4099011706723x_{56} = 97.4099011706723
x57=−69.1439554764926x_{57} = -69.1439554764926
x58=50.3052188363296x_{58} = 50.3052188363296
x59=−66.0037377708277x_{59} = -66.0037377708277
x60=25.2119030642106x_{60} = 25.2119030642106
x61=−31.479374920314x_{61} = -31.479374920314
x62=−81.7058821480364x_{62} = -81.7058821480364
x63=56.5839987378634x_{63} = 56.5839987378634
x64=9.62956034329743x_{64} = 9.62956034329743
x65=18.954681766529x_{65} = 18.954681766529
x66=−56.5839987378634x_{66} = -56.5839987378634
x67=−3.6435971674254x_{67} = -3.6435971674254

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
[97.4099011706723,∞)\left[97.4099011706723, \infty\right)
Convexa en los intervalos
(−∞,−100.550852725424]\left(-\infty, -100.550852725424\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(xsin⁡(x)3)=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x \frac{\sin{\left(x \right)}}{3}\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)3)=⟨−∞,∞⟩\lim_{x \to \infty}\left(x \frac{\sin{\left(x \right)}}{3}\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 (sin(x)/3)*x, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(sin⁡(x)3)=⟨−13,13⟩\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{3}\right) = \left\langle - \frac{1}{3}, \frac{1}{3}\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−13,13⟩xy = \left\langle - \frac{1}{3}, \frac{1}{3}\right\rangle x
lim⁡x→∞(sin⁡(x)3)=⟨−13,13⟩\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{3}\right) = \left\langle - \frac{1}{3}, \frac{1}{3}\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−13,13⟩xy = \left\langle - \frac{1}{3}, \frac{1}{3}\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)3=xsin⁡(x)3x \frac{\sin{\left(x \right)}}{3} = \frac{x \sin{\left(x \right)}}{3}
- No
xsin⁡(x)3=−xsin⁡(x)3x \frac{\sin{\left(x \right)}}{3} = - \frac{x \sin{\left(x \right)}}{3}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = sin(x)/3*x
    © Sr Examen – Калькулятор