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

Gráfico de la función y = sin(x)/x^3

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       sin(x)
f(x) = ------
          3  
         x
f(x)=sin⁡(x)x3f{\left(x \right)} = \frac{\sin{\left(x \right)}}{x^{3}} 
f = sin(x)/x^3
Gráfico de la función
02468-8-6-4-2-1010-500500
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
x1=0x_{1} = 0
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:
sin⁡(x)x3=0\frac{\sin{\left(x \right)}}{x^{3}} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=πx_{1} = \pi
Solución numérica
x1=−59.6902604182061x_{1} = -59.6902604182061
x2=−62.8318530717959x_{2} = -62.8318530717959
x3=−97.3893722612836x_{3} = -97.3893722612836
x4=87.9645943005142x_{4} = 87.9645943005142
x5=−56.5486677646163x_{5} = -56.5486677646163
x6=31.4159265358979x_{6} = 31.4159265358979
x7=69.1150383789755x_{7} = 69.1150383789755
x8=−37.6991118430775x_{8} = -37.6991118430775
x9=−81.6814089933346x_{9} = -81.6814089933346
x10=−84.8230016469244x_{10} = -84.8230016469244
x11=−21.9911485751286x_{11} = -21.9911485751286
x12=47.1238898038469x_{12} = 47.1238898038469
x13=−15.707963267949x_{13} = -15.707963267949
x14=−12.5663706143592x_{14} = -12.5663706143592
x15=12.5663706143592x_{15} = 12.5663706143592
x16=−87.9645943005142x_{16} = -87.9645943005142
x17=53.4070751110265x_{17} = 53.4070751110265
x18=72.2566310325652x_{18} = 72.2566310325652
x19=−100.530964914873x_{19} = -100.530964914873
x20=−3.14159265358979x_{20} = -3.14159265358979
x21=34.5575191894877x_{21} = 34.5575191894877
x22=−94.2477796076938x_{22} = -94.2477796076938
x23=6.28318530717959x_{23} = 6.28318530717959
x24=−69.1150383789755x_{24} = -69.1150383789755
x25=65.9734457253857x_{25} = 65.9734457253857
x26=97.3893722612836x_{26} = 97.3893722612836
x27=15.707963267949x_{27} = 15.707963267949
x28=−50.2654824574367x_{28} = -50.2654824574367
x29=−25.1327412287183x_{29} = -25.1327412287183
x30=3.14159265358979x_{30} = 3.14159265358979
x31=−18.8495559215388x_{31} = -18.8495559215388
x32=40.8407044966673x_{32} = 40.8407044966673
x33=18.8495559215388x_{33} = 18.8495559215388
x34=−53.4070751110265x_{34} = -53.4070751110265
x35=37.6991118430775x_{35} = 37.6991118430775
x36=−43.9822971502571x_{36} = -43.9822971502571
x37=−78.5398163397448x_{37} = -78.5398163397448
x38=−6.28318530717959x_{38} = -6.28318530717959
x39=−40.8407044966673x_{39} = -40.8407044966673
x40=43.9822971502571x_{40} = 43.9822971502571
x41=56.5486677646163x_{41} = 56.5486677646163
x42=−65.9734457253857x_{42} = -65.9734457253857
x43=25.1327412287183x_{43} = 25.1327412287183
x44=78.5398163397448x_{44} = 78.5398163397448
x45=−28.2743338823081x_{45} = -28.2743338823081
x46=75.398223686155x_{46} = 75.398223686155
x47=59.6902604182061x_{47} = 59.6902604182061
x48=−34.5575191894877x_{48} = -34.5575191894877
x49=81.6814089933346x_{49} = 81.6814089933346
x50=−47.1238898038469x_{50} = -47.1238898038469
x51=100.530964914873x_{51} = 100.530964914873
x52=−9.42477796076938x_{52} = -9.42477796076938
x53=−75.398223686155x_{53} = -75.398223686155
x54=−72.2566310325652x_{54} = -72.2566310325652
x55=−31.4159265358979x_{55} = -31.4159265358979
x56=28.2743338823081x_{56} = 28.2743338823081
x57=−109.955742875643x_{57} = -109.955742875643
x58=−91.106186954104x_{58} = -91.106186954104
x59=21.9911485751286x_{59} = 21.9911485751286
x60=62.8318530717959x_{60} = 62.8318530717959
x61=9.42477796076938x_{61} = 9.42477796076938
x62=50.2654824574367x_{62} = 50.2654824574367
x63=94.2477796076938x_{63} = 94.2477796076938
x64=91.106186954104x_{64} = 91.106186954104
x65=141.371669411541x_{65} = 141.371669411541
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)/x^3.
sin⁡(0)03\frac{\sin{\left(0 \right)}}{0^{3}}
Resultado:
f(0)=NaNf{\left(0 \right)} = \text{NaN}
- no hay soluciones de la ecuación
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
cos⁡(x)x3−3sin⁡(x)x4=0\frac{\cos{\left(x \right)}}{x^{3}} - \frac{3 \sin{\left(x \right)}}{x^{4}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−13.924969952549x_{1} = -13.924969952549
x2=−95.7872667660245x_{2} = -95.7872667660245
x3=61.2120859995403x_{3} = 61.2120859995403
x4=13.924969952549x_{4} = 13.924969952549
x5=−26.591193287969x_{5} = -26.591193287969
x6=−23.4346216921802x_{6} = -23.4346216921802
x7=−45.4872362867621x_{7} = -45.4872362867621
x8=−108.357267428671x_{8} = -108.357267428671
x9=−98.9298533613919x_{9} = -98.9298533613919
x10=29.7446115259422x_{10} = 29.7446115259422
x11=76.930043294192x_{11} = 76.930043294192
x12=42.3407653325706x_{12} = 42.3407653325706
x13=−54.9233040395155x_{13} = -54.9233040395155
x14=−32.8957773192946x_{14} = -32.8957773192946
x15=54.9233040395155x_{15} = 54.9233040395155
x16=−186.908713650658x_{16} = -186.908713650658
x17=23.4346216921802x_{17} = 23.4346216921802
x18=−64.3560674689022x_{18} = -64.3560674689022
x19=67.4998267230665x_{19} = 67.4998267230665
x20=39.1935138550425x_{20} = 39.1935138550425
x21=17.1051395364267x_{21} = 17.1051395364267
x22=−92.6446127847888x_{22} = -92.6446127847888
x23=10.7227710626892x_{23} = 10.7227710626892
x24=86.359073259985x_{24} = 86.359073259985
x25=−51.7784042739041x_{25} = -51.7784042739041
x26=70.6433933906731x_{26} = 70.6433933906731
x27=−76.930043294192x_{27} = -76.930043294192
x28=89.5018843244389x_{28} = 89.5018843244389
x29=48.6330777853047x_{29} = 48.6330777853047
x30=−36.0452782424582x_{30} = -36.0452782424582
x31=83.2161702400252x_{31} = 83.2161702400252
x32=−67.4998267230665x_{32} = -67.4998267230665
x33=80.0731644462726x_{33} = 80.0731644462726
x34=−89.5018843244389x_{34} = -89.5018843244389
x35=32.8957773192946x_{35} = 32.8957773192946
x36=3215.41914794509x_{36} = 3215.41914794509
x37=−48.6330777853047x_{37} = -48.6330777853047
x38=98.9298533613919x_{38} = 98.9298533613919
x39=−10.7227710626892x_{39} = -10.7227710626892
x40=26.591193287969x_{40} = 26.591193287969
x41=−42.3407653325706x_{41} = -42.3407653325706
x42=4.07814976485137x_{42} = 4.07814976485137
x43=36.0452782424582x_{43} = 36.0452782424582
x44=−86.359073259985x_{44} = -86.359073259985
x45=95.7872667660245x_{45} = 95.7872667660245
x46=7.47219265966058x_{46} = 7.47219265966058
x47=−58.0678462801751x_{47} = -58.0678462801751
x48=−39.1935138550425x_{48} = -39.1935138550425
x49=−20.2734415170608x_{49} = -20.2734415170608
x50=−83.2161702400252x_{50} = -83.2161702400252
x51=−73.7867920572034x_{51} = -73.7867920572034
x52=−70.6433933906731x_{52} = -70.6433933906731
x53=92.6446127847888x_{53} = 92.6446127847888
x54=−17.1051395364267x_{54} = -17.1051395364267
x55=64.3560674689022x_{55} = 64.3560674689022
x56=20.2734415170608x_{56} = 20.2734415170608
x57=45.4872362867621x_{57} = 45.4872362867621
x58=−7.47219265966058x_{58} = -7.47219265966058
x59=58.0678462801751x_{59} = 58.0678462801751
x60=−61.2120859995403x_{60} = -61.2120859995403
x61=−29.7446115259422x_{61} = -29.7446115259422
x62=73.7867920572034x_{62} = 73.7867920572034
x63=−4.07814976485137x_{63} = -4.07814976485137
x64=−80.0731644462726x_{64} = -80.0731644462726
x65=51.7784042739041x_{65} = 51.7784042739041
Signos de extremos en los puntos:
(-13.92496995254897, 0.000362047304723488)

(-95.78726676602449, 1.1372704641271e-6)

(61.21208599954033, -4.35479288166118e-6)

(13.92496995254897, 0.000362047304723488)

(-26.59119328796898, 5.28494009082656e-5)

(-23.4346216921802, -7.70719574291125e-5)

(-45.48723628676209, 1.06020259212848e-5)

(-108.35726742867121, 7.85704936475449e-7)

(-98.9298533613919, -1.03232943885669e-6)

(29.744611525942226, -3.78074454700618e-5)

(76.93004329419203, 2.19473504875366e-6)

(42.34076533257061, -1.31412441116291e-5)

(-54.92330403951548, -6.02674942320184e-6)

(-32.89577731929462, 2.79757033726946e-5)

(54.92330403951548, -6.02674942320184e-6)

(-186.90871365065752, -1.53128285331065e-7)

(23.4346216921802, -7.70719574291125e-5)

(-64.35606746890217, 3.7476597286644e-6)

(67.49982672306646, -3.24835521431348e-6)

(39.193513855042454, 1.65610881918558e-5)

(17.105139536426744, -0.000196807350078387)

(-92.64461278478876, -1.25693237122389e-6)

(10.722771062689203, -0.00078111312666525)

(86.359073259985, -1.55172297524868e-6)

(-51.77840427390411, 7.1916125507828e-6)

(70.64339339067311, 2.83396240646379e-6)

(-76.93004329419203, 2.19473504875366e-6)

(89.50188432443886, 1.39398991793862e-6)

(48.63307778530466, -8.67720806398467e-6)

(-36.04527824245817, -2.12792275158681e-5)

(83.21617024002518, 1.73418247352317e-6)

(-67.49982672306646, -3.24835521431348e-6)

(80.07316444627257, -1.94641047170913e-6)

(-89.50188432443886, 1.39398991793862e-6)

(32.89577731929462, 2.79757033726946e-5)

(3215.41914794509, -3.00806370783767e-11)

(-48.63307778530466, -8.67720806398467e-6)

(98.9298533613919, -1.03232943885669e-6)

(-10.722771062689203, -0.00078111312666525)

(26.59119328796898, 5.28494009082656e-5)

(-42.34076533257061, -1.31412441116291e-5)

(4.078149764851372, -0.0118764951343876)

(36.04527824245817, -2.12792275158681e-5)

(-86.359073259985, -1.55172297524868e-6)

(95.78726676602449, 1.1372704641271e-6)

(7.472192659660579, 0.00222435242575847)

(-58.067846280175104, 5.1005149012716e-6)

(-39.193513855042454, 1.65610881918558e-5)

(-20.27344151706078, 0.000118717289027919)

(-83.21617024002518, 1.73418247352317e-6)

(-73.78679205720341, -2.48716990126569e-6)

(-70.64339339067311, 2.83396240646379e-6)

(92.64461278478876, -1.25693237122389e-6)

(-17.105139536426744, -0.000196807350078387)

(64.35606746890217, 3.7476597286644e-6)

(20.27344151706078, 0.000118717289027919)

(45.48723628676209, 1.06020259212848e-5)

(-7.472192659660579, 0.00222435242575847)

(58.067846280175104, 5.1005149012716e-6)

(-61.21208599954033, -4.35479288166118e-6)

(-29.744611525942226, -3.78074454700618e-5)

(73.78679205720341, -2.48716990126569e-6)

(-4.078149764851372, -0.0118764951343876)

(-80.07316444627257, -1.94641047170913e-6)

(51.77840427390411, 7.1916125507828e-6)


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=61.2120859995403x_{1} = 61.2120859995403
x2=−23.4346216921802x_{2} = -23.4346216921802
x3=−98.9298533613919x_{3} = -98.9298533613919
x4=29.7446115259422x_{4} = 29.7446115259422
x5=42.3407653325706x_{5} = 42.3407653325706
x6=−54.9233040395155x_{6} = -54.9233040395155
x7=54.9233040395155x_{7} = 54.9233040395155
x8=−186.908713650658x_{8} = -186.908713650658
x9=23.4346216921802x_{9} = 23.4346216921802
x10=67.4998267230665x_{10} = 67.4998267230665
x11=17.1051395364267x_{11} = 17.1051395364267
x12=−92.6446127847888x_{12} = -92.6446127847888
x13=10.7227710626892x_{13} = 10.7227710626892
x14=86.359073259985x_{14} = 86.359073259985
x15=48.6330777853047x_{15} = 48.6330777853047
x16=−36.0452782424582x_{16} = -36.0452782424582
x17=−67.4998267230665x_{17} = -67.4998267230665
x18=80.0731644462726x_{18} = 80.0731644462726
x19=3215.41914794509x_{19} = 3215.41914794509
x20=−48.6330777853047x_{20} = -48.6330777853047
x21=98.9298533613919x_{21} = 98.9298533613919
x22=−10.7227710626892x_{22} = -10.7227710626892
x23=−42.3407653325706x_{23} = -42.3407653325706
x24=4.07814976485137x_{24} = 4.07814976485137
x25=36.0452782424582x_{25} = 36.0452782424582
x26=−86.359073259985x_{26} = -86.359073259985
x27=−73.7867920572034x_{27} = -73.7867920572034
x28=92.6446127847888x_{28} = 92.6446127847888
x29=−17.1051395364267x_{29} = -17.1051395364267
x30=−61.2120859995403x_{30} = -61.2120859995403
x31=−29.7446115259422x_{31} = -29.7446115259422
x32=73.7867920572034x_{32} = 73.7867920572034
x33=−4.07814976485137x_{33} = -4.07814976485137
x34=−80.0731644462726x_{34} = -80.0731644462726
Puntos máximos de la función:
x34=−13.924969952549x_{34} = -13.924969952549
x34=−95.7872667660245x_{34} = -95.7872667660245
x34=13.924969952549x_{34} = 13.924969952549
x34=−26.591193287969x_{34} = -26.591193287969
x34=−45.4872362867621x_{34} = -45.4872362867621
x34=−108.357267428671x_{34} = -108.357267428671
x34=76.930043294192x_{34} = 76.930043294192
x34=−32.8957773192946x_{34} = -32.8957773192946
x34=−64.3560674689022x_{34} = -64.3560674689022
x34=39.1935138550425x_{34} = 39.1935138550425
x34=−51.7784042739041x_{34} = -51.7784042739041
x34=70.6433933906731x_{34} = 70.6433933906731
x34=−76.930043294192x_{34} = -76.930043294192
x34=89.5018843244389x_{34} = 89.5018843244389
x34=83.2161702400252x_{34} = 83.2161702400252
x34=−89.5018843244389x_{34} = -89.5018843244389
x34=32.8957773192946x_{34} = 32.8957773192946
x34=26.591193287969x_{34} = 26.591193287969
x34=95.7872667660245x_{34} = 95.7872667660245
x34=7.47219265966058x_{34} = 7.47219265966058
x34=−58.0678462801751x_{34} = -58.0678462801751
x34=−39.1935138550425x_{34} = -39.1935138550425
x34=−20.2734415170608x_{34} = -20.2734415170608
x34=−83.2161702400252x_{34} = -83.2161702400252
x34=−70.6433933906731x_{34} = -70.6433933906731
x34=64.3560674689022x_{34} = 64.3560674689022
x34=20.2734415170608x_{34} = 20.2734415170608
x34=45.4872362867621x_{34} = 45.4872362867621
x34=−7.47219265966058x_{34} = -7.47219265966058
x34=58.0678462801751x_{34} = 58.0678462801751
x34=51.7784042739041x_{34} = 51.7784042739041
Decrece en los intervalos
[3215.41914794509,∞)\left[3215.41914794509, \infty\right)
Crece en los intervalos
(−∞,−186.908713650658]\left(-\infty, -186.908713650658\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
−sin⁡(x)−6cos⁡(x)x+12sin⁡(x)x2x3=0\frac{- \sin{\left(x \right)} - \frac{6 \cos{\left(x \right)}}{x} + \frac{12 \sin{\left(x \right)}}{x^{2}}}{x^{3}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−28.0605201580983x_{1} = -28.0605201580983
x2=84.7522070698598x_{2} = 84.7522070698598
x3=−75.31856211974x_{3} = -75.31856211974
x4=91.0402820892519x_{4} = 91.0402820892519
x5=−8.74140008690353x_{5} = -8.74140008690353
x6=72.1734981126022x_{6} = 72.1734981126022
x7=87.8963320992957x_{7} = 87.8963320992957
x8=12.0699013399661x_{8} = 12.0699013399661
x9=37.5392815729796x_{9} = 37.5392815729796
x10=50.1458319794503x_{10} = 50.1458319794503
x11=78.4633475726977x_{11} = 78.4633475726977
x12=−37.5392815729796x_{12} = -37.5392815729796
x13=−141.329215347444x_{13} = -141.329215347444
x14=31.223771021093x_{14} = 31.223771021093
x15=43.8454539221714x_{15} = 43.8454539221714
x16=−62.7362147088964x_{16} = -62.7362147088964
x17=−59.5895718893518x_{17} = -59.5895718893518
x18=53.2944935242974x_{18} = 53.2944935242974
x19=−5.15216592622293x_{19} = -5.15216592622293
x20=18.5257597776303x_{20} = 18.5257597776303
x21=97.3277248932537x_{21} = 97.3277248932537
x22=−43.8454539221714x_{22} = -43.8454539221714
x23=−53.2944935242974x_{23} = -53.2944935242974
x24=−18.5257597776303x_{24} = -18.5257597776303
x25=−84.7522070698598x_{25} = -84.7522070698598
x26=69.028117387504x_{26} = 69.028117387504
x27=−69.028117387504x_{27} = -69.028117387504
x28=46.996220714232x_{28} = 46.996220714232
x29=75.31856211974x_{29} = 75.31856211974
x30=94.1840745935286x_{30} = 94.1840745935286
x31=−34.3830180083391x_{31} = -34.3830180083391
x32=−100.47124635336x_{32} = -100.47124635336
x33=65.8823744655118x_{33} = 65.8823744655118
x34=−97.3277248932537x_{34} = -97.3277248932537
x35=−113.044258982077x_{35} = -113.044258982077
x36=−40.6932614780489x_{36} = -40.6932614780489
x37=−50.1458319794503x_{37} = -50.1458319794503
x38=−12.0699013399661x_{38} = -12.0699013399661
x39=59.5895718893518x_{39} = 59.5895718893518
x40=−91.0402820892519x_{40} = -91.0402820892519
x41=34.3830180083391x_{41} = 34.3830180083391
x42=81.6078867352652x_{42} = 81.6078867352652
x43=−21.7148754289157x_{43} = -21.7148754289157
x44=−56.4423649364807x_{44} = -56.4423649364807
x45=62.7362147088964x_{45} = 62.7362147088964
x46=8.74140008690353x_{46} = 8.74140008690353
x47=−31.223771021093x_{47} = -31.223771021093
x48=−72.1734981126022x_{48} = -72.1734981126022
x49=21.7148754289157x_{49} = 21.7148754289157
x50=100.47124635336x_{50} = 100.47124635336
x51=131.901402932105x_{51} = 131.901402932105
x52=116.187287429474x_{52} = 116.187287429474
x53=−87.8963320992957x_{53} = -87.8963320992957
x54=373.833475850202x_{54} = 373.833475850202
x55=5.15216592622293x_{55} = 5.15216592622293
x56=−78.4633475726977x_{56} = -78.4633475726977
x57=−46.996220714232x_{57} = -46.996220714232
x58=−81.6078867352652x_{58} = -81.6078867352652
x59=−24.8917150033836x_{59} = -24.8917150033836
x60=56.4423649364807x_{60} = 56.4423649364807
x61=−94.1840745935286x_{61} = -94.1840745935286
x62=40.6932614780489x_{62} = 40.6932614780489
x63=24.8917150033836x_{63} = 24.8917150033836
x64=28.0605201580983x_{64} = 28.0605201580983
x65=−65.8823744655118x_{65} = -65.8823744655118
x66=−15.3164244547999x_{66} = -15.3164244547999
x67=15.3164244547999x_{67} = 15.3164244547999
Además hay que calcular los límites de y'' para los argumentos tendientes a los puntos de indeterminación de la función:
Puntos donde hay indeterminación:
x1=0x_{1} = 0

lim⁡x→0−(−sin⁡(x)−6cos⁡(x)x+12sin⁡(x)x2x3)=∞\lim_{x \to 0^-}\left(\frac{- \sin{\left(x \right)} - \frac{6 \cos{\left(x \right)}}{x} + \frac{12 \sin{\left(x \right)}}{x^{2}}}{x^{3}}\right) = \infty
lim⁡x→0+(−sin⁡(x)−6cos⁡(x)x+12sin⁡(x)x2x3)=∞\lim_{x \to 0^+}\left(\frac{- \sin{\left(x \right)} - \frac{6 \cos{\left(x \right)}}{x} + \frac{12 \sin{\left(x \right)}}{x^{2}}}{x^{3}}\right) = \infty
- los límites son iguales, es decir omitimos el punto correspondiente

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
[373.833475850202,∞)\left[373.833475850202, \infty\right)
Convexa en los intervalos
(−∞,−113.044258982077]\left(-\infty, -113.044258982077\right]
Asíntotas verticales
Hay:
x1=0x_{1} = 0
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(sin⁡(x)x3)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{x^{3}}\right) = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=0y = 0
lim⁡x→∞(sin⁡(x)x3)=0\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{x^{3}}\right) = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=0y = 0
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función sin(x)/x^3, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(sin⁡(x)xx3)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{x x^{3}}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(sin⁡(x)xx3)=0\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{x x^{3}}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
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:
sin⁡(x)x3=sin⁡(x)x3\frac{\sin{\left(x \right)}}{x^{3}} = \frac{\sin{\left(x \right)}}{x^{3}}
- No
sin⁡(x)x3=−sin⁡(x)x3\frac{\sin{\left(x \right)}}{x^{3}} = - \frac{\sin{\left(x \right)}}{x^{3}}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = sin(x)/x^3
    © Sr Examen – Калькулятор