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  • Gráfico de la función y =:
  • x/(x^2-5) x/(x^2-5)
  • 3*x-x^3 3*x-x^3
  • x/(x^3+2) x/(x^3+2)
  • e^(-x^2) e^(-x^2)

  • Expresiones idénticas

  • (dos sinx/2)/x^ tres
  • (2 seno de x dividir por 2) dividir por x al cubo
  • (dos seno de x dividir por 2) dividir por x en el grado tres
  • (2sinx/2)/x3
  • 2sinx/2/x3
  • (2sinx/2)/x³
  • (2sinx/2)/x en el grado 3
  • 2sinx/2/x^3
  • (2sinx dividir por 2) dividir por x^3
Trazado el gráfico de la función/ (2sinx/2)/x^3

Gráfico de la función y = (2sinx/2)/x^3

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       /2*sin(x)\
       |--------|
       \   2    /
f(x) = ----------
            3    
           x
f(x)=12⋅2sin⁡(x)x3f{\left(x \right)} = \frac{\frac{1}{2} \cdot 2 \sin{\left(x \right)}}{x^{3}} 
f = ((2*sin(x))/2)/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:
12⋅2sin⁡(x)x3=0\frac{\frac{1}{2} \cdot 2 \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=72.2566310325652x_{1} = 72.2566310325652
x2=−59.6902604182061x_{2} = -59.6902604182061
x3=3.14159265358979x_{3} = 3.14159265358979
x4=−43.9822971502571x_{4} = -43.9822971502571
x5=81.6814089933346x_{5} = 81.6814089933346
x6=−100.530964914873x_{6} = -100.530964914873
x7=28.2743338823081x_{7} = 28.2743338823081
x8=65.9734457253857x_{8} = 65.9734457253857
x9=−31.4159265358979x_{9} = -31.4159265358979
x10=−9.42477796076938x_{10} = -9.42477796076938
x11=40.8407044966673x_{11} = 40.8407044966673
x12=56.5486677646163x_{12} = 56.5486677646163
x13=−56.5486677646163x_{13} = -56.5486677646163
x14=12.5663706143592x_{14} = 12.5663706143592
x15=43.9822971502571x_{15} = 43.9822971502571
x16=100.530964914873x_{16} = 100.530964914873
x17=−3.14159265358979x_{17} = -3.14159265358979
x18=−15.707963267949x_{18} = -15.707963267949
x19=59.6902604182061x_{19} = 59.6902604182061
x20=6.28318530717959x_{20} = 6.28318530717959
x21=9.42477796076938x_{21} = 9.42477796076938
x22=−53.4070751110265x_{22} = -53.4070751110265
x23=−47.1238898038469x_{23} = -47.1238898038469
x24=−87.9645943005142x_{24} = -87.9645943005142
x25=69.1150383789755x_{25} = 69.1150383789755
x26=21.9911485751286x_{26} = 21.9911485751286
x27=87.9645943005142x_{27} = 87.9645943005142
x28=18.8495559215388x_{28} = 18.8495559215388
x29=−84.8230016469244x_{29} = -84.8230016469244
x30=−72.2566310325652x_{30} = -72.2566310325652
x31=25.1327412287183x_{31} = 25.1327412287183
x32=37.6991118430775x_{32} = 37.6991118430775
x33=−25.1327412287183x_{33} = -25.1327412287183
x34=50.2654824574367x_{34} = 50.2654824574367
x35=34.5575191894877x_{35} = 34.5575191894877
x36=−6.28318530717959x_{36} = -6.28318530717959
x37=−65.9734457253857x_{37} = -65.9734457253857
x38=−21.9911485751286x_{38} = -21.9911485751286
x39=−62.8318530717959x_{39} = -62.8318530717959
x40=75.398223686155x_{40} = 75.398223686155
x41=84.8230016469244x_{41} = 84.8230016469244
x42=53.4070751110265x_{42} = 53.4070751110265
x43=15.707963267949x_{43} = 15.707963267949
x44=−28.2743338823081x_{44} = -28.2743338823081
x45=−91.106186954104x_{45} = -91.106186954104
x46=47.1238898038469x_{46} = 47.1238898038469
x47=97.3893722612836x_{47} = 97.3893722612836
x48=−69.1150383789755x_{48} = -69.1150383789755
x49=94.2477796076938x_{49} = 94.2477796076938
x50=−18.8495559215388x_{50} = -18.8495559215388
x51=−50.2654824574367x_{51} = -50.2654824574367
x52=−37.6991118430775x_{52} = -37.6991118430775
x53=−81.6814089933346x_{53} = -81.6814089933346
x54=62.8318530717959x_{54} = 62.8318530717959
x55=78.5398163397448x_{55} = 78.5398163397448
x56=31.4159265358979x_{56} = 31.4159265358979
x57=−78.5398163397448x_{57} = -78.5398163397448
x58=−40.8407044966673x_{58} = -40.8407044966673
x59=141.371669411541x_{59} = 141.371669411541
x60=−97.3893722612836x_{60} = -97.3893722612836
x61=−109.955742875643x_{61} = -109.955742875643
x62=−75.398223686155x_{62} = -75.398223686155
x63=91.106186954104x_{63} = 91.106186954104
x64=−12.5663706143592x_{64} = -12.5663706143592
x65=−94.2477796076938x_{65} = -94.2477796076938
x66=−34.5575191894877x_{66} = -34.5575191894877
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*sin(x))/2)/x^3.
12⋅2sin⁡(0)03\frac{\frac{1}{2} \cdot 2 \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=−36.0452782424582x_{1} = -36.0452782424582
x2=51.7784042739041x_{2} = 51.7784042739041
x3=86.359073259985x_{3} = 86.359073259985
x4=13.924969952549x_{4} = 13.924969952549
x5=70.6433933906731x_{5} = 70.6433933906731
x6=−73.7867920572034x_{6} = -73.7867920572034
x7=10.7227710626892x_{7} = 10.7227710626892
x8=20.2734415170608x_{8} = 20.2734415170608
x9=−42.3407653325706x_{9} = -42.3407653325706
x10=−64.3560674689022x_{10} = -64.3560674689022
x11=−186.908713650658x_{11} = -186.908713650658
x12=42.3407653325706x_{12} = 42.3407653325706
x13=−29.7446115259422x_{13} = -29.7446115259422
x14=−67.4998267230665x_{14} = -67.4998267230665
x15=−23.4346216921802x_{15} = -23.4346216921802
x16=−89.5018843244389x_{16} = -89.5018843244389
x17=4.07814976485137x_{17} = 4.07814976485137
x18=89.5018843244389x_{18} = 89.5018843244389
x19=32.8957773192946x_{19} = 32.8957773192946
x20=80.0731644462726x_{20} = 80.0731644462726
x21=64.3560674689022x_{21} = 64.3560674689022
x22=−26.591193287969x_{22} = -26.591193287969
x23=3215.41914794509x_{23} = 3215.41914794509
x24=−10.7227710626892x_{24} = -10.7227710626892
x25=92.6446127847888x_{25} = 92.6446127847888
x26=−4.07814976485137x_{26} = -4.07814976485137
x27=−7.47219265966058x_{27} = -7.47219265966058
x28=−83.2161702400252x_{28} = -83.2161702400252
x29=−80.0731644462726x_{29} = -80.0731644462726
x30=67.4998267230665x_{30} = 67.4998267230665
x31=−95.7872667660245x_{31} = -95.7872667660245
x32=−86.359073259985x_{32} = -86.359073259985
x33=−98.9298533613919x_{33} = -98.9298533613919
x34=−45.4872362867621x_{34} = -45.4872362867621
x35=−51.7784042739041x_{35} = -51.7784042739041
x36=−17.1051395364267x_{36} = -17.1051395364267
x37=54.9233040395155x_{37} = 54.9233040395155
x38=17.1051395364267x_{38} = 17.1051395364267
x39=−54.9233040395155x_{39} = -54.9233040395155
x40=73.7867920572034x_{40} = 73.7867920572034
x41=29.7446115259422x_{41} = 29.7446115259422
x42=−70.6433933906731x_{42} = -70.6433933906731
x43=45.4872362867621x_{43} = 45.4872362867621
x44=26.591193287969x_{44} = 26.591193287969
x45=−13.924969952549x_{45} = -13.924969952549
x46=−20.2734415170608x_{46} = -20.2734415170608
x47=−48.6330777853047x_{47} = -48.6330777853047
x48=58.0678462801751x_{48} = 58.0678462801751
x49=76.930043294192x_{49} = 76.930043294192
x50=39.1935138550425x_{50} = 39.1935138550425
x51=−61.2120859995403x_{51} = -61.2120859995403
x52=−39.1935138550425x_{52} = -39.1935138550425
x53=48.6330777853047x_{53} = 48.6330777853047
x54=98.9298533613919x_{54} = 98.9298533613919
x55=61.2120859995403x_{55} = 61.2120859995403
x56=23.4346216921802x_{56} = 23.4346216921802
x57=−58.0678462801751x_{57} = -58.0678462801751
x58=36.0452782424582x_{58} = 36.0452782424582
x59=83.2161702400252x_{59} = 83.2161702400252
x60=95.7872667660245x_{60} = 95.7872667660245
x61=−32.8957773192946x_{61} = -32.8957773192946
x62=7.47219265966058x_{62} = 7.47219265966058
x63=−76.930043294192x_{63} = -76.930043294192
x64=−92.6446127847888x_{64} = -92.6446127847888
x65=−108.357267428671x_{65} = -108.357267428671
Signos de extremos en los puntos:
(-36.04527824245817, -2.12792275158681e-5)

(51.77840427390411, 7.1916125507828e-6)

(86.359073259985, -1.55172297524868e-6)

(13.92496995254897, 0.000362047304723488)

(70.64339339067311, 2.83396240646379e-6)

(-73.78679205720341, -2.48716990126569e-6)

(10.722771062689203, -0.00078111312666525)

(20.27344151706078, 0.000118717289027919)

(-42.34076533257061, -1.31412441116291e-5)

(-64.35606746890217, 3.7476597286644e-6)

(-186.90871365065752, -1.53128285331065e-7)

(42.34076533257061, -1.31412441116291e-5)

(-29.744611525942226, -3.78074454700618e-5)

(-67.49982672306646, -3.24835521431348e-6)

(-23.4346216921802, -7.70719574291125e-5)

(-89.50188432443886, 1.39398991793862e-6)

(4.078149764851372, -0.0118764951343876)

(89.50188432443886, 1.39398991793862e-6)

(32.89577731929462, 2.79757033726946e-5)

(80.07316444627257, -1.94641047170913e-6)

(64.35606746890217, 3.7476597286644e-6)

(-26.59119328796898, 5.28494009082656e-5)

(3215.41914794509, -3.00806370783767e-11)

(-10.722771062689203, -0.00078111312666525)

(92.64461278478876, -1.25693237122389e-6)

(-4.078149764851372, -0.0118764951343876)

(-7.472192659660579, 0.00222435242575847)

(-83.21617024002518, 1.73418247352317e-6)

(-80.07316444627257, -1.94641047170913e-6)

(67.49982672306646, -3.24835521431348e-6)

(-95.78726676602449, 1.1372704641271e-6)

(-86.359073259985, -1.55172297524868e-6)

(-98.9298533613919, -1.03232943885669e-6)

(-45.48723628676209, 1.06020259212848e-5)

(-51.77840427390411, 7.1916125507828e-6)

(-17.105139536426744, -0.000196807350078387)

(54.92330403951548, -6.02674942320184e-6)

(17.105139536426744, -0.000196807350078387)

(-54.92330403951548, -6.02674942320184e-6)

(73.78679205720341, -2.48716990126569e-6)

(29.744611525942226, -3.78074454700618e-5)

(-70.64339339067311, 2.83396240646379e-6)

(45.48723628676209, 1.06020259212848e-5)

(26.59119328796898, 5.28494009082656e-5)

(-13.92496995254897, 0.000362047304723488)

(-20.27344151706078, 0.000118717289027919)

(-48.63307778530466, -8.67720806398467e-6)

(58.067846280175104, 5.1005149012716e-6)

(76.93004329419203, 2.19473504875366e-6)

(39.193513855042454, 1.65610881918558e-5)

(-61.21208599954033, -4.35479288166118e-6)

(-39.193513855042454, 1.65610881918558e-5)

(48.63307778530466, -8.67720806398467e-6)

(98.9298533613919, -1.03232943885669e-6)

(61.21208599954033, -4.35479288166118e-6)

(23.4346216921802, -7.70719574291125e-5)

(-58.067846280175104, 5.1005149012716e-6)

(36.04527824245817, -2.12792275158681e-5)

(83.21617024002518, 1.73418247352317e-6)

(95.78726676602449, 1.1372704641271e-6)

(-32.89577731929462, 2.79757033726946e-5)

(7.472192659660579, 0.00222435242575847)

(-76.93004329419203, 2.19473504875366e-6)

(-92.64461278478876, -1.25693237122389e-6)

(-108.35726742867121, 7.85704936475449e-7)


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=−36.0452782424582x_{1} = -36.0452782424582
x2=86.359073259985x_{2} = 86.359073259985
x3=−73.7867920572034x_{3} = -73.7867920572034
x4=10.7227710626892x_{4} = 10.7227710626892
x5=−42.3407653325706x_{5} = -42.3407653325706
x6=−186.908713650658x_{6} = -186.908713650658
x7=42.3407653325706x_{7} = 42.3407653325706
x8=−29.7446115259422x_{8} = -29.7446115259422
x9=−67.4998267230665x_{9} = -67.4998267230665
x10=−23.4346216921802x_{10} = -23.4346216921802
x11=4.07814976485137x_{11} = 4.07814976485137
x12=80.0731644462726x_{12} = 80.0731644462726
x13=3215.41914794509x_{13} = 3215.41914794509
x14=−10.7227710626892x_{14} = -10.7227710626892
x15=92.6446127847888x_{15} = 92.6446127847888
x16=−4.07814976485137x_{16} = -4.07814976485137
x17=−80.0731644462726x_{17} = -80.0731644462726
x18=67.4998267230665x_{18} = 67.4998267230665
x19=−86.359073259985x_{19} = -86.359073259985
x20=−98.9298533613919x_{20} = -98.9298533613919
x21=−17.1051395364267x_{21} = -17.1051395364267
x22=54.9233040395155x_{22} = 54.9233040395155
x23=17.1051395364267x_{23} = 17.1051395364267
x24=−54.9233040395155x_{24} = -54.9233040395155
x25=73.7867920572034x_{25} = 73.7867920572034
x26=29.7446115259422x_{26} = 29.7446115259422
x27=−48.6330777853047x_{27} = -48.6330777853047
x28=−61.2120859995403x_{28} = -61.2120859995403
x29=48.6330777853047x_{29} = 48.6330777853047
x30=98.9298533613919x_{30} = 98.9298533613919
x31=61.2120859995403x_{31} = 61.2120859995403
x32=23.4346216921802x_{32} = 23.4346216921802
x33=36.0452782424582x_{33} = 36.0452782424582
x34=−92.6446127847888x_{34} = -92.6446127847888
Puntos máximos de la función:
x34=51.7784042739041x_{34} = 51.7784042739041
x34=13.924969952549x_{34} = 13.924969952549
x34=70.6433933906731x_{34} = 70.6433933906731
x34=20.2734415170608x_{34} = 20.2734415170608
x34=−64.3560674689022x_{34} = -64.3560674689022
x34=−89.5018843244389x_{34} = -89.5018843244389
x34=89.5018843244389x_{34} = 89.5018843244389
x34=32.8957773192946x_{34} = 32.8957773192946
x34=64.3560674689022x_{34} = 64.3560674689022
x34=−26.591193287969x_{34} = -26.591193287969
x34=−7.47219265966058x_{34} = -7.47219265966058
x34=−83.2161702400252x_{34} = -83.2161702400252
x34=−95.7872667660245x_{34} = -95.7872667660245
x34=−45.4872362867621x_{34} = -45.4872362867621
x34=−51.7784042739041x_{34} = -51.7784042739041
x34=−70.6433933906731x_{34} = -70.6433933906731
x34=45.4872362867621x_{34} = 45.4872362867621
x34=26.591193287969x_{34} = 26.591193287969
x34=−13.924969952549x_{34} = -13.924969952549
x34=−20.2734415170608x_{34} = -20.2734415170608
x34=58.0678462801751x_{34} = 58.0678462801751
x34=76.930043294192x_{34} = 76.930043294192
x34=39.1935138550425x_{34} = 39.1935138550425
x34=−39.1935138550425x_{34} = -39.1935138550425
x34=−58.0678462801751x_{34} = -58.0678462801751
x34=83.2161702400252x_{34} = 83.2161702400252
x34=95.7872667660245x_{34} = 95.7872667660245
x34=−32.8957773192946x_{34} = -32.8957773192946
x34=7.47219265966058x_{34} = 7.47219265966058
x34=−76.930043294192x_{34} = -76.930043294192
x34=−108.357267428671x_{34} = -108.357267428671
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=−141.329215347444x_{1} = -141.329215347444
x2=72.1734981126022x_{2} = 72.1734981126022
x3=46.996220714232x_{3} = 46.996220714232
x4=−56.4423649364807x_{4} = -56.4423649364807
x5=5.15216592622293x_{5} = 5.15216592622293
x6=94.1840745935286x_{6} = 94.1840745935286
x7=−113.044258982077x_{7} = -113.044258982077
x8=−78.4633475726977x_{8} = -78.4633475726977
x9=37.5392815729796x_{9} = 37.5392815729796
x10=87.8963320992957x_{10} = 87.8963320992957
x11=−15.3164244547999x_{11} = -15.3164244547999
x12=−18.5257597776303x_{12} = -18.5257597776303
x13=−34.3830180083391x_{13} = -34.3830180083391
x14=−12.0699013399661x_{14} = -12.0699013399661
x15=24.8917150033836x_{15} = 24.8917150033836
x16=−59.5895718893518x_{16} = -59.5895718893518
x17=−53.2944935242974x_{17} = -53.2944935242974
x18=−94.1840745935286x_{18} = -94.1840745935286
x19=−100.47124635336x_{19} = -100.47124635336
x20=34.3830180083391x_{20} = 34.3830180083391
x21=−69.028117387504x_{21} = -69.028117387504
x22=373.833475850202x_{22} = 373.833475850202
x23=31.223771021093x_{23} = 31.223771021093
x24=−65.8823744655118x_{24} = -65.8823744655118
x25=81.6078867352652x_{25} = 81.6078867352652
x26=40.6932614780489x_{26} = 40.6932614780489
x27=50.1458319794503x_{27} = 50.1458319794503
x28=−84.7522070698598x_{28} = -84.7522070698598
x29=59.5895718893518x_{29} = 59.5895718893518
x30=53.2944935242974x_{30} = 53.2944935242974
x31=131.901402932105x_{31} = 131.901402932105
x32=−40.6932614780489x_{32} = -40.6932614780489
x33=21.7148754289157x_{33} = 21.7148754289157
x34=−37.5392815729796x_{34} = -37.5392815729796
x35=75.31856211974x_{35} = 75.31856211974
x36=−81.6078867352652x_{36} = -81.6078867352652
x37=15.3164244547999x_{37} = 15.3164244547999
x38=43.8454539221714x_{38} = 43.8454539221714
x39=65.8823744655118x_{39} = 65.8823744655118
x40=56.4423649364807x_{40} = 56.4423649364807
x41=−72.1734981126022x_{41} = -72.1734981126022
x42=−75.31856211974x_{42} = -75.31856211974
x43=8.74140008690353x_{43} = 8.74140008690353
x44=−46.996220714232x_{44} = -46.996220714232
x45=−24.8917150033836x_{45} = -24.8917150033836
x46=69.028117387504x_{46} = 69.028117387504
x47=−28.0605201580983x_{47} = -28.0605201580983
x48=18.5257597776303x_{48} = 18.5257597776303
x49=62.7362147088964x_{49} = 62.7362147088964
x50=−8.74140008690353x_{50} = -8.74140008690353
x51=−21.7148754289157x_{51} = -21.7148754289157
x52=−50.1458319794503x_{52} = -50.1458319794503
x53=84.7522070698598x_{53} = 84.7522070698598
x54=12.0699013399661x_{54} = 12.0699013399661
x55=28.0605201580983x_{55} = 28.0605201580983
x56=78.4633475726977x_{56} = 78.4633475726977
x57=91.0402820892519x_{57} = 91.0402820892519
x58=−43.8454539221714x_{58} = -43.8454539221714
x59=97.3277248932537x_{59} = 97.3277248932537
x60=−87.8963320992957x_{60} = -87.8963320992957
x61=−31.223771021093x_{61} = -31.223771021093
x62=−5.15216592622293x_{62} = -5.15216592622293
x63=100.47124635336x_{63} = 100.47124635336
x64=−97.3277248932537x_{64} = -97.3277248932537
x65=116.187287429474x_{65} = 116.187287429474
x66=−62.7362147088964x_{66} = -62.7362147088964
x67=−91.0402820892519x_{67} = -91.0402820892519
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→−∞(12⋅2sin⁡(x)x3)=0\lim_{x \to -\infty}\left(\frac{\frac{1}{2} \cdot 2 \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→∞(12⋅2sin⁡(x)x3)=0\lim_{x \to \infty}\left(\frac{\frac{1}{2} \cdot 2 \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 ((2*sin(x))/2)/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:
12⋅2sin⁡(x)x3=sin⁡(x)x3\frac{\frac{1}{2} \cdot 2 \sin{\left(x \right)}}{x^{3}} = \frac{\sin{\left(x \right)}}{x^{3}}
- No
12⋅2sin⁡(x)x3=−sin⁡(x)x3\frac{\frac{1}{2} \cdot 2 \sin{\left(x \right)}}{x^{3}} = - \frac{\sin{\left(x \right)}}{x^{3}}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор