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  • Gráfico de la función y =:
  • y=(x+1)^3 y=(x+1)^3
  • 2*x^2-6*x 2*x^2-6*x
  • y=2x y=2x
  • y=1/(x^2+1) y=1/(x^2+1)

  • Expresiones idénticas

  • sin(x)/((tres *x^ dos))
  • seno de (x) dividir por ((3 multiplicar por x al cuadrado ))
  • seno de (x) dividir por ((tres multiplicar por x en el grado dos))
  • sin(x)/((3*x2))
  • sinx/3*x2
  • sin(x)/((3*x²))
  • sin(x)/((3*x en el grado 2))
  • sin(x)/((3x^2))
  • sin(x)/((3x2))
  • sinx/3x2
  • sinx/3x^2
  • sin(x) dividir por ((3*x^2))

  • Expresiones semejantes

  • sinx/((3*x^2))

  • Expresiones con funciones

  • Seno sin
  • sin(3*x)+3
  • sin(2*x)+5
  • sin(22*x)
  • sin(2x)/(sinx)
  • sin(x)-sin(x)^2
Trazado el gráfico de la función/ sin(x)/((3*x^2))

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

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       sin(x)
f(x) = ------
           2 
        3*x
f(x)=sin⁡(x)3x2f{\left(x \right)} = \frac{\sin{\left(x \right)}}{3 x^{2}} 
f = sin(x)/((3*x^2))
Gráfico de la función
02468-8-6-4-2-1010-1010
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)3x2=0\frac{\sin{\left(x \right)}}{3 x^{2}} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=πx_{1} = \pi
Solución numérica
x1=62.8318530717959x_{1} = 62.8318530717959
x2=−50.2654824574367x_{2} = -50.2654824574367
x3=47.1238898038469x_{3} = 47.1238898038469
x4=84.8230016469244x_{4} = 84.8230016469244
x5=−53.4070751110265x_{5} = -53.4070751110265
x6=−226.194671058465x_{6} = -226.194671058465
x7=91.106186954104x_{7} = 91.106186954104
x8=−84.8230016469244x_{8} = -84.8230016469244
x9=25.1327412287183x_{9} = 25.1327412287183
x10=−3.14159265358979x_{10} = -3.14159265358979
x11=−6.28318530717959x_{11} = -6.28318530717959
x12=−502.654824574367x_{12} = -502.654824574367
x13=−40.8407044966673x_{13} = -40.8407044966673
x14=−18.8495559215388x_{14} = -18.8495559215388
x15=78.5398163397448x_{15} = 78.5398163397448
x16=−75.398223686155x_{16} = -75.398223686155
x17=779.114978090269x_{17} = 779.114978090269
x18=−9.42477796076938x_{18} = -9.42477796076938
x19=72.2566310325652x_{19} = 72.2566310325652
x20=−43.9822971502571x_{20} = -43.9822971502571
x21=31.4159265358979x_{21} = 31.4159265358979
x22=9.42477796076938x_{22} = 9.42477796076938
x23=40.8407044966673x_{23} = 40.8407044966673
x24=−69.1150383789755x_{24} = -69.1150383789755
x25=12.5663706143592x_{25} = 12.5663706143592
x26=87.9645943005142x_{26} = 87.9645943005142
x27=59.6902604182061x_{27} = 59.6902604182061
x28=−37.6991118430775x_{28} = -37.6991118430775
x29=−100.530964914873x_{29} = -100.530964914873
x30=−91.106186954104x_{30} = -91.106186954104
x31=97.3893722612836x_{31} = 97.3893722612836
x32=18.8495559215388x_{32} = 18.8495559215388
x33=−12.5663706143592x_{33} = -12.5663706143592
x34=−78.5398163397448x_{34} = -78.5398163397448
x35=34.5575191894877x_{35} = 34.5575191894877
x36=−94.2477796076938x_{36} = -94.2477796076938
x37=43.9822971502571x_{37} = 43.9822971502571
x38=−31.4159265358979x_{38} = -31.4159265358979
x39=10115.9283445591x_{39} = 10115.9283445591
x40=−65.9734457253857x_{40} = -65.9734457253857
x41=75.398223686155x_{41} = 75.398223686155
x42=56.5486677646163x_{42} = 56.5486677646163
x43=−81.6814089933346x_{43} = -81.6814089933346
x44=3.14159265358979x_{44} = 3.14159265358979
x45=15.707963267949x_{45} = 15.707963267949
x46=−56.5486677646163x_{46} = -56.5486677646163
x47=−21.9911485751286x_{47} = -21.9911485751286
x48=50.2654824574367x_{48} = 50.2654824574367
x49=−15.707963267949x_{49} = -15.707963267949
x50=28.2743338823081x_{50} = 28.2743338823081
x51=94.2477796076938x_{51} = 94.2477796076938
x52=−59.6902604182061x_{52} = -59.6902604182061
x53=−62.8318530717959x_{53} = -62.8318530717959
x54=69.1150383789755x_{54} = 69.1150383789755
x55=−34.5575191894877x_{55} = -34.5575191894877
x56=−97.3893722612836x_{56} = -97.3893722612836
x57=21.9911485751286x_{57} = 21.9911485751286
x58=65.9734457253857x_{58} = 65.9734457253857
x59=37.6991118430775x_{59} = 37.6991118430775
x60=−87.9645943005142x_{60} = -87.9645943005142
x61=−72.2566310325652x_{61} = -72.2566310325652
x62=−25.1327412287183x_{62} = -25.1327412287183
x63=−28.2743338823081x_{63} = -28.2743338823081
x64=81.6814089933346x_{64} = 81.6814089933346
x65=6.28318530717959x_{65} = 6.28318530717959
x66=216.769893097696x_{66} = 216.769893097696
x67=100.530964914873x_{67} = 100.530964914873
x68=53.4070751110265x_{68} = 53.4070751110265
x69=−47.1238898038469x_{69} = -47.1238898038469
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^2)).
sin⁡(0)3⋅02\frac{\sin{\left(0 \right)}}{3 \cdot 0^{2}}
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
13x2cos⁡(x)−2sin⁡(x)3x3=0\frac{1}{3 x^{2}} \cos{\left(x \right)} - \frac{2 \sin{\left(x \right)}}{3 x^{3}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=4.27478227145813x_{1} = 4.27478227145813
x2=−39.2189565596149x_{2} = -39.2189565596149
x3=−48.6536023357065x_{3} = -48.6536023357065
x4=29.7780674009765x_{4} = 29.7780674009765
x5=−73.8003338423053x_{5} = -73.8003338423053
x6=39.2189565596149x_{6} = 39.2189565596149
x7=124.076792162751x_{7} = 124.076792162751
x8=−10.8126733338873x_{8} = -10.8126733338873
x9=−42.3643263176719x_{9} = -42.3643263176719
x10=−95.7977016393173x_{10} = -95.7977016393173
x11=−4.27478227145813x_{11} = -4.27478227145813
x12=42.3643263176719x_{12} = 42.3643263176719
x13=73.8003338423053x_{13} = 73.8003338423053
x14=89.5130512336412x_{14} = 89.5130512336412
x15=−36.0729289833362x_{15} = -36.0729289833362
x16=−26.6285710115144x_{16} = -26.6285710115144
x17=61.2284037765214x_{17} = 61.2284037765214
x18=−54.9414851392857x_{18} = -54.9414851392857
x19=−89.5130512336412x_{19} = -89.5130512336412
x20=95.7977016393173x_{20} = 95.7977016393173
x21=98.9399570606555x_{21} = 98.9399570606555
x22=70.6575367178468x_{22} = 70.6575367178468
x23=7.59654601975059x_{23} = 7.59654601975059
x24=26.6285710115144x_{24} = 26.6285710115144
x25=−51.797686192112x_{25} = -51.797686192112
x26=20.3222538599925x_{26} = 20.3222538599925
x27=−17.1627513884202x_{27} = -17.1627513884202
x28=−61.2284037765214x_{28} = -61.2284037765214
x29=−199.481107826777x_{29} = -199.481107826777
x30=−76.9430326079594x_{30} = -76.9430326079594
x31=80.0856445915527x_{31} = 80.0856445915527
x32=−83.2281796214841x_{32} = -83.2281796214841
x33=58.0850454185866x_{33} = 58.0850454185866
x34=−86.3706460958767x_{34} = -86.3706460958767
x35=−64.3715897831264x_{35} = -64.3715897831264
x36=−58.0850454185866x_{36} = -58.0850454185866
x37=−98.9399570606555x_{37} = -98.9399570606555
x38=−80.0856445915527x_{38} = -80.0856445915527
x39=10.8126733338873x_{39} = 10.8126733338873
x40=13.9952220914795x_{40} = 13.9952220914795
x41=−45.5091745543365x_{41} = -45.5091745543365
x42=−32.9260552340905x_{42} = -32.9260552340905
x43=−13.9952220914795x_{43} = -13.9952220914795
x44=64.3715897831264x_{44} = 64.3715897831264
x45=92.6554012744443x_{45} = 92.6554012744443
x46=36.0729289833362x_{46} = 36.0729289833362
x47=51.797686192112x_{47} = 51.797686192112
x48=86.3706460958767x_{48} = 86.3706460958767
x49=−177.488717082806x_{49} = -177.488717082806
x50=−102.082171688207x_{50} = -102.082171688207
x51=76.9430326079594x_{51} = 76.9430326079594
x52=−20.3222538599925x_{52} = -20.3222538599925
x53=−29.7780674009765x_{53} = -29.7780674009765
x54=67.5146275025823x_{54} = 67.5146275025823
x55=83.2281796214841x_{55} = 83.2281796214841
x56=23.4769601879883x_{56} = 23.4769601879883
x57=54.9414851392857x_{57} = 54.9414851392857
x58=−23.4769601879883x_{58} = -23.4769601879883
x59=−92.6554012744443x_{59} = -92.6554012744443
x60=17.1627513884202x_{60} = 17.1627513884202
x61=−70.6575367178468x_{61} = -70.6575367178468
x62=32.9260552340905x_{62} = 32.9260552340905
x63=−7.59654601975059x_{63} = -7.59654601975059
x64=48.6536023357065x_{64} = 48.6536023357065
x65=45.5091745543365x_{65} = 45.5091745543365
x66=−67.5146275025823x_{66} = -67.5146275025823
Signos de extremos en los puntos:
(4.274782271458128, -0.0165222026248708)

(-39.21895655961492, -0.00021643261302593)

(-48.653602335706516, 0.00014069612023177)

(29.778067400976507, -0.000375066601060979)

(-73.80033384230535, 6.1179042290794e-5)

(39.21895655961492, 0.00021643261302593)

(124.07679216275135, -2.16491684117845e-5)

(-10.812673333887274, 0.00280354505419173)

(-42.3643263176719, 0.000185521697713509)

(-95.79770163931728, -3.63139875306427e-5)

(-4.274782271458128, 0.0165222026248708)

(42.3643263176719, -0.000185521697713509)

(73.80033384230535, -6.1179042290794e-5)

(89.51305123364119, 4.15908356992034e-5)

(-36.07292898333623, 0.000255769912663386)

(-26.62857101151445, -0.000468771839390892)

(61.2284037765214, -8.88671603748385e-5)

(-54.941485139285724, 0.000110354588940655)

(-89.51305123364119, -4.15908356992034e-5)

(95.79770163931728, 3.63139875306427e-5)

(98.93995706065554, -3.4044471623029e-5)

(70.65753671784677, 6.67402532072293e-5)

(7.596546019750588, 0.00558590513684958)

(26.62857101151445, 0.000468771839390892)

(-51.79768619211198, -0.000124146513669294)

(20.32225385999246, 0.00080323378856485)

(-17.162751388420226, 0.0011240250682907)

(-61.2284037765214, 8.88671603748385e-5)

(-199.4811078267769, 8.37632222524937e-6)

(-76.94303260795941, -5.62851049888947e-5)

(80.0856445915527, -5.19557968064342e-5)

(-83.22817962148409, -4.81074787655215e-5)

(58.08504541858663, 9.87399232952215e-5)

(-86.37064609587671, 4.46714454381092e-5)

(-64.37158978312642, -8.04045748101565e-5)

(-58.08504541858663, -9.87399232952215e-5)

(-98.93995706065554, 3.4044471623029e-5)

(-80.0856445915527, 5.19557968064342e-5)

(10.812673333887274, -0.00280354505419173)

(13.995222091479503, 0.00168472580447811)

(-45.509174554336525, -0.000160791040165716)

(-32.926055234090526, -0.000306901934584219)

(-13.995222091479503, -0.00168472580447811)

(64.37158978312642, 8.04045748101565e-5)

(92.65540127444433, -3.88182641896619e-5)

(36.07292898333623, -0.000255769912663386)

(51.79768619211198, 0.000124146513669294)

(86.37064609587671, -4.46714454381092e-5)

(-177.4887170828061, -1.05805848471219e-5)

(-102.08217168820711, -3.19812628135683e-5)

(76.94303260795941, 5.62851049888947e-5)

(-20.32225385999246, -0.00080323378856485)

(-29.778067400976507, 0.000375066601060979)

(67.51462750258234, -7.30958167066375e-5)

(83.22817962148409, 4.81074787655215e-5)

(23.4769601879883, -0.000602593998794516)

(54.941485139285724, -0.000110354588940655)

(-23.4769601879883, 0.000602593998794516)

(-92.65540127444433, 3.88182641896619e-5)

(17.162751388420226, -0.0011240250682907)

(-70.65753671784677, -6.67402532072293e-5)

(32.926055234090526, 0.000306901934584219)

(-7.596546019750588, -0.00558590513684958)

(48.653602335706516, -0.00014069612023177)

(45.509174554336525, 0.000160791040165716)

(-67.51462750258234, 7.30958167066375e-5)


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=4.27478227145813x_{1} = 4.27478227145813
x2=−39.2189565596149x_{2} = -39.2189565596149
x3=29.7780674009765x_{3} = 29.7780674009765
x4=124.076792162751x_{4} = 124.076792162751
x5=−95.7977016393173x_{5} = -95.7977016393173
x6=42.3643263176719x_{6} = 42.3643263176719
x7=73.8003338423053x_{7} = 73.8003338423053
x8=−26.6285710115144x_{8} = -26.6285710115144
x9=61.2284037765214x_{9} = 61.2284037765214
x10=−89.5130512336412x_{10} = -89.5130512336412
x11=98.9399570606555x_{11} = 98.9399570606555
x12=−51.797686192112x_{12} = -51.797686192112
x13=−76.9430326079594x_{13} = -76.9430326079594
x14=80.0856445915527x_{14} = 80.0856445915527
x15=−83.2281796214841x_{15} = -83.2281796214841
x16=−64.3715897831264x_{16} = -64.3715897831264
x17=−58.0850454185866x_{17} = -58.0850454185866
x18=10.8126733338873x_{18} = 10.8126733338873
x19=−45.5091745543365x_{19} = -45.5091745543365
x20=−32.9260552340905x_{20} = -32.9260552340905
x21=−13.9952220914795x_{21} = -13.9952220914795
x22=92.6554012744443x_{22} = 92.6554012744443
x23=36.0729289833362x_{23} = 36.0729289833362
x24=86.3706460958767x_{24} = 86.3706460958767
x25=−177.488717082806x_{25} = -177.488717082806
x26=−102.082171688207x_{26} = -102.082171688207
x27=−20.3222538599925x_{27} = -20.3222538599925
x28=67.5146275025823x_{28} = 67.5146275025823
x29=23.4769601879883x_{29} = 23.4769601879883
x30=54.9414851392857x_{30} = 54.9414851392857
x31=17.1627513884202x_{31} = 17.1627513884202
x32=−70.6575367178468x_{32} = -70.6575367178468
x33=−7.59654601975059x_{33} = -7.59654601975059
x34=48.6536023357065x_{34} = 48.6536023357065
Puntos máximos de la función:
x34=−48.6536023357065x_{34} = -48.6536023357065
x34=−73.8003338423053x_{34} = -73.8003338423053
x34=39.2189565596149x_{34} = 39.2189565596149
x34=−10.8126733338873x_{34} = -10.8126733338873
x34=−42.3643263176719x_{34} = -42.3643263176719
x34=−4.27478227145813x_{34} = -4.27478227145813
x34=89.5130512336412x_{34} = 89.5130512336412
x34=−36.0729289833362x_{34} = -36.0729289833362
x34=−54.9414851392857x_{34} = -54.9414851392857
x34=95.7977016393173x_{34} = 95.7977016393173
x34=70.6575367178468x_{34} = 70.6575367178468
x34=7.59654601975059x_{34} = 7.59654601975059
x34=26.6285710115144x_{34} = 26.6285710115144
x34=20.3222538599925x_{34} = 20.3222538599925
x34=−17.1627513884202x_{34} = -17.1627513884202
x34=−61.2284037765214x_{34} = -61.2284037765214
x34=−199.481107826777x_{34} = -199.481107826777
x34=58.0850454185866x_{34} = 58.0850454185866
x34=−86.3706460958767x_{34} = -86.3706460958767
x34=−98.9399570606555x_{34} = -98.9399570606555
x34=−80.0856445915527x_{34} = -80.0856445915527
x34=13.9952220914795x_{34} = 13.9952220914795
x34=64.3715897831264x_{34} = 64.3715897831264
x34=51.797686192112x_{34} = 51.797686192112
x34=76.9430326079594x_{34} = 76.9430326079594
x34=−29.7780674009765x_{34} = -29.7780674009765
x34=83.2281796214841x_{34} = 83.2281796214841
x34=−23.4769601879883x_{34} = -23.4769601879883
x34=−92.6554012744443x_{34} = -92.6554012744443
x34=32.9260552340905x_{34} = 32.9260552340905
x34=45.5091745543365x_{34} = 45.5091745543365
x34=−67.5146275025823x_{34} = -67.5146275025823
Decrece en los intervalos
[124.076792162751,∞)\left[124.076792162751, \infty\right)
Crece en los intervalos
(−∞,−177.488717082806]\left(-\infty, -177.488717082806\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)3−4cos⁡(x)3x+2sin⁡(x)x2x2=0\frac{- \frac{\sin{\left(x \right)}}{3} - \frac{4 \cos{\left(x \right)}}{3 x} + \frac{2 \sin{\left(x \right)}}{x^{2}}}{x^{2}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=100.49115779344x_{1} = 100.49115779344
x2=56.4778287709489x_{2} = 56.4778287709489
x3=−34.4413150584931x_{3} = -34.4413150584931
x4=40.7424877717949x_{4} = 40.7424877717949
x5=94.2053159739443x_{5} = 94.2053159739443
x6=69.0571072290369x_{6} = 69.0571072290369
x7=−103.633957788301x_{7} = -103.633957788301
x8=−59.6231598593086x_{8} = -59.6231598593086
x9=−12.2381969308869x_{9} = -12.2381969308869
x10=−78.4888481827298x_{10} = -78.4888481827298
x11=62.7681157023437x_{11} = 62.7681157023437
x12=−18.6345038295593x_{12} = -18.6345038295593
x13=47.0388282034809x_{13} = 47.0388282034809
x14=31.2879960874193x_{14} = 31.2879960874193
x15=−56.4778287709489x_{15} = -56.4778287709489
x16=72.2012232421495x_{16} = 72.2012232421495
x17=21.8074752137182x_{17} = 21.8074752137182
x18=8.97605051257904x_{18} = 8.97605051257904
x19=−40.7424877717949x_{19} = -40.7424877717949
x20=−5.55357469359905x_{20} = -5.55357469359905
x21=97.3482797940221x_{21} = 97.3482797940221
x22=−72.2012232421495x_{22} = -72.2012232421495
x23=43.8911312435672x_{23} = 43.8911312435672
x24=−53.332055816622x_{24} = -53.332055816622
x25=−97.3482797940221x_{25} = -97.3482797940221
x26=12.2381969308869x_{26} = 12.2381969308869
x27=−8.97605051257904x_{27} = -8.97605051257904
x28=−81.6324039514272x_{28} = -81.6324039514272
x29=−50.1857575826447x_{29} = -50.1857575826447
x30=87.9190940091069x_{30} = 87.9190940091069
x31=−43.8911312435672x_{31} = -43.8911312435672
x32=−100.49115779344x_{32} = -100.49115779344
x33=18.6345038295593x_{33} = 18.6345038295593
x34=37.5926583617233x_{34} = 37.5926583617233
x35=53.332055816622x_{35} = 53.332055816622
x36=−65.9127501554x_{36} = -65.9127501554
x37=−94.2053159739443x_{37} = -94.2053159739443
x38=113.061954853212x_{38} = 113.061954853212
x39=−84.775814009638x_{39} = -84.775814009638
x40=5.55357469359905x_{40} = 5.55357469359905
x41=−113.061954853212x_{41} = -113.061954853212
x42=−122.489456168277x_{42} = -122.489456168277
x43=84.775814009638x_{43} = 84.775814009638
x44=−75.3451284332546x_{44} = -75.3451284332546
x45=−47.0388282034809x_{45} = -47.0388282034809
x46=65.9127501554x_{46} = 65.9127501554
x47=75.3451284332546x_{47} = 75.3451284332546
x48=−62.7681157023437x_{48} = -62.7681157023437
x49=−87.9190940091069x_{49} = -87.9190940091069
x50=50.1857575826447x_{50} = 50.1857575826447
x51=78.4888481827298x_{51} = 78.4888481827298
x52=−24.9723967539363x_{52} = -24.9723967539363
x53=34.4413150584931x_{53} = 34.4413150584931
x54=−28.1320294160852x_{54} = -28.1320294160852
x55=−21.8074752137182x_{55} = -21.8074752137182
x56=24.9723967539363x_{56} = 24.9723967539363
x57=524.63834883134x_{57} = 524.63834883134
x58=81.6324039514272x_{58} = 81.6324039514272
x59=28.1320294160852x_{59} = 28.1320294160852
x60=91.062257436179x_{60} = 91.062257436179
x61=−31.2879960874193x_{61} = -31.2879960874193
x62=−69.0571072290369x_{62} = -69.0571072290369
x63=15.4483523863598x_{63} = 15.4483523863598
x64=380.122188103653x_{64} = 380.122188103653
x65=−37.5926583617233x_{65} = -37.5926583617233
x66=−15.4483523863598x_{66} = -15.4483523863598
x67=285.87093903435x_{67} = 285.87093903435
x68=59.6231598593086x_{68} = 59.6231598593086
x69=−91.062257436179x_{69} = -91.062257436179
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)3−4cos⁡(x)3x+2sin⁡(x)x2x2)=−∞\lim_{x \to 0^-}\left(\frac{- \frac{\sin{\left(x \right)}}{3} - \frac{4 \cos{\left(x \right)}}{3 x} + \frac{2 \sin{\left(x \right)}}{x^{2}}}{x^{2}}\right) = -\infty
lim⁡x→0+(−sin⁡(x)3−4cos⁡(x)3x+2sin⁡(x)x2x2)=∞\lim_{x \to 0^+}\left(\frac{- \frac{\sin{\left(x \right)}}{3} - \frac{4 \cos{\left(x \right)}}{3 x} + \frac{2 \sin{\left(x \right)}}{x^{2}}}{x^{2}}\right) = \infty
- los límites no son iguales, signo
x1=0x_{1} = 0
- es el punto de flexión

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
[524.63834883134,∞)\left[524.63834883134, \infty\right)
Convexa en los intervalos
(−∞,−122.489456168277]\left(-\infty, -122.489456168277\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)3x2)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{3 x^{2}}\right) = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=0y = 0
lim⁡x→∞(sin⁡(x)3x2)=0\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{3 x^{2}}\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)/((3*x^2)), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(13x2sin⁡(x)x)=0\lim_{x \to -\infty}\left(\frac{\frac{1}{3 x^{2}} \sin{\left(x \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(13x2sin⁡(x)x)=0\lim_{x \to \infty}\left(\frac{\frac{1}{3 x^{2}} \sin{\left(x \right)}}{x}\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)3x2=−13x2sin⁡(x)\frac{\sin{\left(x \right)}}{3 x^{2}} = - \frac{1}{3 x^{2}} \sin{\left(x \right)}
- No
sin⁡(x)3x2=13x2sin⁡(x)\frac{\sin{\left(x \right)}}{3 x^{2}} = \frac{1}{3 x^{2}} \sin{\left(x \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор