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Trazado el gráfico de la función/ (-tan(x)+sin(x))/x^2

Gráfico de la función y = (-tan(x)+sin(x))/x^2

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       -tan(x) + sin(x)
f(x) = ----------------
               2       
              x
f(x)=sin⁡(x)−tan⁡(x)x2f{\left(x \right)} = \frac{\sin{\left(x \right)} - \tan{\left(x \right)}}{x^{2}} 
f = (sin(x) - tan(x))/x^2
Gráfico de la función
02468-8-6-4-2-1010-5050
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)−tan⁡(x)x2=0\frac{\sin{\left(x \right)} - \tan{\left(x \right)}}{x^{2}} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−πx_{1} = - \pi
x2=πx_{2} = \pi
x3=2πx_{3} = 2 \pi
Solución numérica
x1=18.8499705557576x_{1} = 18.8499705557576
x2=−69.115190002488x_{2} = -69.115190002488
x3=−15.707963267949x_{3} = -15.707963267949
x4=−12.5662132152219x_{4} = -12.5662132152219
x5=84.8230016469244x_{5} = 84.8230016469244
x6=21.9911485751286x_{6} = 21.9911485751286
x7=−69.1146296243476x_{7} = -69.1146296243476
x8=81.6814952966863x_{8} = 81.6814952966863
x9=−21.9911485751286x_{9} = -21.9911485751286
x10=69.1152917430574x_{10} = 69.1152917430574
x11=28.2743338823081x_{11} = 28.2743338823081
x12=−56.5485217299594x_{12} = -56.5485217299594
x13=72.2566310325652x_{13} = 72.2566310325652
x14=−12.5667507896127x_{14} = -12.5667507896127
x15=43.9823032529319x_{15} = 43.9823032529319
x16=−40.8407044966673x_{16} = -40.8407044966673
x17=−25.1328857738208x_{17} = -25.1328857738208
x18=−62.8316150966479x_{18} = -62.8316150966479
x19=−97.3893722612836x_{19} = -97.3893722612836
x20=−43.9823032328965x_{20} = -43.9823032328965
x21=59.6902604182061x_{21} = 59.6902604182061
x22=−18.8497845786293x_{22} = -18.8497845786293
x23=−91.106186954104x_{23} = -91.106186954104
x24=94.2477801894711x_{24} = 94.2477801894711
x25=−62.8320963183562x_{25} = -62.8320963183562
x26=−53.4070751110265x_{26} = -53.4070751110265
x27=62.831712710125x_{27} = 62.831712710125
x28=12.566293169695x_{28} = 12.566293169695
x29=100.53089752613x_{29} = 100.53089752613
x30=25.132981592904x_{30} = 25.132981592904
x31=53.4070751110265x_{31} = 53.4070751110265
x32=−28.2743338823081x_{32} = -28.2743338823081
x33=−94.2477097292694x_{33} = -94.2477097292694
x34=−72.2566310325652x_{34} = -72.2566310325652
x35=75.3983812155628x_{35} = 75.3983812155628
x36=−37.6991249673766x_{36} = -37.6991249673766
x37=50.2654784069467x_{37} = 50.2654784069467
x38=−6.28310226447675x_{38} = -6.28310226447675
x39=9.42477796076938x_{39} = 9.42477796076938
x40=65.9734457253857x_{40} = 65.9734457253857
x41=25.1325002165247x_{41} = 25.1325002165247
x42=31.4155161069179x_{42} = 31.4155161069179
x43=−84.8230016469244x_{43} = -84.8230016469244
x44=−75.3962870884282x_{44} = -75.3962870884282
x45=87.9646063264249x_{45} = 87.9646063264249
x46=31.4160773323774x_{46} = 31.4160773323774
x47=3.14159265358979x_{47} = 3.14159265358979
x48=40.8407044966673x_{48} = 40.8407044966673
x49=−78.5398163397448x_{49} = -78.5398163397448
x50=47.1238898038469x_{50} = 47.1238898038469
x51=−18.8493020291405x_{51} = -18.8493020291405
x52=91.106186954104x_{52} = 91.106186954104
x53=69.1148097354674x_{53} = 69.1148097354674
x54=81.6801148690188x_{54} = 81.6801148690188
x55=−56.5490909250485x_{55} = -56.5490909250485
x56=78.5398163397448x_{56} = 78.5398163397448
x57=15.707963267949x_{57} = 15.707963267949
x58=62.8323048592662x_{58} = 62.8323048592662
x59=−3.14159265358979x_{59} = -3.14159265358979
x60=56.5485961317107x_{60} = 56.5485961317107
x61=−81.6814265554779x_{61} = -81.6814265554779
x62=−25.1323022679877x_{62} = -25.1323022679877
x63=−65.9734457253857x_{63} = -65.9734457253857
x64=−34.5575191894877x_{64} = -34.5575191894877
x65=6.2831766239039x_{65} = 6.2831766239039
x66=−59.6902604182061x_{66} = -59.6902604182061
x67=18.8494072742531x_{67} = 18.8494072742531
x68=37.6991934748829x_{68} = 37.6991934748829
x69=−75.3983065960259x_{69} = -75.3983065960259
x70=−31.4160048810679x_{70} = -31.4160048810679
x71=34.5575191894877x_{71} = 34.5575191894877
x72=−87.9646059894675x_{72} = -87.9646059894675
x73=−47.1238898038469x_{73} = -47.1238898038469
x74=−50.2654080159534x_{74} = -50.2654080159534
x75=−9.42477796076938x_{75} = -9.42477796076938
x76=97.3893722612836x_{76} = 97.3893722612836
x77=−100.530824375464x_{77} = -100.530824375464
x78=75.3978374769382x_{78} = 75.3978374769382
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 (-tan(x) + sin(x))/x^2.
−tan⁡(0)+sin⁡(0)02\frac{- \tan{\left(0 \right)} + \sin{\left(0 \right)}}{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
cos⁡(x)−tan⁡2(x)−1x2−2(sin⁡(x)−tan⁡(x))x3=0\frac{\cos{\left(x \right)} - \tan^{2}{\left(x \right)} - 1}{x^{2}} - \frac{2 \left(\sin{\left(x \right)} - \tan{\left(x \right)}\right)}{x^{3}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−1156.10608070793x_{1} = -1156.10608070793
x2=18.8495554664323x_{2} = 18.8495554664323
x3=62.8318545472756x_{3} = 62.8318545472756
x4=11447.9637185929x_{4} = 11447.9637185929
x5=−87.9645943580839x_{5} = -87.9645943580839
x6=56.5486904064043x_{6} = 56.5486904064043
x7=81.6814092168155x_{7} = 81.6814092168155
x8=6.28318571765258x_{8} = 6.28318571765258
x9=125.663722285741x_{9} = 125.663722285741
x10=87.9645943361183x_{10} = 87.9645943361183
x11=−43.9822971743842x_{11} = -43.9822971743842
x12=−56.5486704437837x_{12} = -56.5486704437837
x13=18.8495589320187x_{13} = 18.8495589320187
x14=−62.8318521213994x_{14} = -62.8318521213994
x15=446.106360287555x_{15} = 446.106360287555
x16=−62.8318540471604x_{16} = -62.8318540471604
x17=94.2477796093519x_{17} = 94.2477796093519
x18=−18.849556783468x_{18} = -18.849556783468
x19=−56.5486708391066x_{19} = -56.5486708391066
x20=−69.1150272493433x_{20} = -69.1150272493433
x21=−37.6991118773074x_{21} = -37.6991118773074
x22=37.6991109715204x_{22} = 37.6991109715204
x23=100.530964744173x_{23} = 100.530964744173
x24=−87.9646453390757x_{24} = -87.9646453390757
x25=75.3982211826328x_{25} = 75.3982211826328
x26=−31.4159193329553x_{26} = -31.4159193329553
x27=81.6814033208689x_{27} = 81.6814033208689
x28=62.8318566731154x_{28} = 62.8318566731154
x29=−69.1150355143013x_{29} = -69.1150355143013
x30=12.5663722955771x_{30} = 12.5663722955771
x31=−113.097343315674x_{31} = -113.097343315674
x32=−797.964534586798x_{32} = -797.964534586798
x33=−31.4159153392304x_{33} = -31.4159153392304
x34=12.566370255665x_{34} = 12.566370255665
x35=−18.8495548402421x_{35} = -18.8495548402421
x36=69.1150315456483x_{36} = 69.1150315456483
x37=69.1150321122122x_{37} = 69.1150321122122
x38=−12.5663730816243x_{38} = -12.5663730816243
x39=31.4159236906738x_{39} = 31.4159236906738
x40=−75.398213104482x_{40} = -75.398213104482
x41=−75.3982240366897x_{41} = -75.3982240366897
x42=62.8318518591974x_{42} = 62.8318518591974
x43=−150.796496172887x_{43} = -150.796496172887
x44=12.5663699149855x_{44} = 12.5663699149855
x45=−81.6814093267247x_{45} = -81.6814093267247
x46=−383.274319745291x_{46} = -383.274319745291
x47=−31.4159267321981x_{47} = -31.4159267321981
x48=94.2477798839718x_{48} = 94.2477798839718
x49=25.1327402547553x_{49} = 25.1327402547553
x50=6.28318528363928x_{50} = 6.28318528363928
x51=43.982294196519x_{51} = 43.982294196519
x52=−56.5486673282356x_{52} = -56.5486673282356
x53=−75.3982238973503x_{53} = -75.3982238973503
x54=31.4159265700968x_{54} = 31.4159265700968
x55=69.1150394396063x_{55} = 69.1150394396063
x56=56.5486675815965x_{56} = 56.5486675815965
x57=−119.380522005839x_{57} = -119.380522005839
x58=−31.4159249350464x_{58} = -31.4159249350464
x59=43.9822874055792x_{59} = 43.9822874055792
x60=−94.247800478884x_{60} = -94.247800478884
x61=−25.1327416418926x_{61} = -25.1327416418926
x62=−43.9822967106817x_{62} = -43.9822967106817
x63=37.6991120515325x_{63} = 37.6991120515325
x64=−50.2654822633581x_{64} = -50.2654822633581
x65=−12.5663701097364x_{65} = -12.5663701097364
x66=31.415926978842x_{66} = 31.415926978842
x67=94.247788860923x_{67} = 94.247788860923
x68=−31.4159325737557x_{68} = -31.4159325737557
x69=−56.5486676993217x_{69} = -56.5486676993217
x70=69.1150375000423x_{70} = 69.1150375000423
x71=12.5663704080972x_{71} = 12.5663704080972
x72=−94.2477794270741x_{72} = -94.2477794270741
x73=62.8318526612428x_{73} = 62.8318526612428
x74=100.530963894357x_{74} = 100.530963894357
x75=43.9822971694917x_{75} = 43.9822971694917
x76=75.3982241632366x_{76} = 75.3982241632366
x77=81.6814063718606x_{77} = 81.6814063718606
x78=−94.2477804566038x_{78} = -94.2477804566038
x79=50.2654824463089x_{79} = 50.2654824463089
x80=56.5486678154258x_{80} = 56.5486678154258
x81=−25.1327379006296x_{81} = -25.1327379006296
x82=25.1327409532572x_{82} = 25.1327409532572
x83=87.9646020448506x_{83} = 87.9646020448506
x84=−100.530964503023x_{84} = -100.530964503023
x85=−69.1150388279099x_{85} = -69.1150388279099
x86=−81.6814090385276x_{86} = -81.6814090385276
x87=−37.6991120138589x_{87} = -37.6991120138589
x88=25.1327421838749x_{88} = 25.1327421838749
x89=−6.2831850697993x_{89} = -6.2831850697993
Signos de extremos en los puntos:
(-1156.106080707933, -1.4791990664389e-21)

(18.849555466432278, 1.32607504514291e-22)

(62.831854547275576, -4.06798065885684e-22)

(11447.963718592906, -2.68157684858385e-21)

(-87.96459435808394, 1.19729883771663e-26)

(56.5486904064043, -1.81491833854508e-18)

(81.6814092168155, -8.37117337725645e-25)

(6.2831857176525805, -8.75656364687435e-22)

(125.66372228574147, -1.33178707198341e-19)

(87.96459433611828, -2.56564036781697e-27)

(-43.98229717438416, 3.42085382277207e-27)

(-56.54867044378374, 3.00696164976335e-21)

(18.84955893201873, -3.8394775346208e-20)

(-62.83185212139935, -1.0872623196502e-22)

(446.1063602875554, -2.11662688328545e-17)

(-62.83185404716038, 1.17523019059098e-22)

(94.24777960935188, 0)

(-18.84955678346803, 9.01134915986591e-22)

(-56.54867083910665, 4.54395022019461e-21)

(-69.11502724934327, -1.44300449926285e-19)

(-37.699111877307445, 1.3968486432945e-26)

(37.69911097152045, 2.32957115598771e-22)

(100.53096474417282, 2.46194574663805e-25)

(-87.96464533907574, 8.59110372107709e-18)

(75.39822118263282, 1.38008655372991e-21)

(-31.415919332955337, -1.89321684187199e-19)

(81.68140332086892, 1.36785151426515e-20)

(62.831856673115375, -5.91552147446529e-21)

(-69.11503551430128, -2.46065553116755e-21)

(12.566372295577121, -1.50457321081269e-20)

(-113.0973433156742, 1.84536635182418e-20)

(-797.9645345867976, 1.49320513219997e-25)

(-31.41591533923042, -7.11109306159166e-19)

(12.566370255665037, 1.46166250644098e-22)

(-18.84955484024213, -1.77902663943669e-21)

(69.11503154564825, 3.33980343388759e-20)

(69.11503211221218, 2.57605497910039e-20)

(-12.566373081624262, 4.75563080864335e-20)

(31.415923690673846, 1.1668842119061e-20)

(-75.39821310448201, -1.04210153131107e-19)

(-75.39822403668971, 3.79011595711375e-24)

(62.8318518591974, 2.25820148195894e-22)

(-150.79649617288732, 2.55542052520409e-18)

(12.56636991498552, 1.08350767820219e-21)

(-81.68140932672466, 2.77716651578661e-24)

(-383.2743197452912, 1.39607239040796e-20)

(-31.41592673219809, 3.83518759406612e-24)

(94.24777988397176, -1.18601761660029e-24)

(25.132740254755262, 7.31166511843277e-22)

(6.283185283639279, 1.67621838755743e-25)

(43.98229419651897, 6.66086853101854e-21)

(-56.548667328235624, -1.29793108768428e-23)

(-75.39822389735026, 8.28796858550101e-25)

(31.41592657009683, -2.01146204561751e-26)

(69.11503943960635, -1.24876879800169e-22)

(56.54866758159649, 9.60204112386715e-25)

(-119.38052200583878, 5.61054888419897e-23)

(-31.415924935046437, -2.07840371883782e-21)

(43.982287405579214, 2.39175696670774e-19)

(-94.24780047888402, 5.11763207243069e-19)

(-25.132741641892622, 5.58180700521486e-23)

(-43.98229671068173, -2.19481985897024e-23)

(37.699112051532516, -3.18481487727445e-24)

(-50.26548226335814, -1.4457383595994e-24)

(-12.566370109736413, -4.06985854135691e-22)

(31.415926978842, -4.40376079061269e-23)

(94.24778886092298, -4.45971146345717e-20)

(-31.415932573755715, 1.11511551181653e-19)

(-56.54866769932167, -4.55269189322245e-26)

(69.11503750004229, 7.10605784716989e-23)

(12.566370408097232, 2.78252259383914e-23)

(-94.24777942707406, -3.3077376060062e-25)

(62.83185266124285, 8.76997465259479e-24)

(100.5309638943567, 5.25703998531663e-23)

(43.98229716949169, -1.71042691176656e-27)

(75.39822416323665, -9.55444461657348e-24)

(81.68140637186058, 1.3500521538547e-21)

(-94.24778045660378, 3.44362296755962e-23)

(50.265482446308916, 6.54772803023241e-28)

(56.54866781542581, -2.06940539751252e-26)

(-25.132737900629582, -2.91789467123813e-20)

(25.132740953257205, 1.65945622762347e-23)

(87.96460204485058, -3.0012869445813e-20)

(-100.53096450302264, -3.45720042675861e-24)

(-69.11503882790991, 9.47548226118709e-24)

(-81.68140903852758, 6.94291633846001e-27)

(-37.699112013858915, 1.75071695357976e-24)

(25.132742183874935, -6.89931430707941e-22)

(-6.283185069799302, -1.69633312367307e-22)


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:
La función no tiene puntos mínimos
La función no tiene puntos máximos
Decrece en todo el eje numérico
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
−2(tan⁡2(x)+1)tan⁡(x)−sin⁡(x)+4(−cos⁡(x)+tan⁡2(x)+1)x+6(sin⁡(x)−tan⁡(x))x2x2=0\frac{- 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \sin{\left(x \right)} + \frac{4 \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)}{x} + \frac{6 \left(\sin{\left(x \right)} - \tan{\left(x \right)}\right)}{x^{2}}}{x^{2}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−43.9822971502571x_{1} = -43.9822971502571
x2=−31.4159265358979x_{2} = -31.4159265358979
x3=−53.5485033332354x_{3} = -53.5485033332354
x4=34.7628137456958x_{4} = 34.7628137456958
x5=−97.4699892938459x_{5} = -97.4699892938459
x6=−22.2791470609148x_{6} = -22.2791470609148
x7=−28.5145580814312x_{7} = -28.5145580814312
x8=59.8181276206052x_{8} = 59.8181276206052
x9=6.28318530717959x_{9} = 6.28318530717959
x10=84.9150381857849x_{10} = 84.9150381857849
x11=3.81019252919313x_{11} = 3.81019252919313
x12=47.2819227750125x_{12} = 47.2819227750125
x13=16.064895766025x_{13} = 16.064895766025
x14=94.2477796076938x_{14} = 94.2477796076938
x15=50.2654824574367x_{15} = 50.2654824574367
x16=56.5486677646163x_{16} = 56.5486677646163
x17=43.9822971502571x_{17} = 43.9822971502571
x18=−66.090050226592x_{18} = -66.090050226592
x19=−50.2654824574367x_{19} = -50.2654824574367
x20=37.6991118430775x_{20} = 37.6991118430775
x21=−56.5486677646163x_{21} = -56.5486677646163
x22=−62.8318530717959x_{22} = -62.8318530717959
x23=22.2791470609148x_{23} = 22.2791470609148
x24=53.5485033332354x_{24} = 53.5485033332354
x25=−81.6814089933346x_{25} = -81.6814089933346
x26=−6.28318530717959x_{26} = -6.28318530717959
x27=−91.1921433712405x_{27} = -91.1921433712405
x28=91.1921433712405x_{28} = 91.1921433712405
x29=−78.6388353763319x_{29} = -78.6388353763319
x30=97.4699892938459x_{30} = 97.4699892938459
x31=66.090050226592x_{31} = 66.090050226592
x32=−25.1327412287183x_{32} = -25.1327412287183
x33=−75.398223686155x_{33} = -75.398223686155
x34=−72.363745968728x_{34} = -72.363745968728
x35=−69.1150383789755x_{35} = -69.1150383789755
x36=78.6388353763319x_{36} = 78.6388353763319
x37=−47.2819227750125x_{37} = -47.2819227750125
x38=62.8318530717959x_{38} = 62.8318530717959
x39=−18.8495559215388x_{39} = -18.8495559215388
x40=9.89036297373071x_{40} = 9.89036297373071
x41=25.1327412287183x_{41} = 25.1327412287183
x42=100.530964914873x_{42} = 100.530964914873
x43=−87.9645943005142x_{43} = -87.9645943005142
x44=−34.7628137456958x_{44} = -34.7628137456958
x45=41.0194757257576x_{45} = 41.0194757257576
x46=81.6814089933346x_{46} = 81.6814089933346
x47=75.398223686155x_{47} = 75.398223686155
x48=−9.89036297373071x_{48} = -9.89036297373071
x49=−41.0194757257576x_{49} = -41.0194757257576
x50=12.5663706143592x_{50} = 12.5663706143592
x51=87.9645943005142x_{51} = 87.9645943005142
x52=69.1150383789755x_{52} = 69.1150383789755
x53=−16.064895766025x_{53} = -16.064895766025
x54=−37.6991118430775x_{54} = -37.6991118430775
x55=31.4159265358979x_{55} = 31.4159265358979
x56=−12.5663706143592x_{56} = -12.5663706143592
x57=−84.9150381857849x_{57} = -84.9150381857849
x58=−94.2477796076938x_{58} = -94.2477796076938
x59=72.363745968728x_{59} = 72.363745968728
x60=28.5145580814312x_{60} = 28.5145580814312
x61=−100.530964914873x_{61} = -100.530964914873
x62=−3.81019252919313x_{62} = -3.81019252919313
x63=18.8495559215388x_{63} = 18.8495559215388
x64=−59.8181276206052x_{64} = -59.8181276206052
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−(−2(tan⁡2(x)+1)tan⁡(x)−sin⁡(x)+4(−cos⁡(x)+tan⁡2(x)+1)x+6(sin⁡(x)−tan⁡(x))x2x2)=0\lim_{x \to 0^-}\left(\frac{- 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \sin{\left(x \right)} + \frac{4 \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)}{x} + \frac{6 \left(\sin{\left(x \right)} - \tan{\left(x \right)}\right)}{x^{2}}}{x^{2}}\right) = 0
lim⁡x→0+(−2(tan⁡2(x)+1)tan⁡(x)−sin⁡(x)+4(−cos⁡(x)+tan⁡2(x)+1)x+6(sin⁡(x)−tan⁡(x))x2x2)=0\lim_{x \to 0^+}\left(\frac{- 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \sin{\left(x \right)} + \frac{4 \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)}{x} + \frac{6 \left(\sin{\left(x \right)} - \tan{\left(x \right)}\right)}{x^{2}}}{x^{2}}\right) = 0
- 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
(−∞,−100.530964914873]\left(-\infty, -100.530964914873\right]
Convexa en los intervalos
[100.530964914873,∞)\left[100.530964914873, \infty\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
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=lim⁡x→−∞(sin⁡(x)−tan⁡(x)x2)y = \lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} - \tan{\left(x \right)}}{x^{2}}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(sin⁡(x)−tan⁡(x)x2)y = \lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} - \tan{\left(x \right)}}{x^{2}}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (-tan(x) + sin(x))/x^2, dividida por x con x->+oo y x ->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=xlim⁡x→−∞(sin⁡(x)−tan⁡(x)xx2)y = x \lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} - \tan{\left(x \right)}}{x x^{2}}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(sin⁡(x)−tan⁡(x)xx2)y = x \lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} - \tan{\left(x \right)}}{x x^{2}}\right)
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)−tan⁡(x)x2=−sin⁡(x)+tan⁡(x)x2\frac{\sin{\left(x \right)} - \tan{\left(x \right)}}{x^{2}} = \frac{- \sin{\left(x \right)} + \tan{\left(x \right)}}{x^{2}}
- No
sin⁡(x)−tan⁡(x)x2=−−sin⁡(x)+tan⁡(x)x2\frac{\sin{\left(x \right)} - \tan{\left(x \right)}}{x^{2}} = - \frac{- \sin{\left(x \right)} + \tan{\left(x \right)}}{x^{2}}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор