Sr Examen

Otras calculadoras

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

Gráfico de la función y = x^3*tan(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
        3       
f(x) = x *tan(x)
f(x)=x3tan⁡(x)f{\left(x \right)} = x^{3} \tan{\left(x \right)} 
f = x^3*tan(x)
Gráfico de la función
02468-8-6-4-2-1010-2500025000
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:
x3tan⁡(x)=0x^{3} \tan{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=πx_{2} = \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=97.3893722612836x_{25} = 97.3893722612836
x26=0x_{26} = 0
x27=65.9734457253857x_{27} = 65.9734457253857
x28=−50.2654824574367x_{28} = -50.2654824574367
x29=15.707963267949x_{29} = 15.707963267949
x30=3.14159265358979x_{30} = 3.14159265358979
x31=−25.1327412287183x_{31} = -25.1327412287183
x32=−18.8495559215388x_{32} = -18.8495559215388
x33=40.8407044966673x_{33} = 40.8407044966673
x34=−53.4070751110265x_{34} = -53.4070751110265
x35=37.6991118430775x_{35} = 37.6991118430775
x36=−43.9822971502571x_{36} = -43.9822971502571
x37=18.8495559215388x_{37} = 18.8495559215388
x38=−78.5398163397448x_{38} = -78.5398163397448
x39=−6.28318530717959x_{39} = -6.28318530717959
x40=−40.8407044966673x_{40} = -40.8407044966673
x41=43.9822971502571x_{41} = 43.9822971502571
x42=56.5486677646163x_{42} = 56.5486677646163
x43=−65.9734457253857x_{43} = -65.9734457253857
x44=25.1327412287183x_{44} = 25.1327412287183
x45=78.5398163397448x_{45} = 78.5398163397448
x46=−28.2743338823081x_{46} = -28.2743338823081
x47=75.398223686155x_{47} = 75.398223686155
x48=59.6902604182061x_{48} = 59.6902604182061
x49=−34.5575191894877x_{49} = -34.5575191894877
x50=81.6814089933346x_{50} = 81.6814089933346
x51=−47.1238898038469x_{51} = -47.1238898038469
x52=100.530964914873x_{52} = 100.530964914873
x53=−9.42477796076938x_{53} = -9.42477796076938
x54=−75.398223686155x_{54} = -75.398223686155
x55=−72.2566310325652x_{55} = -72.2566310325652
x56=−31.4159265358979x_{56} = -31.4159265358979
x57=28.2743338823081x_{57} = 28.2743338823081
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=84.8230016469244x_{65} = 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 x^3*tan(x).
03tan⁡(0)0^{3} \tan{\left(0 \right)}
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
x3(tan⁡2(x)+1)+3x2tan⁡(x)=0x^{3} \left(\tan^{2}{\left(x \right)} + 1\right) + 3 x^{2} \tan{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=0x_{1} = 0
Signos de extremos en los puntos:
(0, 0)


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=0x_{1} = 0
La función no tiene puntos máximos
Decrece en los intervalos
[0,∞)\left[0, \infty\right)
Crece en los intervalos
(−∞,0]\left(-\infty, 0\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
2x(x2(tan⁡2(x)+1)tan⁡(x)+3x(tan⁡2(x)+1)+3tan⁡(x))=02 x \left(x^{2} \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 3 x \left(\tan^{2}{\left(x \right)} + 1\right) + 3 \tan{\left(x \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=43.9141932134087x_{1} = 43.9141932134087
x2=−34.4709239616025x_{2} = -34.4709239616025
x3=−75.3584559165082x_{3} = -75.3584559165082
x4=−69.0716596975142x_{4} = -69.0716596975142
x5=72.215136170101x_{5} = 72.215136170101
x6=−15.519223683895x_{6} = -15.519223683895
x7=50.2058699843667x_{7} = 50.2058699843667
x8=97.3585778134693x_{8} = 97.3585778134693
x9=−78.5016377050335x_{9} = -78.5016377050335
x10=−97.3585778134693x_{10} = -97.3585778134693
x11=9.1163105629354x_{11} = 9.1163105629354
x12=56.4956657575039x_{12} = 56.4956657575039
x13=47.0603135069479x_{13} = 47.0603135069479
x14=5.8359021346707x_{14} = 5.8359021346707
x15=2.35439147153727x_{15} = 2.35439147153727
x16=−100.501132213838x_{16} = -100.501132213838
x17=18.6917139541728x_{17} = 18.6917139541728
x18=0x_{18} = 0
x19=25.0139345299387x_{19} = 25.0139345299387
x20=15.519223683895x_{20} = 15.519223683895
x21=−31.3207213900674x_{21} = -31.3207213900674
x22=53.350961685601x_{22} = 53.350961685601
x23=40.767379826252x_{23} = 40.767379826252
x24=28.1686246258595x_{24} = 28.1686246258595
x25=−28.1686246258595x_{25} = -28.1686246258595
x26=31.3207213900674x_{26} = 31.3207213900674
x27=−87.9305028781763x_{27} = -87.9305028781763
x28=87.9305028781763x_{28} = 87.9305028781763
x29=75.3584559165082x_{29} = 75.3584559165082
x30=−50.2058699843667x_{30} = -50.2058699843667
x31=−12.3319476111186x_{31} = -12.3319476111186
x32=37.6197013629268x_{32} = 37.6197013629268
x33=−37.6197013629268x_{33} = -37.6197013629268
x34=−84.7876486115311x_{34} = -84.7876486115311
x35=−72.215136170101x_{35} = -72.215136170101
x36=84.7876486115311x_{36} = 84.7876486115311
x37=94.2159593594328x_{37} = 94.2159593594328
x38=78.5016377050335x_{38} = 78.5016377050335
x39=−5.8359021346707x_{39} = -5.8359021346707
x40=62.7841427948537x_{40} = 62.7841427948537
x41=−21.8555619233376x_{41} = -21.8555619233376
x42=−81.6446974235673x_{42} = -81.6446974235673
x43=34.4709239616025x_{43} = 34.4709239616025
x44=12.3319476111186x_{44} = 12.3319476111186
x45=−65.9280041667617x_{45} = -65.9280041667617
x46=−56.4956657575039x_{46} = -56.4956657575039
x47=−25.0139345299387x_{47} = -25.0139345299387
x48=−91.0732702345829x_{48} = -91.0732702345829
x49=−53.350961685601x_{49} = -53.350961685601
x50=−2.35439147153727x_{50} = -2.35439147153727
x51=−47.0603135069479x_{51} = -47.0603135069479
x52=−40.767379826252x_{52} = -40.767379826252
x53=100.501132213838x_{53} = 100.501132213838
x54=−18.6917139541728x_{54} = -18.6917139541728
x55=−43.9141932134087x_{55} = -43.9141932134087
x56=59.6400431817002x_{56} = 59.6400431817002
x57=−59.6400431817002x_{57} = -59.6400431817002
x58=21.8555619233376x_{58} = 21.8555619233376
x59=−9.1163105629354x_{59} = -9.1163105629354
x60=65.9280041667617x_{60} = 65.9280041667617
x61=69.0716596975142x_{61} = 69.0716596975142
x62=91.0732702345829x_{62} = 91.0732702345829
x63=−94.2159593594328x_{63} = -94.2159593594328
x64=81.6446974235673x_{64} = 81.6446974235673
x65=−62.7841427948537x_{65} = -62.7841427948537

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
[100.501132213838,∞)\left[100.501132213838, \infty\right)
Convexa en los intervalos
[−2.35439147153727,2.35439147153727]\left[-2.35439147153727, 2.35439147153727\right]
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→−∞(x3tan⁡(x))y = \lim_{x \to -\infty}\left(x^{3} \tan{\left(x \right)}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(x3tan⁡(x))y = \lim_{x \to \infty}\left(x^{3} \tan{\left(x \right)}\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:
x3tan⁡(x)=x3tan⁡(x)x^{3} \tan{\left(x \right)} = x^{3} \tan{\left(x \right)}
- Sí
x3tan⁡(x)=−x3tan⁡(x)x^{3} \tan{\left(x \right)} = - x^{3} \tan{\left(x \right)}
- No
es decir, función
es
par
Gráfico
Gráfico de la función y = x^3*tan(x)
    © Sr Examen – Калькулятор