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

Gráfico de la función y = tan(x-sin(x))/x^3

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       tan(x - sin(x))
f(x) = ---------------
               3      
              x
f(x)=tan⁡(x−sin⁡(x))x3f{\left(x \right)} = \frac{\tan{\left(x - \sin{\left(x \right)} \right)}}{x^{3}} 
f = tan(x - sin(x))/x^3
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:
tan⁡(x−sin⁡(x))x3=0\frac{\tan{\left(x - \sin{\left(x \right)} \right)}}{x^{3}} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−25.1324728822804x_{1} = -25.1324728822804
x2=87.9641655984797x_{2} = 87.9641655984797
x3=81.6814921027211x_{3} = 81.6814921027211
x4=−81.6814265200916x_{4} = -81.6814265200916
x5=−18.8497315431443x_{5} = -18.8497315431443
x6=94.2482424975493x_{6} = 94.2482424975493
x7=−75.3978986635068x_{7} = -75.3978986635068
x8=100.530898830812x_{8} = 100.530898830812
x9=37.698778776622x_{9} = 37.698778776622
x10=−72.2566310325652x_{10} = -72.2566310325652
x11=50.265478406628x_{11} = 50.265478406628
x12=−87.9650396171259x_{12} = -87.9650396171259
x13=−59.6902604182061x_{13} = -59.6902604182061
x14=62.8321017543193x_{14} = 62.8321017543193
x15=6.28231679061329x_{15} = 6.28231679061329
x16=18.8497846863839x_{16} = 18.8497846863839
x17=40.8407044966673x_{17} = 40.8407044966673
x18=87.9655385614538x_{18} = 87.9655385614538
x19=72.2566310325652x_{19} = 72.2566310325652
x20=−47.1238898038469x_{20} = -47.1238898038469
x21=−69.1151740462077x_{21} = -69.1151740462077
x22=−37.6998697855723x_{22} = -37.6998697855723
x23=94.2470703587443x_{23} = 94.2470703587443
x24=87.9646063142811x_{24} = 87.9646063142811
x25=25.1325440344471x_{25} = 25.1325440344471
x26=12.5662940505807x_{26} = 12.5662940505807
x27=−37.6986402500634x_{27} = -37.6986402500634
x28=−81.6809652272225x_{28} = -81.6809652272225
x29=56.5489870792075x_{29} = 56.5489870792075
x30=−25.132870171073x_{30} = -25.132870171073
x31=50.2647170587874x_{31} = 50.2647170587874
x32=59.6902604182061x_{32} = 59.6902604182061
x33=69.1148519976598x_{33} = 69.1148519976598
x34=−6.2834179250097x_{34} = -6.2834179250097
x35=84.8230016469244x_{35} = 84.8230016469244
x36=43.9823032502594x_{36} = 43.9823032502594
x37=75.3983636239366x_{37} = 75.3983636239366
x38=−94.2481021348468x_{38} = -94.2481021348468
x39=−53.4070751110265x_{39} = -53.4070751110265
x40=94.2477801894633x_{40} = 94.2477801894633
x41=31.4156680612568x_{41} = 31.4156680612568
x42=−43.9814607813464x_{42} = -43.9814607813464
x43=−21.9911485751286x_{43} = -21.9911485751286
x44=43.9818456517709x_{44} = 43.9818456517709
x45=69.1152316173255x_{45} = 69.1152316173255
x46=−34.5575191894877x_{46} = -34.5575191894877
x47=−3.14159265358979x_{47} = -3.14159265358979
x48=53.4070751110265x_{48} = 53.4070751110265
x49=−43.9827197521296x_{49} = -43.9827197521296
x50=−87.9638293276092x_{50} = -87.9638293276092
x51=−69.114787001397x_{51} = -69.114787001397
x52=−87.9646059786093x_{52} = -87.9646059786093
x53=−65.9734457253857x_{53} = -65.9734457253857
x54=−62.8320415397184x_{54} = -62.8320415397184
x55=−62.8316615858525x_{55} = -62.8316615858525
x56=6.28317660175695x_{56} = 6.28317660175695
x57=−100.530835837348x_{57} = -100.530835837348
x58=37.6991904940296x_{58} = 37.6991904940296
x59=−78.5398163397448x_{59} = -78.5398163397448
x60=−50.2654096337633x_{60} = -50.2654096337633
x61=28.2743338823081x_{61} = 28.2743338823081
x62=50.2659232646623x_{62} = 50.2659232646623
x63=−37.6991249458949x_{63} = -37.6991249458949
x64=−81.6822506349978x_{64} = -81.6822506349978
x65=−91.106186954104x_{65} = -91.106186954104
x66=43.9831424136765x_{66} = 43.9831424136765
x67=81.6810918891131x_{67} = 81.6810918891131
x68=−9.42477796076938x_{68} = -9.42477796076938
x69=65.9734457253857x_{69} = 65.9734457253857
x70=−15.707963267949x_{70} = -15.707963267949
x71=97.3893722612836x_{71} = 97.3893722612836
x72=12.5666463634001x_{72} = 12.5666463634001
x73=−43.9823032307113x_{73} = -43.9823032307113
x74=−56.5485340216575x_{74} = -56.5485340216575
x75=−12.5665850466909x_{75} = -12.5665850466909
x76=15.707963267949x_{76} = 15.707963267949
x77=9.42477796076938x_{77} = 9.42477796076938
x78=−75.3983037256206x_{78} = -75.3983037256206
x79=18.8494179092913x_{79} = 18.8494179092913
x80=−12.5662238749128x_{80} = -12.5662238749128
x81=62.8317238048662x_{81} = 62.8317238048662
x82=−50.2657931848479x_{82} = -50.2657931848479
x83=−31.4155814144572x_{83} = -31.4155814144572
x84=−6.28310204194151x_{84} = -6.28310204194151
x85=21.9911485751286x_{85} = 21.9911485751286
x86=34.5575191894877x_{86} = 34.5575191894877
x87=25.1329242034183x_{87} = 25.1329242034183
x88=−97.3893722612836x_{88} = -97.3893722612836
x89=−18.8493494721619x_{89} = -18.8493494721619
x90=−94.2477111785437x_{90} = -94.2477111785437
x91=31.4160604351946x_{91} = 31.4160604351946
x92=−31.4160021310103x_{92} = -31.4160021310103
x93=6.28350330747282x_{93} = 6.28350330747282
x94=−28.2743338823081x_{94} = -28.2743338823081
x95=78.5398163397448x_{95} = 78.5398163397448
x96=56.5485975957041x_{96} = 56.5485975957041
x97=−56.5489107656825x_{97} = -56.5489107656825
x98=75.3979781349956x_{98} = 75.3979781349956
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^3.
tan⁡(−sin⁡(0))03\frac{\tan{\left(- \sin{\left(0 \right)} \right)}}{0^{3}}
Resultado:
f(0)=NaNf{\left(0 \right)} = \text{NaN}
- no hay soluciones de la ecuación
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→−∞(tan⁡(x−sin⁡(x))x3)y = \lim_{x \to -\infty}\left(\frac{\tan{\left(x - \sin{\left(x \right)} \right)}}{x^{3}}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(tan⁡(x−sin⁡(x))x3)y = \lim_{x \to \infty}\left(\frac{\tan{\left(x - \sin{\left(x \right)} \right)}}{x^{3}}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función tan(x - sin(x))/x^3, 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→−∞(tan⁡(x−sin⁡(x))xx3)y = x \lim_{x \to -\infty}\left(\frac{\tan{\left(x - \sin{\left(x \right)} \right)}}{x x^{3}}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(tan⁡(x−sin⁡(x))xx3)y = x \lim_{x \to \infty}\left(\frac{\tan{\left(x - \sin{\left(x \right)} \right)}}{x x^{3}}\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:
tan⁡(x−sin⁡(x))x3=tan⁡(x−sin⁡(x))x3\frac{\tan{\left(x - \sin{\left(x \right)} \right)}}{x^{3}} = \frac{\tan{\left(x - \sin{\left(x \right)} \right)}}{x^{3}}
- No
tan⁡(x−sin⁡(x))x3=−tan⁡(x−sin⁡(x))x3\frac{\tan{\left(x - \sin{\left(x \right)} \right)}}{x^{3}} = - \frac{\tan{\left(x - \sin{\left(x \right)} \right)}}{x^{3}}
- No
es decir, función
no es
par ni impar
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