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Trazado el gráfico de la función/ tan2x+sin2x

Gráfico de la función y = tan2x+sin2x

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = tan(2*x) + sin(2*x)
f(x)=sin⁡(2x)+tan⁡(2x)f{\left(x \right)} = \sin{\left(2 x \right)} + \tan{\left(2 x \right)} 
f = sin(2*x) + tan(2*x)
Gráfico de la función
02468-8-6-4-2-1010-200200
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⁡(2x)+tan⁡(2x)=0\sin{\left(2 x \right)} + \tan{\left(2 x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=−π2x_{2} = - \frac{\pi}{2}
x3=π2x_{3} = \frac{\pi}{2}
x4=πx_{4} = \pi
Solución numérica
x1=−72.2566310325652x_{1} = -72.2566310325652
x2=−59.6902604182061x_{2} = -59.6902604182061
x3=−14.1371241329818x_{3} = -14.1371241329818
x4=−6.28318530717959x_{4} = -6.28318530717959
x5=12.5663706143592x_{5} = 12.5663706143592
x6=56.5486677646163x_{6} = 56.5486677646163
x7=40.8407044966673x_{7} = 40.8407044966673
x8=58.1194602352783x_{8} = 58.1194602352783
x9=72.2566310325652x_{9} = 72.2566310325652
x10=37.6991118430775x_{10} = 37.6991118430775
x11=100.530964914873x_{11} = 100.530964914873
x12=−47.1238898038469x_{12} = -47.1238898038469
x13=94.2477796076938x_{13} = 94.2477796076938
x14=−12.5663706143592x_{14} = -12.5663706143592
x15=−45.5531430049699x_{15} = -45.5531430049699
x16=73.8274802320386x_{16} = 73.8274802320386
x17=−87.9645943005142x_{17} = -87.9645943005142
x18=−31.4159265358979x_{18} = -31.4159265358979
x19=59.6902604182061x_{19} = 59.6902604182061
x20=−36.1282752374094x_{20} = -36.1282752374094
x21=84.8230016469244x_{21} = 84.8230016469244
x22=0x_{22} = 0
x23=64.4026109201766x_{23} = 64.4026109201766
x24=50.2654824574367x_{24} = 50.2654824574367
x25=−53.4070751110265x_{25} = -53.4070751110265
x26=−67.5442938266249x_{26} = -67.5442938266249
x27=51.836329140843x_{27} = 51.836329140843
x28=−1.57084140427182x_{28} = -1.57084140427182
x29=−21.9911485751286x_{29} = -21.9911485751286
x30=20.4203093788003x_{30} = 20.4203093788003
x31=−29.8451149451132x_{31} = -29.8451149451132
x32=−23.5619921981979x_{32} = -23.5619921981979
x33=−34.5575191894877x_{33} = -34.5575191894877
x34=42.4114601529741x_{34} = 42.4114601529741
x35=75.398223686155x_{35} = 75.398223686155
x36=14.1371750231145x_{36} = 14.1371750231145
x37=80.1106033207563x_{37} = 80.1106033207563
x38=87.9645943005142x_{38} = 87.9645943005142
x39=−80.1105774908369x_{39} = -80.1105774908369
x40=53.4070751110265x_{40} = 53.4070751110265
x41=−3.14159265358979x_{41} = -3.14159265358979
x42=−69.1150383789755x_{42} = -69.1150383789755
x43=86.3937616823144x_{43} = 86.3937616823144
x44=−25.1327412287183x_{44} = -25.1327412287183
x45=−75.398223686155x_{45} = -75.398223686155
x46=81.6814089933346x_{46} = 81.6814089933346
x47=−43.9822971502571x_{47} = -43.9822971502571
x48=−37.6991118430775x_{48} = -37.6991118430775
x49=−65.9734457253857x_{49} = -65.9734457253857
x50=18.8495559215388x_{50} = 18.8495559215388
x51=−89.5354446652553x_{51} = -89.5354446652553
x52=6.28318530717959x_{52} = 6.28318530717959
x53=−78.5398163397448x_{53} = -78.5398163397448
x54=28.2743338823081x_{54} = 28.2743338823081
x55=7.85402696220054x_{55} = 7.85402696220054
x56=−95.8185601488805x_{56} = -95.8185601488805
x57=−94.2477796076938x_{57} = -94.2477796076938
x58=−91.106186954104x_{58} = -91.106186954104
x59=95.8186313295079x_{59} = 95.8186313295079
x60=43.9822971502571x_{60} = 43.9822971502571
x61=62.8318530717959x_{61} = 62.8318530717959
x62=36.1283178447041x_{62} = 36.1283178447041
x63=−9.42477796076938x_{63} = -9.42477796076938
x64=65.9734457253857x_{64} = 65.9734457253857
x65=31.4159265358979x_{65} = 31.4159265358979
x66=−100.530964914873x_{66} = -100.530964914873
x67=−15.707963267949x_{67} = -15.707963267949
x68=97.3893722612836x_{68} = 97.3893722612836
x69=29.8451780521704x_{69} = 29.8451780521704
x70=−50.2654824574367x_{70} = -50.2654824574367
x71=15.707963267949x_{71} = 15.707963267949
x72=9.42477796076938x_{72} = 9.42477796076938
x73=−56.5486677646163x_{73} = -56.5486677646163
x74=21.9911485751286x_{74} = 21.9911485751286
x75=34.5575191894877x_{75} = 34.5575191894877
x76=−97.3893722612836x_{76} = -97.3893722612836
x77=−51.8362622743528x_{77} = -51.8362622743528
x78=−28.2743338823081x_{78} = -28.2743338823081
x79=78.5398163397448x_{79} = 78.5398163397448
x80=−73.8274107880694x_{80} = -73.8274107880694
x81=−58.1194263552532x_{81} = -58.1194263552532
x82=−81.6814089933346x_{82} = -81.6814089933346
x83=−7.85396913241537x_{83} = -7.85396913241537
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(2*x) + sin(2*x).
tan⁡(0⋅2)+sin⁡(0⋅2)\tan{\left(0 \cdot 2 \right)} + \sin{\left(0 \cdot 2 \right)}
Resultado:
f(0)=0f{\left(0 \right)} = 0
Punto:
(0, 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⁡(2x)+tan⁡(2x))y = \lim_{x \to -\infty}\left(\sin{\left(2 x \right)} + \tan{\left(2 x \right)}\right)
True

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

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