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Trazado el gráfico de la función/ |tan(2x+1)|

Gráfico de la función y = |tan(2x+1)|

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = |tan(2*x + 1)|
f(x)=∣tan⁡(2x+1)∣f{\left(x \right)} = \left|{\tan{\left(2 x + 1 \right)}}\right| 
f = Abs(tan(2*x + 1))
Gráfico de la función
02468-8-6-4-2-10100200
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⁡(2x+1)∣=0\left|{\tan{\left(2 x + 1 \right)}}\right| = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−12x_{1} = - \frac{1}{2}
Solución numérica
x1=10.4955742875643x_{1} = 10.4955742875643
x2=−25.6327412287183x_{2} = -25.6327412287183
x3=−22.4911485751286x_{3} = -22.4911485751286
x4=−77.4690200129499x_{4} = -77.4690200129499
x5=−47.6238898038469x_{5} = -47.6238898038469
x6=−69.6150383789755x_{6} = -69.6150383789755
x7=49.7654824574367x_{7} = 49.7654824574367
x8=−0.5x_{8} = -0.5
x9=−55.4778714378214x_{9} = -55.4778714378214
x10=71.7566310325652x_{10} = 71.7566310325652
x11=−30.345130209103x_{11} = -30.345130209103
x12=100.030964914873x_{12} = 100.030964914873
x13=43.4822971502571x_{13} = 43.4822971502571
x14=48.1946861306418x_{14} = 48.1946861306418
x15=−33.4867228626928x_{15} = -33.4867228626928
x16=−27.2035375555132x_{16} = -27.2035375555132
x17=56.0486677646163x_{17} = 56.0486677646163
x18=29.345130209103x_{18} = 29.345130209103
x19=92.1769832808989x_{19} = 92.1769832808989
x20=27.7743338823081x_{20} = 27.7743338823081
x21=78.0398163397448x_{21} = 78.0398163397448
x22=−58.6194640914112x_{22} = -58.6194640914112
x23=−14.6371669411541x_{23} = -14.6371669411541
x24=−93.1769832808989x_{24} = -93.1769832808989
x25=−17.7787595947439x_{25} = -17.7787595947439
x26=2.64159265358979x_{26} = 2.64159265358979
x27=62.3318530717959x_{27} = 62.3318530717959
x28=41.9115008234622x_{28} = 41.9115008234622
x29=96.8893722612836x_{29} = 96.8893722612836
x30=26.2035375555132x_{30} = 26.2035375555132
x31=−36.6283155162826x_{31} = -36.6283155162826
x32=54.4778714378214x_{32} = 54.4778714378214
x33=−99.4601685880785x_{33} = -99.4601685880785
x34=−2.0707963267949x_{34} = -2.0707963267949
x35=−63.3318530717959x_{35} = -63.3318530717959
x36=−74.3274273593601x_{36} = -74.3274273593601
x37=−61.761056745001x_{37} = -61.761056745001
x38=−90.0353906273091x_{38} = -90.0353906273091
x39=−71.1858347057703x_{39} = -71.1858347057703
x40=90.606186954104x_{40} = 90.606186954104
x41=−16.207963267949x_{41} = -16.207963267949
x42=−83.7522053201295x_{42} = -83.7522053201295
x43=93.7477796076938x_{43} = 93.7477796076938
x44=−19.3495559215388x_{44} = -19.3495559215388
x45=63.9026493985908x_{45} = 63.9026493985908
x46=19.9203522483337x_{46} = 19.9203522483337
x47=84.3230016469244x_{47} = 84.3230016469244
x48=−60.1902604182061x_{48} = -60.1902604182061
x49=−41.3407044966673x_{49} = -41.3407044966673
x50=57.6194640914112x_{50} = 57.6194640914112
x51=82.7522053201295x_{51} = 82.7522053201295
x52=35.6283155162826x_{52} = 35.6283155162826
x53=−85.3230016469244x_{53} = -85.3230016469244
x54=−96.3185759344887x_{54} = -96.3185759344887
x55=−75.898223686155x_{55} = -75.898223686155
x56=21.4911485751286x_{56} = 21.4911485751286
x57=23.0619449019235x_{57} = 23.0619449019235
x58=98.4601685880785x_{58} = 98.4601685880785
x59=−91.606186954104x_{59} = -91.606186954104
x60=−5.21238898038469x_{60} = -5.21238898038469
x61=−38.1991118430775x_{61} = -38.1991118430775
x62=−46.053093477052x_{62} = -46.053093477052
x63=87.4645943005142x_{63} = 87.4645943005142
x64=40.3407044966673x_{64} = 40.3407044966673
x65=68.6150383789755x_{65} = 68.6150383789755
x66=5.78318530717959x_{66} = 5.78318530717959
x67=60.761056745001x_{67} = 60.761056745001
x68=16.7787595947439x_{68} = 16.7787595947439
x69=38.7699081698724x_{69} = 38.7699081698724
x70=−82.1814089933346x_{70} = -82.1814089933346
x71=46.6238898038469x_{71} = 46.6238898038469
x72=−44.4822971502571x_{72} = -44.4822971502571
x73=18.3495559215388x_{73} = 18.3495559215388
x74=−66.4734457253857x_{74} = -66.4734457253857
x75=13.6371669411541x_{75} = 13.6371669411541
x76=−3.64159265358979x_{76} = -3.64159265358979
x77=79.6106126665397x_{77} = 79.6106126665397
x78=−80.6106126665397x_{78} = -80.6106126665397
x79=−88.4645943005142x_{79} = -88.4645943005142
x80=65.4734457253857x_{80} = 65.4734457253857
x81=−24.0619449019235x_{81} = -24.0619449019235
x82=−112.026539202438x_{82} = -112.026539202438
x83=4.21238898038469x_{83} = 4.21238898038469
x84=−68.0442420521806x_{84} = -68.0442420521806
x85=−39.7699081698724x_{85} = -39.7699081698724
x86=32.4867228626928x_{86} = 32.4867228626928
x87=−52.3362787842316x_{87} = -52.3362787842316
x88=76.4690200129499x_{88} = 76.4690200129499
x89=24.6327412287183x_{89} = 24.6327412287183
x90=7.35398163397448x_{90} = 7.35398163397448
x91=−8.35398163397448x_{91} = -8.35398163397448
x92=−11.4955742875643x_{92} = -11.4955742875643
x93=70.1858347057703x_{93} = 70.1858347057703
x94=−49.1946861306418x_{94} = -49.1946861306418
x95=85.8937979737193x_{95} = 85.8937979737193
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 Abs(tan(2*x + 1)).
∣tan⁡(0⋅2+1)∣\left|{\tan{\left(0 \cdot 2 + 1 \right)}}\right|
Resultado:
f(0)=tan⁡(1)f{\left(0 \right)} = \tan{\left(1 \right)}
Punto:
(0, tan(1))
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
(2tan⁡2(2x+1)+2)sign⁡(tan⁡(2x+1))=0\left(2 \tan^{2}{\left(2 x + 1 \right)} + 2\right) \operatorname{sign}{\left(\tan{\left(2 x + 1 \right)} \right)} = 0
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga extremos
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⁡(2x+1)∣y = \lim_{x \to -\infty} \left|{\tan{\left(2 x + 1 \right)}}\right|
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞∣tan⁡(2x+1)∣y = \lim_{x \to \infty} \left|{\tan{\left(2 x + 1 \right)}}\right|
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función Abs(tan(2*x + 1)), 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⁡(2x+1)∣x)y = x \lim_{x \to -\infty}\left(\frac{\left|{\tan{\left(2 x + 1 \right)}}\right|}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(∣tan⁡(2x+1)∣x)y = x \lim_{x \to \infty}\left(\frac{\left|{\tan{\left(2 x + 1 \right)}}\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:
∣tan⁡(2x+1)∣=∣tan⁡(2x−1)∣\left|{\tan{\left(2 x + 1 \right)}}\right| = \left|{\tan{\left(2 x - 1 \right)}}\right|
- No
∣tan⁡(2x+1)∣=−∣tan⁡(2x−1)∣\left|{\tan{\left(2 x + 1 \right)}}\right| = - \left|{\tan{\left(2 x - 1 \right)}}\right|
- No
es decir, función
no es
par ni impar
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