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  • Gráfico de la función y =:
  • x-x^3 x-x^3
  • x^4-x^3 x^4-x^3
  • x^4-2x^2 x^4-2x^2
  • x^2-3*x+1 x^2-3*x+1

  • Expresiones idénticas

  • dos tg(x/2)- tres tg(x/3)
  • 2tg(x dividir por 2) menos 3tg(x dividir por 3)
  • dos tg(x dividir por 2) menos tres tg(x dividir por 3)
  • 2tgx/2-3tgx/3
  • 2tg(x dividir por 2)-3tg(x dividir por 3)

  • Expresiones semejantes

  • 2tg(x/2)+3tg(x/3)
Trazado el gráfico de la función/ 2tg(x/2)-3tg(x/3)

Gráfico de la función y = 2tg(x/2)-3tg(x/3)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
            /x\        /x\
f(x) = 2*tan|-| - 3*tan|-|
            \2/        \3/
f(x)=2tan⁡(x2)−3tan⁡(x3)f{\left(x \right)} = 2 \tan{\left(\frac{x}{2} \right)} - 3 \tan{\left(\frac{x}{3} \right)} 
f = 2*tan(x/2) - 3*tan(x/3)
Gráfico de la función
02468-8-6-4-2-1010-500500
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:
2tan⁡(x2)−3tan⁡(x3)=02 \tan{\left(\frac{x}{2} \right)} - 3 \tan{\left(\frac{x}{3} \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−37.6991249834011x_{1} = -37.6991249834011
x2=0x_{2} = 0
x3=113.097391225309x_{3} = 113.097391225309
x4=−18.8494360793216x_{4} = -18.8494360793216
x5=−18.8493439170613x_{5} = -18.8493439170613
x6=37.699193297096x_{6} = 37.699193297096
x7=−75.3983059810054x_{7} = -75.3983059810054
x8=−37.6991561813778x_{8} = -37.6991561813778
x9=−94.2477105736013x_{9} = -94.2477105736013
x10=−56.5485293284907x_{10} = -56.5485293284907
x11=18.8494181849477x_{11} = 18.8494181849477
x12=−56.5489625230931x_{12} = -56.5489625230931
x13=−18.8497664467988x_{13} = -18.8497664467988
x14=75.3983745731581x_{14} = 75.3983745731581
x15=94.2477801894851x_{15} = 94.2477801894851
x16=56.5485972057412x_{16} = 56.5485972057412
x17=−18.8496897937415x_{17} = -18.8496897937415
x18=37.6992158597262x_{18} = 37.6992158597262
x19=56.5489449849439x_{19} = 56.5489449849439
x20=75.3979449177581x_{20} = 75.3979449177581
x21=18.8498527690197x_{21} = 18.8498527690197
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 2*tan(x/2) - 3*tan(x/3).
2tan⁡(02)−3tan⁡(03)2 \tan{\left(\frac{0}{2} \right)} - 3 \tan{\left(\frac{0}{3} \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
tan⁡2(x2)−tan⁡2(x3)=0\tan^{2}{\left(\frac{x}{2} \right)} - \tan^{2}{\left(\frac{x}{3} \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−101.787601976309x_{1} = -101.787601976309
x2=98.0176907920015x_{2} = 98.0176907920015
x3=−94.2477794353855x_{3} = -94.2477794353855
x4=−86.7079572390783x_{4} = -86.7079572390783
x5=37.6991120464662x_{5} = 37.6991120464662
x6=−71.6283125018473x_{6} = -71.6283125018473
x7=94.2477796093522x_{7} = 94.2477796093522
x8=7.5398223686155x_{8} = 7.5398223686155
x9=−56.5486674035903x_{9} = -56.5486674035903
x10=94.2477822090248x_{10} = 94.2477822090248
x11=3.76991118430775x_{11} = 3.76991118430775
x12=−33.9292006587698x_{12} = -33.9292006587698
x13=−52.7787565803085x_{13} = -52.7787565803085
x14=45.238934211693x_{14} = 45.238934211693
x15=−3.76991118430775x_{15} = -3.76991118430775
x16=18.8495568996415x_{16} = 18.8495568996415
x17=−30.159289474462x_{17} = -30.159289474462
x18=−37.6991094748363x_{18} = -37.6991094748363
x19=56.5486675911744x_{19} = 56.5486675911744
x20=−45.238934211693x_{20} = -45.238934211693
x21=−18.8495553109968x_{21} = -18.8495553109968
x22=18.8495555637676x_{22} = 18.8495555637676
x23=−7.5398223686155x_{23} = -7.5398223686155
x24=82.9380460547705x_{24} = 82.9380460547705
x25=−64.0884901332318x_{25} = -64.0884901332318
x26=−49.0088453960008x_{26} = -49.0088453960008
x27=−98.0176907920015x_{27} = -98.0176907920015
x28=60.318578948924x_{28} = 60.318578948924
x29=−26.3893782901543x_{29} = -26.3893782901543
x30=−90.477868423386x_{30} = -90.477868423386
x31=−82.9380460547705x_{31} = -82.9380460547705
x32=52.7787565803085x_{32} = 52.7787565803085
x33=11.3097335529233x_{33} = 11.3097335529233
x34=75.3982227952472x_{34} = 75.3982227952472
x35=56.5486693309499x_{35} = 56.5486693309499
x36=−2.33509546708044⋅10−6x_{36} = -2.33509546708044 \cdot 10^{-6}
x37=26.3893782901543x_{37} = 26.3893782901543
x38=22.6194671058465x_{38} = 22.6194671058465
x39=−75.3982222470693x_{39} = -75.3982222470693
x40=−60.318578948924x_{40} = -60.318578948924
x41=75.3982240854388x_{41} = 75.3982240854388
x42=−79.1681348704628x_{42} = -79.1681348704628
x43=−37.699111877405x_{43} = -37.699111877405
x44=101.787601976309x_{44} = 101.787601976309
x45=−75.3982238894751x_{45} = -75.3982238894751
x46=33.9292006587698x_{46} = 33.9292006587698
x47=−94.2477811543151x_{47} = -94.2477811543151
x48=90.477868423386x_{48} = 90.477868423386
x49=30.159289474462x_{49} = 30.159289474462
x50=−11.3097335529233x_{50} = -11.3097335529233
x51=86.7079572390783x_{51} = 86.7079572390783
x52=64.0884901332318x_{52} = 64.0884901332318
x53=71.6283125018473x_{53} = 71.6283125018473
x54=67.8584013175395x_{54} = 67.8584013175395
x55=−41.4690230273853x_{55} = -41.4690230273853
x56=−67.8584013175395x_{56} = -67.8584013175395
x57=−56.5486687315199x_{57} = -56.5486687315199
x58=−18.8495565256249x_{58} = -18.8495565256249
x59=49.0088453960008x_{59} = 49.0088453960008
x60=41.4690230273853x_{60} = 41.4690230273853
x61=0x_{61} = 0
x62=37.6991104217622x_{62} = 37.6991104217622
Signos de extremos en los puntos:
(-101.7876019763093, -3.63271264002682)

(98.01769079200155, -15.3884176858763)

(-94.24777943538545, -3.55271346704226e-15)

(-86.7079572390783, 3.63271264002679)

(37.69911204646622, 3.55271407584719e-15)

(-71.62831250184729, -15.3884176858763)

(94.24777960935215, 3.55271367859371e-15)

(7.5398223686155035, 3.6327126400268)

(-56.54866740359026, -7.10542518707907e-15)

(94.24778220902485, 8.14845695258637e-19)

(3.7699111843077517, -15.3884176858763)

(-33.929200658769766, -15.3884176858763)

(-52.778756580308524, -15.3884176858763)

(45.23893421169302, 3.6327126400268)

(-3.7699111843077517, 15.3884176858763)

(18.84955689964146, 8.88221830138672e-16)

(-30.159289474462014, 3.6327126400268)

(-37.699109474836284, -1.77574189348054e-15)

(56.548667591174365, -2.38228016415272e-22)

(-45.23893421169302, -3.6327126400268)

(-18.849555310996752, 1.0482032722272e-20)

(18.84955556376761, 1.77635472181788e-15)

(-7.5398223686155035, -3.6327126400268)

(82.93804605477054, 3.6327126400268)

(-64.08849013323179, -3.63271264002682)

(-49.00884539600077, 3.6327126400268)

(-98.01769079200155, 15.3884176858763)

(60.31857894892403, -15.3884176858763)

(-26.389378290154262, -3.6327126400268)

(-90.47786842338604, -15.3884176858763)

(-82.93804605477054, -3.6327126400268)

(52.778756580308524, 15.3884176858763)

(11.309733552923255, -3.6327126400268)

(75.39822279524725, -3.27166475876974e-20)

(56.548669330949885, 7.10560523451993e-15)

(-2.335095467080436e-06, -5.89534931288993e-19)

(26.389378290154262, 3.6327126400268)

(22.61946710584651, -15.3884176858763)

(-75.39822224706931, -3.55257582418834e-15)

(-60.31857894892403, 15.3884176858763)

(75.39822408543877, 3.55271669635538e-15)

(-79.1681348704628, 15.3884176858762)

(-37.69911187740496, 0)

(101.7876019763093, 3.63271264002682)

(-75.39822388947508, -3.55271407584719e-15)

(33.929200658769766, 15.3884176858763)

(-94.24778115431506, -7.10559867001458e-15)

(90.47786842338604, 15.3884176858763)

(30.159289474462014, -3.6327126400268)

(-11.309733552923255, 3.6327126400268)

(86.7079572390783, -3.63271264002679)

(64.08849013323179, 3.63271264002682)

(71.62831250184729, 15.3884176858763)

(67.85840131753953, -3.6327126400268)

(-41.46902302738527, 15.3884176858763)

(-67.85840131753953, 3.6327126400268)

(-56.5486687315199, -3.55275560693139e-15)

(-18.84955652562491, -8.88188584095492e-16)

(49.00884539600077, -3.6327126400268)

(41.46902302738527, -15.3884176858763)

(0, 0)

(37.699110421762164, -1.32984172718925e-19)


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=−86.7079572390783x_{1} = -86.7079572390783
x2=7.5398223686155x_{2} = 7.5398223686155
x3=45.238934211693x_{3} = 45.238934211693
x4=−3.76991118430775x_{4} = -3.76991118430775
x5=−30.159289474462x_{5} = -30.159289474462
x6=82.9380460547705x_{6} = 82.9380460547705
x7=−49.0088453960008x_{7} = -49.0088453960008
x8=−98.0176907920015x_{8} = -98.0176907920015
x9=52.7787565803085x_{9} = 52.7787565803085
x10=26.3893782901543x_{10} = 26.3893782901543
x11=−60.318578948924x_{11} = -60.318578948924
x12=−79.1681348704628x_{12} = -79.1681348704628
x13=101.787601976309x_{13} = 101.787601976309
x14=33.9292006587698x_{14} = 33.9292006587698
x15=90.477868423386x_{15} = 90.477868423386
x16=−11.3097335529233x_{16} = -11.3097335529233
x17=64.0884901332318x_{17} = 64.0884901332318
x18=71.6283125018473x_{18} = 71.6283125018473
x19=−41.4690230273853x_{19} = -41.4690230273853
x20=−67.8584013175395x_{20} = -67.8584013175395
Puntos máximos de la función:
x20=−101.787601976309x_{20} = -101.787601976309
x20=98.0176907920015x_{20} = 98.0176907920015
x20=−71.6283125018473x_{20} = -71.6283125018473
x20=3.76991118430775x_{20} = 3.76991118430775
x20=−33.9292006587698x_{20} = -33.9292006587698
x20=−52.7787565803085x_{20} = -52.7787565803085
x20=−45.238934211693x_{20} = -45.238934211693
x20=−18.8495553109968x_{20} = -18.8495553109968
x20=18.8495555637676x_{20} = 18.8495555637676
x20=−7.5398223686155x_{20} = -7.5398223686155
x20=−64.0884901332318x_{20} = -64.0884901332318
x20=60.318578948924x_{20} = 60.318578948924
x20=−26.3893782901543x_{20} = -26.3893782901543
x20=−90.477868423386x_{20} = -90.477868423386
x20=−82.9380460547705x_{20} = -82.9380460547705
x20=11.3097335529233x_{20} = 11.3097335529233
x20=22.6194671058465x_{20} = 22.6194671058465
x20=30.159289474462x_{20} = 30.159289474462
x20=86.7079572390783x_{20} = 86.7079572390783
x20=67.8584013175395x_{20} = 67.8584013175395
x20=49.0088453960008x_{20} = 49.0088453960008
x20=41.4690230273853x_{20} = 41.4690230273853
Decrece en los intervalos
[101.787601976309,∞)\left[101.787601976309, \infty\right)
Crece en los intervalos
(−∞,−98.0176907920015]\left(-\infty, -98.0176907920015\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
−2(tan⁡2(x3)+1)tan⁡(x3)3+(tan⁡2(x2)+1)tan⁡(x2)=0- \frac{2 \left(\tan^{2}{\left(\frac{x}{3} \right)} + 1\right) \tan{\left(\frac{x}{3} \right)}}{3} + \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(\frac{x}{2} \right)} = 0
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga flexiones
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→−∞(2tan⁡(x2)−3tan⁡(x3))y = \lim_{x \to -\infty}\left(2 \tan{\left(\frac{x}{2} \right)} - 3 \tan{\left(\frac{x}{3} \right)}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(2tan⁡(x2)−3tan⁡(x3))y = \lim_{x \to \infty}\left(2 \tan{\left(\frac{x}{2} \right)} - 3 \tan{\left(\frac{x}{3} \right)}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función 2*tan(x/2) - 3*tan(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→−∞(2tan⁡(x2)−3tan⁡(x3)x)y = x \lim_{x \to -\infty}\left(\frac{2 \tan{\left(\frac{x}{2} \right)} - 3 \tan{\left(\frac{x}{3} \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(2tan⁡(x2)−3tan⁡(x3)x)y = x \lim_{x \to \infty}\left(\frac{2 \tan{\left(\frac{x}{2} \right)} - 3 \tan{\left(\frac{x}{3} \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:
2tan⁡(x2)−3tan⁡(x3)=3tan⁡(x3)−2tan⁡(x2)2 \tan{\left(\frac{x}{2} \right)} - 3 \tan{\left(\frac{x}{3} \right)} = 3 \tan{\left(\frac{x}{3} \right)} - 2 \tan{\left(\frac{x}{2} \right)}
- No
2tan⁡(x2)−3tan⁡(x3)=−3tan⁡(x3)+2tan⁡(x2)2 \tan{\left(\frac{x}{2} \right)} - 3 \tan{\left(\frac{x}{3} \right)} = - 3 \tan{\left(\frac{x}{3} \right)} + 2 \tan{\left(\frac{x}{2} \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор