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- Gráfico de la función implícita
- Derivadas paso a paso
- Integrales paso a paso
- Gráfico de la función paramétrica
- Gráfico en coordenadas polares
- Superficie especificada paramétricamente
- Superficie dada por la ecuación
- Curva en el espacio especificada paramétricamente
- Superficie de una figura limitada con líneas
- Puntos de cruce de las funciones
-
¿Cómo usar?
- Gráfico de la función y =:
-
(x+4)/e^(x+4)
-
x^3/3-4*x
-
x^3-6*x^2+9*x+1
-
y=x+2
-
Expresiones idénticas
- tgx+ctg(x/ dos)+tg(2x/ tres)
- tgx más ctg(x dividir por 2) más tg(2x dividir por 3)
- tgx más ctg(x dividir por dos) más tg(2x dividir por tres)
- tgx+ctgx/2+tg2x/3
- tgx+ctg(x dividir por 2)+tg(2x dividir por 3)
-
Expresiones semejantes
- tgx+ctg(x/2)-tg(2x/3)
- tgx-ctg(x/2)+tg(2x/3)
-
Expresiones con funciones
- tgx
- tgx+cosx/sin^2x-5x/2
- tgx|cosx|
- ctg
- ctg(0.02x)
- ctg(pix)
- ctg(sqrt(x))
- ctg3x/5
- ctg(3x/5)
- tg
- tg((1-x^2)/(4-x^2))
- tg(x/2)
- tg(sin(abs(x))+0.5)
- tg2x-ctg3x+1
- tg(0.3x+0.4)
Gráfico de la función y = tgx+ctg(x/2)+tg(2x/3)
Solución
Ha introducido
[src]
/x\ /2*x\
f(x) = tan(x) + cot|-| + tan|---|
\2/ \ 3 /
$$f{\left(x \right)} = \left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)}$$
f = tan(x) + cot(x/2) + tan((2*x)/3)
Gráfico de la función
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:
$$\left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = 49.0991017443071$$
$$x_{2} = -79.3215426106732$$
$$x_{3} = -39.5429310220932$$
$$x_{4} = -33.7757929185592$$
$$x_{5} = 67.9486576658459$$
$$x_{6} = 98.1710985322121$$
$$x_{7} = 33.7757929185592$$
$$x_{8} = -7.44956602030916$$
$$x_{9} = -96.0915987867095$$
$$x_{10} = 47.1238898038469$$
$$x_{11} = 92.4039604286781$$
$$x_{12} = -3.92331892451831$$
$$x_{13} = 82.8477897064642$$
$$x_{14} = 65.9734457253857$$
$$x_{15} = 26.2991219418479$$
$$x_{16} = -60.4719866891346$$
$$x_{17} = -45.1486778633867$$
$$x_{18} = 1.84381917901569$$
$$x_{19} = -9.42477796076938$$
$$x_{20} = -41.6224307675958$$
$$x_{21} = -67.9486576658459$$
$$x_{22} = 11.3999899012296$$
$$x_{23} = -35.8552926640618$$
$$x_{24} = 52.625348840098$$
$$x_{25} = 58.392486943632$$
$$x_{26} = -14.9262369970204$$
$$x_{27} = 22.7728748460571$$
$$x_{28} = 518.362787842316$$
$$x_{29} = -47.1238898038469$$
$$x_{30} = 63.9982337849254$$
$$x_{31} = 28.2743338823081$$
$$x_{32} = -90.3244606831755$$
$$x_{33} = 79.3215426106733$$
$$x_{34} = 71.4749047616367$$
$$x_{35} = -26.2991219418479$$
$$x_{36} = -30.2495458227684$$
$$x_{37} = -65.9734457253857$$
$$x_{38} = -52.625348840098$$
$$x_{39} = -22.7728748460571$$
$$x_{40} = 96.0915987867095$$
$$x_{41} = -98.1710985322121$$
$$x_{42} = 103.672557568463$$
$$x_{43} = -63.9982337849254$$
$$x_{44} = -79.3215426106733$$
$$x_{45} = -71.4749047616367$$
$$x_{46} = 3.92331892451831$$
$$x_{47} = 84.8230016469244$$
$$x_{48} = -1.84381917901569$$
$$x_{49} = 60.4719866891346$$
$$x_{50} = -128.023572526253$$
$$x_{51} = -86.7982135873846$$
$$x_{52} = 9.42477796076938$$
$$x_{53} = -84.8230016469244$$
$$x_{54} = -11.3999899012296$$
$$x_{55} = -20.6933751005544$$
$$x_{56} = 41.6224307675958$$
$$x_{57} = 90.3244606831755$$
$$x_{58} = -28.2743338823081$$
$$x_{59} = 30.2495458227684$$
$$x_{60} = 14.9262369970204$$
$$x_{61} = 54.7048485856006$$
o sea hay que resolver la ecuación:
$$\left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = 49.0991017443071$$
$$x_{2} = -79.3215426106732$$
$$x_{3} = -39.5429310220932$$
$$x_{4} = -33.7757929185592$$
$$x_{5} = 67.9486576658459$$
$$x_{6} = 98.1710985322121$$
$$x_{7} = 33.7757929185592$$
$$x_{8} = -7.44956602030916$$
$$x_{9} = -96.0915987867095$$
$$x_{10} = 47.1238898038469$$
$$x_{11} = 92.4039604286781$$
$$x_{12} = -3.92331892451831$$
$$x_{13} = 82.8477897064642$$
$$x_{14} = 65.9734457253857$$
$$x_{15} = 26.2991219418479$$
$$x_{16} = -60.4719866891346$$
$$x_{17} = -45.1486778633867$$
$$x_{18} = 1.84381917901569$$
$$x_{19} = -9.42477796076938$$
$$x_{20} = -41.6224307675958$$
$$x_{21} = -67.9486576658459$$
$$x_{22} = 11.3999899012296$$
$$x_{23} = -35.8552926640618$$
$$x_{24} = 52.625348840098$$
$$x_{25} = 58.392486943632$$
$$x_{26} = -14.9262369970204$$
$$x_{27} = 22.7728748460571$$
$$x_{28} = 518.362787842316$$
$$x_{29} = -47.1238898038469$$
$$x_{30} = 63.9982337849254$$
$$x_{31} = 28.2743338823081$$
$$x_{32} = -90.3244606831755$$
$$x_{33} = 79.3215426106733$$
$$x_{34} = 71.4749047616367$$
$$x_{35} = -26.2991219418479$$
$$x_{36} = -30.2495458227684$$
$$x_{37} = -65.9734457253857$$
$$x_{38} = -52.625348840098$$
$$x_{39} = -22.7728748460571$$
$$x_{40} = 96.0915987867095$$
$$x_{41} = -98.1710985322121$$
$$x_{42} = 103.672557568463$$
$$x_{43} = -63.9982337849254$$
$$x_{44} = -79.3215426106733$$
$$x_{45} = -71.4749047616367$$
$$x_{46} = 3.92331892451831$$
$$x_{47} = 84.8230016469244$$
$$x_{48} = -1.84381917901569$$
$$x_{49} = 60.4719866891346$$
$$x_{50} = -128.023572526253$$
$$x_{51} = -86.7982135873846$$
$$x_{52} = 9.42477796076938$$
$$x_{53} = -84.8230016469244$$
$$x_{54} = -11.3999899012296$$
$$x_{55} = -20.6933751005544$$
$$x_{56} = 41.6224307675958$$
$$x_{57} = 90.3244606831755$$
$$x_{58} = -28.2743338823081$$
$$x_{59} = 30.2495458227684$$
$$x_{60} = 14.9262369970204$$
$$x_{61} = 54.7048485856006$$
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
$$\frac{d}{d x} f{\left(x \right)} = $$
primera derivada
$$\tan^{2}{\left(x \right)} + \frac{2 \tan^{2}{\left(\frac{2 x}{3} \right)}}{3} - \frac{\cot^{2}{\left(\frac{x}{2} \right)}}{2} + \frac{7}{6} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 88.7964096300637$$
$$x_{2} = 76.224965172799$$
$$x_{3} = -55.7219262779724$$
$$x_{4} = -113.924077015876$$
$$x_{5} = -13.3981859439086$$
$$x_{6} = -24.3009258991689$$
$$x_{7} = -88.7964096300637$$
$$x_{8} = 1375.19084078569$$
$$x_{9} = 19.6762974081827$$
$$x_{10} = -5.45136997763013$$
$$x_{11} = -25.5428083266919$$
$$x_{12} = -201.893745159296$$
$$x_{13} = -57.3754092512602$$
$$x_{14} = -80.8495936637852$$
$$x_{15} = 5.45136997763013$$
$$x_{16} = -38.5258533297214$$
$$x_{17} = -82.0914760913082$$
$$x_{18} = 63.2419201697694$$
$$x_{19} = 82.0914760913082$$
$$x_{20} = 95.0745210943377$$
$$x_{21} = 32.2477418654474$$
$$x_{22} = 62.0000377422464$$
$$x_{23} = -69.9468537085249$$
$$x_{24} = -32.2477418654474$$
$$x_{25} = -95.0745210943377$$
$$x_{26} = 93.4210381210499$$
$$x_{27} = -74.5714821995111$$
$$x_{28} = 74.5714821995111$$
$$x_{29} = -19.6762974081827$$
$$x_{30} = -36.8723703564336$$
$$x_{31} = -51.0972977869861$$
$$x_{32} = 49.8554153594631$$
$$x_{33} = 24.3009258991689$$
$$x_{34} = -49.8554153594631$$
$$x_{35} = 36.8723703564336$$
$$x_{36} = -62.0000377422464$$
$$x_{37} = -99.6991495853239$$
$$x_{38} = -87.5545272025406$$
$$x_{39} = 18.0228144348948$$
$$x_{40} = -93.4210381210499$$
$$x_{41} = 13.3981859439086$$
$$x_{42} = -76.224965172799$$
$$x_{43} = 44.3923642482307$$
$$x_{44} = -68.7049712810019$$
$$x_{45} = 12.1563035163856$$
$$x_{46} = -43.1504818207076$$
$$x_{47} = 99.6991495853239$$
$$x_{48} = -12.1563035163856$$
$$x_{49} = 126.495521473141$$
$$x_{50} = 38.5258533297214$$
$$x_{51} = 80.8495936637852$$
$$x_{52} = -18.0228144348948$$
$$x_{53} = 55.7219262779724$$
$$x_{54} = 69.9468537085249$$
$$x_{55} = -0.826741486643925$$
$$x_{56} = 51.0972977869861$$
Signos de extremos en los puntos:
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:
$$x_{1} = 88.7964096300637$$
$$x_{2} = 76.224965172799$$
$$x_{3} = -55.7219262779724$$
$$x_{4} = -24.3009258991689$$
$$x_{5} = 19.6762974081827$$
$$x_{6} = -5.45136997763013$$
$$x_{7} = -80.8495936637852$$
$$x_{8} = 63.2419201697694$$
$$x_{9} = 82.0914760913082$$
$$x_{10} = 95.0745210943377$$
$$x_{11} = 32.2477418654474$$
$$x_{12} = -74.5714821995111$$
$$x_{13} = -36.8723703564336$$
$$x_{14} = -49.8554153594631$$
$$x_{15} = -62.0000377422464$$
$$x_{16} = -99.6991495853239$$
$$x_{17} = -87.5545272025406$$
$$x_{18} = -93.4210381210499$$
$$x_{19} = 13.3981859439086$$
$$x_{20} = 44.3923642482307$$
$$x_{21} = -68.7049712810019$$
$$x_{22} = -43.1504818207076$$
$$x_{23} = -12.1563035163856$$
$$x_{24} = 126.495521473141$$
$$x_{25} = 38.5258533297214$$
$$x_{26} = -18.0228144348948$$
$$x_{27} = 69.9468537085249$$
$$x_{28} = 51.0972977869861$$
Puntos máximos de la función:
$$x_{28} = -113.924077015876$$
$$x_{28} = -13.3981859439086$$
$$x_{28} = -88.7964096300637$$
$$x_{28} = 1375.19084078569$$
$$x_{28} = -25.5428083266919$$
$$x_{28} = -201.893745159296$$
$$x_{28} = -57.3754092512602$$
$$x_{28} = 5.45136997763013$$
$$x_{28} = -38.5258533297214$$
$$x_{28} = -82.0914760913082$$
$$x_{28} = 62.0000377422464$$
$$x_{28} = -69.9468537085249$$
$$x_{28} = -32.2477418654474$$
$$x_{28} = -95.0745210943377$$
$$x_{28} = 93.4210381210499$$
$$x_{28} = 74.5714821995111$$
$$x_{28} = -19.6762974081827$$
$$x_{28} = -51.0972977869861$$
$$x_{28} = 49.8554153594631$$
$$x_{28} = 24.3009258991689$$
$$x_{28} = 36.8723703564336$$
$$x_{28} = 18.0228144348948$$
$$x_{28} = -76.224965172799$$
$$x_{28} = 12.1563035163856$$
$$x_{28} = 99.6991495853239$$
$$x_{28} = 80.8495936637852$$
$$x_{28} = 55.7219262779724$$
$$x_{28} = -0.826741486643925$$
Decrece en los intervalos
$$\left[126.495521473141, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -99.6991495853239\right]$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
$$\frac{d}{d x} f{\left(x \right)} = $$
primera derivada
$$\tan^{2}{\left(x \right)} + \frac{2 \tan^{2}{\left(\frac{2 x}{3} \right)}}{3} - \frac{\cot^{2}{\left(\frac{x}{2} \right)}}{2} + \frac{7}{6} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 88.7964096300637$$
$$x_{2} = 76.224965172799$$
$$x_{3} = -55.7219262779724$$
$$x_{4} = -113.924077015876$$
$$x_{5} = -13.3981859439086$$
$$x_{6} = -24.3009258991689$$
$$x_{7} = -88.7964096300637$$
$$x_{8} = 1375.19084078569$$
$$x_{9} = 19.6762974081827$$
$$x_{10} = -5.45136997763013$$
$$x_{11} = -25.5428083266919$$
$$x_{12} = -201.893745159296$$
$$x_{13} = -57.3754092512602$$
$$x_{14} = -80.8495936637852$$
$$x_{15} = 5.45136997763013$$
$$x_{16} = -38.5258533297214$$
$$x_{17} = -82.0914760913082$$
$$x_{18} = 63.2419201697694$$
$$x_{19} = 82.0914760913082$$
$$x_{20} = 95.0745210943377$$
$$x_{21} = 32.2477418654474$$
$$x_{22} = 62.0000377422464$$
$$x_{23} = -69.9468537085249$$
$$x_{24} = -32.2477418654474$$
$$x_{25} = -95.0745210943377$$
$$x_{26} = 93.4210381210499$$
$$x_{27} = -74.5714821995111$$
$$x_{28} = 74.5714821995111$$
$$x_{29} = -19.6762974081827$$
$$x_{30} = -36.8723703564336$$
$$x_{31} = -51.0972977869861$$
$$x_{32} = 49.8554153594631$$
$$x_{33} = 24.3009258991689$$
$$x_{34} = -49.8554153594631$$
$$x_{35} = 36.8723703564336$$
$$x_{36} = -62.0000377422464$$
$$x_{37} = -99.6991495853239$$
$$x_{38} = -87.5545272025406$$
$$x_{39} = 18.0228144348948$$
$$x_{40} = -93.4210381210499$$
$$x_{41} = 13.3981859439086$$
$$x_{42} = -76.224965172799$$
$$x_{43} = 44.3923642482307$$
$$x_{44} = -68.7049712810019$$
$$x_{45} = 12.1563035163856$$
$$x_{46} = -43.1504818207076$$
$$x_{47} = 99.6991495853239$$
$$x_{48} = -12.1563035163856$$
$$x_{49} = 126.495521473141$$
$$x_{50} = 38.5258533297214$$
$$x_{51} = 80.8495936637852$$
$$x_{52} = -18.0228144348948$$
$$x_{53} = 55.7219262779724$$
$$x_{54} = 69.9468537085249$$
$$x_{55} = -0.826741486643925$$
$$x_{56} = 51.0972977869861$$
Signos de extremos en los puntos:
(88.79640963006366, 2.82474292020604)
(76.22496517279896, 3.98075765927311)
(-55.72192627797235, 3.98075765927311)
(-113.92407701587648, -3.9807576592731)
(-13.39818594390863, -2.82474292020604)
(-24.300925899168888, 2.82474292020604)
(-88.79640963006366, -2.82474292020604)
(1375.1908407856856, -3.98075765927311)
(19.676297408182684, 3.98075765927311)
(-5.451369977630129, 2.82474292020604)
(-25.54280832669192, -9.15613936847922)
(-201.89374515929623, -2.82474292020601)
(-57.3754092512602, -3.98075765927311)
(-80.84959366378517, 2.82474292020604)
(5.451369977630129, -2.82474292020604)
(-38.52585332972144, -3.98075765927311)
(-82.0914760913082, -9.15613936847922)
(63.241920169769436, 9.15613936847922)
(82.0914760913082, 9.15613936847922)
(95.07452109433773, 3.98075765927311)
(32.24774186544739, 2.82474292020604)
(62.000037742246406, -2.82474292020604)
(-69.94685370852491, -2.82474292020604)
(-32.24774186544739, -2.82474292020604)
(-95.07452109433773, -3.98075765927311)
(93.42103812104988, -3.98075765927311)
(-74.57148219951111, 3.98075765927312)
(74.57148219951111, -3.98075765927312)
(-19.676297408182684, -3.98075765927311)
(-36.87237035643359, 3.98075765927311)
(-51.09729778698615, -2.82474292020604)
(49.85541535946312, -9.1561393684793)
(24.300925899168888, -2.82474292020604)
(-49.85541535946312, 9.1561393684793)
(36.87237035643359, -3.98075765927311)
(-62.000037742246406, 2.82474292020604)
(-99.69914958532392, 2.82474292020604)
(-87.55452720254064, 9.1561393684793)
(18.022814434894833, -3.98075765927311)
(-93.42103812104988, 3.98075765927311)
(13.39818594390863, 2.82474292020604)
(-76.22496517279896, -3.98075765927311)
(44.39236424823068, 9.15613936847922)
(-68.70497128100187, 9.15613936847934)
(12.1563035163856, -9.15613936847927)
(-43.15048182070765, 2.82474292020604)
(99.69914958532392, -2.82474292020604)
(-12.1563035163856, 9.15613936847927)
(126.49552147314118, 2.82474292020603)
(38.52585332972144, 3.98075765927311)
(80.84959366378517, -2.82474292020604)
(-18.022814434894833, 3.98075765927311)
(55.72192627797235, -3.98075765927311)
(69.94685370852491, 2.82474292020604)
(-0.826741486643925, -3.98075765927311)
(51.09729778698615, 2.82474292020604)
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:
$$x_{1} = 88.7964096300637$$
$$x_{2} = 76.224965172799$$
$$x_{3} = -55.7219262779724$$
$$x_{4} = -24.3009258991689$$
$$x_{5} = 19.6762974081827$$
$$x_{6} = -5.45136997763013$$
$$x_{7} = -80.8495936637852$$
$$x_{8} = 63.2419201697694$$
$$x_{9} = 82.0914760913082$$
$$x_{10} = 95.0745210943377$$
$$x_{11} = 32.2477418654474$$
$$x_{12} = -74.5714821995111$$
$$x_{13} = -36.8723703564336$$
$$x_{14} = -49.8554153594631$$
$$x_{15} = -62.0000377422464$$
$$x_{16} = -99.6991495853239$$
$$x_{17} = -87.5545272025406$$
$$x_{18} = -93.4210381210499$$
$$x_{19} = 13.3981859439086$$
$$x_{20} = 44.3923642482307$$
$$x_{21} = -68.7049712810019$$
$$x_{22} = -43.1504818207076$$
$$x_{23} = -12.1563035163856$$
$$x_{24} = 126.495521473141$$
$$x_{25} = 38.5258533297214$$
$$x_{26} = -18.0228144348948$$
$$x_{27} = 69.9468537085249$$
$$x_{28} = 51.0972977869861$$
Puntos máximos de la función:
$$x_{28} = -113.924077015876$$
$$x_{28} = -13.3981859439086$$
$$x_{28} = -88.7964096300637$$
$$x_{28} = 1375.19084078569$$
$$x_{28} = -25.5428083266919$$
$$x_{28} = -201.893745159296$$
$$x_{28} = -57.3754092512602$$
$$x_{28} = 5.45136997763013$$
$$x_{28} = -38.5258533297214$$
$$x_{28} = -82.0914760913082$$
$$x_{28} = 62.0000377422464$$
$$x_{28} = -69.9468537085249$$
$$x_{28} = -32.2477418654474$$
$$x_{28} = -95.0745210943377$$
$$x_{28} = 93.4210381210499$$
$$x_{28} = 74.5714821995111$$
$$x_{28} = -19.6762974081827$$
$$x_{28} = -51.0972977869861$$
$$x_{28} = 49.8554153594631$$
$$x_{28} = 24.3009258991689$$
$$x_{28} = 36.8723703564336$$
$$x_{28} = 18.0228144348948$$
$$x_{28} = -76.224965172799$$
$$x_{28} = 12.1563035163856$$
$$x_{28} = 99.6991495853239$$
$$x_{28} = 80.8495936637852$$
$$x_{28} = 55.7219262779724$$
$$x_{28} = -0.826741486643925$$
Decrece en los intervalos
$$\left[126.495521473141, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -99.6991495853239\right]$$
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \lim_{x \to -\infty}\left(\left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)}\right)$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \lim_{x \to \infty}\left(\left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \lim_{x \to -\infty}\left(\left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \lim_{x \to \infty}\left(\left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)}\right)$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función tan(x) + cot(x/2) + tan((2*x)/3), dividida por x con x->+oo y x ->-oo
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = x \lim_{x \to -\infty}\left(\frac{\left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)}}{x}\right)$$
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = x \lim_{x \to \infty}\left(\frac{\left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)}}{x}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = x \lim_{x \to -\infty}\left(\frac{\left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)}}{x}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = x \lim_{x \to \infty}\left(\frac{\left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)}}{x}\right)$$
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:
$$\left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)} = - \tan{\left(\frac{2 x}{3} \right)} - \tan{\left(x \right)} - \cot{\left(\frac{x}{2} \right)}$$
- No
$$\left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)} = \tan{\left(\frac{2 x}{3} \right)} + \tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$\left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)} = - \tan{\left(\frac{2 x}{3} \right)} - \tan{\left(x \right)} - \cot{\left(\frac{x}{2} \right)}$$
- No
$$\left(\tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}\right) + \tan{\left(\frac{2 x}{3} \right)} = \tan{\left(\frac{2 x}{3} \right)} + \tan{\left(x \right)} + \cot{\left(\frac{x}{2} \right)}$$
- No
es decir, función
no es
par ni impar