Sr Examen
Otras calculadoras
- 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-1)/(x+2)
-
-1-x
-
-exp(-x)+(-cos(x*sqrt(3)/2)-sin(x*sqrt(3)/2))*exp(x/2)
-
3/(x^2+1)
-
Expresiones idénticas
- xsinx/(cuatro +tg^ dos (x))
- x seno de x dividir por (4 más tg al cuadrado (x))
- x seno de x dividir por (cuatro más tg en el grado dos (x))
- xsinx/(4+tg2(x))
- xsinx/4+tg2x
- xsinx/(4+tg²(x))
- xsinx/(4+tg en el grado 2(x))
- xsinx/4+tg^2x
- xsinx dividir por (4+tg^2(x))
-
Expresiones semejantes
- xsinx/(4-tg^2(x))
-
Expresiones con funciones
- xsinx
- xsinx+(e^x-e^x)/(e^-x+e^x)
- xsinx+(+e^x-e^x)/(e^-x+e^x)
- xsinx+(e^(-x)(-e)^x)/(e^(-x)+e^x)
- xsinx+(e^(-x)(-e)^x)/(e^(-x)+(e)^x)
- tg
- tg2x/x
- tgx-2x-1
- tgx-1
- tg(x/3)-2
- tg(x)+1
Gráfico de la función y = xsinx/(4+tg^2(x))
Solución
Ha introducido
[src]
x*sin(x)
f(x) = -----------
2
4 + tan (x)
$$f{\left(x \right)} = \frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}$$
f = (x*sin(x))/(tan(x)^2 + 4)
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:
$$\frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución analítica
$$x_{1} = 0$$
$$x_{2} = \pi$$
Solución numérica
$$x_{1} = 65.9734457253857$$
$$x_{2} = -89.5353907014139$$
$$x_{3} = -21.9911485751286$$
$$x_{4} = 21.9911485751286$$
$$x_{5} = -3.14159265358979$$
$$x_{6} = -15.707963267949$$
$$x_{7} = 9.42477796076938$$
$$x_{8} = 6.28318530717959$$
$$x_{9} = -34.5575191894877$$
$$x_{10} = -73.8274272831926$$
$$x_{11} = -67.544242126936$$
$$x_{12} = 64.4026493290031$$
$$x_{13} = 28.2743338823081$$
$$x_{14} = -94.2477796076938$$
$$x_{15} = -7.85398152870528$$
$$x_{16} = -53.4070751110265$$
$$x_{17} = 84.8230016469244$$
$$x_{18} = -45.5530935521522$$
$$x_{19} = 86.3937979058448$$
$$x_{20} = 29.8451302874799$$
$$x_{21} = 42.4115006809338$$
$$x_{22} = 42.4115007525711$$
$$x_{23} = -1.5707964157513$$
$$x_{24} = 59.6902604182061$$
$$x_{25} = 56.5486677646163$$
$$x_{26} = -23.5619449773569$$
$$x_{27} = 72.2566310325652$$
$$x_{28} = -50.2654824574367$$
$$x_{29} = 95.8185759189139$$
$$x_{30} = -95.818575869486$$
$$x_{31} = 78.5398163397448$$
$$x_{32} = -87.9645943005142$$
$$x_{33} = 37.6991118430775$$
$$x_{34} = -6.28318530717959$$
$$x_{35} = -37.6991118430775$$
$$x_{36} = -43.9822971502571$$
$$x_{37} = 47.1238898038469$$
$$x_{38} = -14.1371668678372$$
$$x_{39} = 20.42035217694$$
$$x_{40} = -100.530964914873$$
$$x_{41} = 3.14159265358979$$
$$x_{42} = -72.2566310325652$$
$$x_{43} = -81.6814089933346$$
$$x_{44} = -65.9734457253857$$
$$x_{45} = 0$$
$$x_{46} = -28.2743338823081$$
$$x_{47} = -56.5486677646163$$
$$x_{48} = 1.57079626923918$$
$$x_{49} = 7.85398171361397$$
$$x_{50} = 31.4159265358979$$
$$x_{51} = 43.9822971502571$$
$$x_{52} = -47.1238898038469$$
$$x_{53} = 100.530964914873$$
$$x_{54} = -97.3893722612836$$
$$x_{55} = -51.8362786963082$$
$$x_{56} = 81.6814089933346$$
$$x_{57} = -75.398223686155$$
$$x_{58} = -78.5398163397448$$
$$x_{59} = 95.8185760136054$$
$$x_{60} = 50.2654824574367$$
$$x_{61} = 94.2477796076938$$
$$x_{62} = 73.8274274384211$$
$$x_{63} = -23.5619448833633$$
$$x_{64} = -59.6902604182061$$
$$x_{65} = 12.5663706143592$$
$$x_{66} = 14.1371670350454$$
$$x_{67} = 34.5575191894877$$
$$x_{68} = -29.8451301097218$$
$$x_{69} = -58.1194640203505$$
$$x_{70} = 51.836278862996$$
$$x_{71} = 15.707963267949$$
$$x_{72} = 87.9645943005142$$
$$x_{73} = -80.1106125976626$$
$$x_{74} = -9.42477796076938$$
$$x_{75} = -36.128315443513$$
$$x_{76} = -31.4159265358979$$
o sea hay que resolver la ecuación:
$$\frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución analítica
$$x_{1} = 0$$
$$x_{2} = \pi$$
Solución numérica
$$x_{1} = 65.9734457253857$$
$$x_{2} = -89.5353907014139$$
$$x_{3} = -21.9911485751286$$
$$x_{4} = 21.9911485751286$$
$$x_{5} = -3.14159265358979$$
$$x_{6} = -15.707963267949$$
$$x_{7} = 9.42477796076938$$
$$x_{8} = 6.28318530717959$$
$$x_{9} = -34.5575191894877$$
$$x_{10} = -73.8274272831926$$
$$x_{11} = -67.544242126936$$
$$x_{12} = 64.4026493290031$$
$$x_{13} = 28.2743338823081$$
$$x_{14} = -94.2477796076938$$
$$x_{15} = -7.85398152870528$$
$$x_{16} = -53.4070751110265$$
$$x_{17} = 84.8230016469244$$
$$x_{18} = -45.5530935521522$$
$$x_{19} = 86.3937979058448$$
$$x_{20} = 29.8451302874799$$
$$x_{21} = 42.4115006809338$$
$$x_{22} = 42.4115007525711$$
$$x_{23} = -1.5707964157513$$
$$x_{24} = 59.6902604182061$$
$$x_{25} = 56.5486677646163$$
$$x_{26} = -23.5619449773569$$
$$x_{27} = 72.2566310325652$$
$$x_{28} = -50.2654824574367$$
$$x_{29} = 95.8185759189139$$
$$x_{30} = -95.818575869486$$
$$x_{31} = 78.5398163397448$$
$$x_{32} = -87.9645943005142$$
$$x_{33} = 37.6991118430775$$
$$x_{34} = -6.28318530717959$$
$$x_{35} = -37.6991118430775$$
$$x_{36} = -43.9822971502571$$
$$x_{37} = 47.1238898038469$$
$$x_{38} = -14.1371668678372$$
$$x_{39} = 20.42035217694$$
$$x_{40} = -100.530964914873$$
$$x_{41} = 3.14159265358979$$
$$x_{42} = -72.2566310325652$$
$$x_{43} = -81.6814089933346$$
$$x_{44} = -65.9734457253857$$
$$x_{45} = 0$$
$$x_{46} = -28.2743338823081$$
$$x_{47} = -56.5486677646163$$
$$x_{48} = 1.57079626923918$$
$$x_{49} = 7.85398171361397$$
$$x_{50} = 31.4159265358979$$
$$x_{51} = 43.9822971502571$$
$$x_{52} = -47.1238898038469$$
$$x_{53} = 100.530964914873$$
$$x_{54} = -97.3893722612836$$
$$x_{55} = -51.8362786963082$$
$$x_{56} = 81.6814089933346$$
$$x_{57} = -75.398223686155$$
$$x_{58} = -78.5398163397448$$
$$x_{59} = 95.8185760136054$$
$$x_{60} = 50.2654824574367$$
$$x_{61} = 94.2477796076938$$
$$x_{62} = 73.8274274384211$$
$$x_{63} = -23.5619448833633$$
$$x_{64} = -59.6902604182061$$
$$x_{65} = 12.5663706143592$$
$$x_{66} = 14.1371670350454$$
$$x_{67} = 34.5575191894877$$
$$x_{68} = -29.8451301097218$$
$$x_{69} = -58.1194640203505$$
$$x_{70} = 51.836278862996$$
$$x_{71} = 15.707963267949$$
$$x_{72} = 87.9645943005142$$
$$x_{73} = -80.1106125976626$$
$$x_{74} = -9.42477796076938$$
$$x_{75} = -36.128315443513$$
$$x_{76} = -31.4159265358979$$
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
$$- \frac{x \left(2 \tan^{2}{\left(x \right)} + 2\right) \sin{\left(x \right)} \tan{\left(x \right)}}{\left(\tan^{2}{\left(x \right)} + 4\right)^{2}} + \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 87.138945811754$$
$$x_{2} = -90.2804556957995$$
$$x_{3} = 24.3132699931952$$
$$x_{4} = 18.0330900698586$$
$$x_{5} = -29.845130209103$$
$$x_{6} = -98.2194935076171$$
$$x_{7} = 1.5707963267949$$
$$x_{8} = 4.71238898038469$$
$$x_{9} = 36.1283155162826$$
$$x_{10} = -85.65343015591$$
$$x_{11} = 2.40467079662226$$
$$x_{12} = 83.997442131108$$
$$x_{13} = 5.49385370718343$$
$$x_{14} = -32.2503175803598$$
$$x_{15} = 60.5216851226385$$
$$x_{16} = -80.1106126665397$$
$$x_{17} = -95.8185759344887$$
$$x_{18} = 38.5324692900873$$
$$x_{19} = 454.703366375065$$
$$x_{20} = 11.7561606649435$$
$$x_{21} = 99.7050166950322$$
$$x_{22} = -76.2289489691309$$
$$x_{23} = 67.5442420521806$$
$$x_{24} = 10.2725607549115$$
$$x_{25} = 69.9460058299699$$
$$x_{26} = 70.6858347057703$$
$$x_{27} = -36.8767140943411$$
$$x_{28} = -46.3003430565376$$
$$x_{29} = 54.238892641524$$
$$x_{30} = -5.49385370718343$$
$$x_{31} = 0.997817540674201$$
$$x_{32} = -51.8362787842316$$
$$x_{33} = 58.1194640914112$$
$$x_{34} = 73.0874722075759$$
$$x_{35} = -73.8274273593601$$
$$x_{36} = 4.01872293357174$$
$$x_{37} = 16.5483332246309$$
$$x_{38} = -10.2725607549115$$
$$x_{39} = -99.7050166950322$$
$$x_{40} = -4.01872293357174$$
$$x_{41} = 27.453878484238$$
$$x_{42} = 80.1106126665397$$
$$x_{43} = 46.3003430565376$$
$$x_{44} = -16.5483332246309$$
$$x_{45} = -47.9562027081837$$
$$x_{46} = 90.2804556957995$$
$$x_{47} = 98.2194935076171$$
$$x_{48} = 76.2289489691309$$
$$x_{49} = 0$$
$$x_{50} = -91.9364513523705$$
$$x_{51} = 33.735647763708$$
$$x_{52} = -7.85398163397448$$
$$x_{53} = -27.453878484238$$
$$x_{54} = -11.7561606649435$$
$$x_{55} = -58.865755516954$$
$$x_{56} = -93.4219711563462$$
$$x_{57} = -83.997442131108$$
$$x_{58} = -54.238892641524$$
$$x_{59} = -62.0071694687546$$
$$x_{60} = -68.2900468139916$$
$$x_{61} = 32.2503175803598$$
$$x_{62} = -69.9460058299699$$
$$x_{63} = -33.735647763708$$
$$x_{64} = -55.7243617726486$$
$$x_{65} = -19.6879744764593$$
$$x_{66} = 14.1371669411541$$
$$x_{67} = -71.4315058489604$$
$$x_{68} = 55.7243617726486$$
$$x_{69} = -25.9686624297459$$
$$x_{70} = 62.0071694687546$$
$$x_{71} = -63.663110358029$$
$$x_{72} = 77.7144563954775$$
$$x_{73} = 45.553093477052$$
$$x_{74} = 25.9686624297459$$
$$x_{75} = -18.0330900698586$$
$$x_{76} = -40.0178633797347$$
$$x_{77} = -41.6736614988808$$
$$x_{78} = 92.6769832808989$$
$$x_{79} = 82.5119289102023$$
$$x_{80} = 40.0178633797347$$
$$x_{81} = -7.13941996437343$$
$$x_{82} = -49.4416503630997$$
$$x_{83} = 91.9364513523705$$
$$x_{84} = 47.9562027081837$$
$$x_{85} = -77.7144563954775$$
$$x_{86} = 68.2900468139916$$
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:
$$x_{1} = 87.138945811754$$
$$x_{2} = 24.3132699931952$$
$$x_{3} = 18.0330900698586$$
$$x_{4} = -98.2194935076171$$
$$x_{5} = 1.5707963267949$$
$$x_{6} = -85.65343015591$$
$$x_{7} = 5.49385370718343$$
$$x_{8} = 60.5216851226385$$
$$x_{9} = -95.8185759344887$$
$$x_{10} = 11.7561606649435$$
$$x_{11} = 99.7050166950322$$
$$x_{12} = 10.2725607549115$$
$$x_{13} = 70.6858347057703$$
$$x_{14} = -36.8767140943411$$
$$x_{15} = 54.238892641524$$
$$x_{16} = -5.49385370718343$$
$$x_{17} = -51.8362787842316$$
$$x_{18} = 58.1194640914112$$
$$x_{19} = 73.0874722075759$$
$$x_{20} = 4.01872293357174$$
$$x_{21} = 16.5483332246309$$
$$x_{22} = -10.2725607549115$$
$$x_{23} = -99.7050166950322$$
$$x_{24} = -4.01872293357174$$
$$x_{25} = -16.5483332246309$$
$$x_{26} = -47.9562027081837$$
$$x_{27} = 98.2194935076171$$
$$x_{28} = 0$$
$$x_{29} = -91.9364513523705$$
$$x_{30} = -7.85398163397448$$
$$x_{31} = -11.7561606649435$$
$$x_{32} = -93.4219711563462$$
$$x_{33} = -54.238892641524$$
$$x_{34} = -62.0071694687546$$
$$x_{35} = -68.2900468139916$$
$$x_{36} = -55.7243617726486$$
$$x_{37} = 14.1371669411541$$
$$x_{38} = 55.7243617726486$$
$$x_{39} = 62.0071694687546$$
$$x_{40} = 45.553093477052$$
$$x_{41} = -18.0330900698586$$
$$x_{42} = -41.6736614988808$$
$$x_{43} = -49.4416503630997$$
$$x_{44} = 91.9364513523705$$
$$x_{45} = 47.9562027081837$$
$$x_{46} = 68.2900468139916$$
Puntos máximos de la función:
$$x_{46} = -90.2804556957995$$
$$x_{46} = -29.845130209103$$
$$x_{46} = 4.71238898038469$$
$$x_{46} = 36.1283155162826$$
$$x_{46} = 2.40467079662226$$
$$x_{46} = 83.997442131108$$
$$x_{46} = -32.2503175803598$$
$$x_{46} = -80.1106126665397$$
$$x_{46} = 38.5324692900873$$
$$x_{46} = 454.703366375065$$
$$x_{46} = -76.2289489691309$$
$$x_{46} = 67.5442420521806$$
$$x_{46} = 69.9460058299699$$
$$x_{46} = -46.3003430565376$$
$$x_{46} = 0.997817540674201$$
$$x_{46} = -73.8274273593601$$
$$x_{46} = 27.453878484238$$
$$x_{46} = 80.1106126665397$$
$$x_{46} = 46.3003430565376$$
$$x_{46} = 90.2804556957995$$
$$x_{46} = 76.2289489691309$$
$$x_{46} = 33.735647763708$$
$$x_{46} = -27.453878484238$$
$$x_{46} = -58.865755516954$$
$$x_{46} = -83.997442131108$$
$$x_{46} = 32.2503175803598$$
$$x_{46} = -69.9460058299699$$
$$x_{46} = -33.735647763708$$
$$x_{46} = -19.6879744764593$$
$$x_{46} = -71.4315058489604$$
$$x_{46} = -25.9686624297459$$
$$x_{46} = -63.663110358029$$
$$x_{46} = 77.7144563954775$$
$$x_{46} = 25.9686624297459$$
$$x_{46} = -40.0178633797347$$
$$x_{46} = 92.6769832808989$$
$$x_{46} = 82.5119289102023$$
$$x_{46} = 40.0178633797347$$
$$x_{46} = -7.13941996437343$$
$$x_{46} = -77.7144563954775$$
Decrece en los intervalos
$$\left[99.7050166950322, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -99.7050166950322\right]$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(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
$$- \frac{x \left(2 \tan^{2}{\left(x \right)} + 2\right) \sin{\left(x \right)} \tan{\left(x \right)}}{\left(\tan^{2}{\left(x \right)} + 4\right)^{2}} + \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 87.138945811754$$
$$x_{2} = -90.2804556957995$$
$$x_{3} = 24.3132699931952$$
$$x_{4} = 18.0330900698586$$
$$x_{5} = -29.845130209103$$
$$x_{6} = -98.2194935076171$$
$$x_{7} = 1.5707963267949$$
$$x_{8} = 4.71238898038469$$
$$x_{9} = 36.1283155162826$$
$$x_{10} = -85.65343015591$$
$$x_{11} = 2.40467079662226$$
$$x_{12} = 83.997442131108$$
$$x_{13} = 5.49385370718343$$
$$x_{14} = -32.2503175803598$$
$$x_{15} = 60.5216851226385$$
$$x_{16} = -80.1106126665397$$
$$x_{17} = -95.8185759344887$$
$$x_{18} = 38.5324692900873$$
$$x_{19} = 454.703366375065$$
$$x_{20} = 11.7561606649435$$
$$x_{21} = 99.7050166950322$$
$$x_{22} = -76.2289489691309$$
$$x_{23} = 67.5442420521806$$
$$x_{24} = 10.2725607549115$$
$$x_{25} = 69.9460058299699$$
$$x_{26} = 70.6858347057703$$
$$x_{27} = -36.8767140943411$$
$$x_{28} = -46.3003430565376$$
$$x_{29} = 54.238892641524$$
$$x_{30} = -5.49385370718343$$
$$x_{31} = 0.997817540674201$$
$$x_{32} = -51.8362787842316$$
$$x_{33} = 58.1194640914112$$
$$x_{34} = 73.0874722075759$$
$$x_{35} = -73.8274273593601$$
$$x_{36} = 4.01872293357174$$
$$x_{37} = 16.5483332246309$$
$$x_{38} = -10.2725607549115$$
$$x_{39} = -99.7050166950322$$
$$x_{40} = -4.01872293357174$$
$$x_{41} = 27.453878484238$$
$$x_{42} = 80.1106126665397$$
$$x_{43} = 46.3003430565376$$
$$x_{44} = -16.5483332246309$$
$$x_{45} = -47.9562027081837$$
$$x_{46} = 90.2804556957995$$
$$x_{47} = 98.2194935076171$$
$$x_{48} = 76.2289489691309$$
$$x_{49} = 0$$
$$x_{50} = -91.9364513523705$$
$$x_{51} = 33.735647763708$$
$$x_{52} = -7.85398163397448$$
$$x_{53} = -27.453878484238$$
$$x_{54} = -11.7561606649435$$
$$x_{55} = -58.865755516954$$
$$x_{56} = -93.4219711563462$$
$$x_{57} = -83.997442131108$$
$$x_{58} = -54.238892641524$$
$$x_{59} = -62.0071694687546$$
$$x_{60} = -68.2900468139916$$
$$x_{61} = 32.2503175803598$$
$$x_{62} = -69.9460058299699$$
$$x_{63} = -33.735647763708$$
$$x_{64} = -55.7243617726486$$
$$x_{65} = -19.6879744764593$$
$$x_{66} = 14.1371669411541$$
$$x_{67} = -71.4315058489604$$
$$x_{68} = 55.7243617726486$$
$$x_{69} = -25.9686624297459$$
$$x_{70} = 62.0071694687546$$
$$x_{71} = -63.663110358029$$
$$x_{72} = 77.7144563954775$$
$$x_{73} = 45.553093477052$$
$$x_{74} = 25.9686624297459$$
$$x_{75} = -18.0330900698586$$
$$x_{76} = -40.0178633797347$$
$$x_{77} = -41.6736614988808$$
$$x_{78} = 92.6769832808989$$
$$x_{79} = 82.5119289102023$$
$$x_{80} = 40.0178633797347$$
$$x_{81} = -7.13941996437343$$
$$x_{82} = -49.4416503630997$$
$$x_{83} = 91.9364513523705$$
$$x_{84} = 47.9562027081837$$
$$x_{85} = -77.7144563954775$$
$$x_{86} = 68.2900468139916$$
Signos de extremos en los puntos:
(87.13894581175403, -12.3763087646776)
(-90.28045569579949, 12.8225080937804)
(24.313269993195227, -3.45264222691292)
(18.033090069858616, -2.56044421510836)
(-29.845130209103036, -1.12127665170554e-29)
(-98.21949350761713, -13.9501156336138)
(1.5707963267948966, 5.8895428941999e-33)
(4.71238898038469, -1.59017658143397e-31)
(36.12831551628262, -3.66424875021481e-28)
(-85.65343015590999, -12.1653166830211)
(2.4046707966222645, 0.335020556538555)
(83.99744213110796, 11.9301098752818)
(5.493853707183429, -0.777532226748693)
(-32.2503175803598, 4.58011040647008)
(60.52168512263849, -8.59574594780144)
(-80.11061266653972, -1.92283264304371e-27)
(-95.81857593448869, 3.676520165044e-28)
(38.53246929008733, 5.47244715183819)
(454.7033663750651, 64.582180890724)
(11.756160664943506, -1.66847511356391)
(99.70501669503224, -14.1611083032433)
(-76.2289489691309, 10.8267221900235)
(67.54424205218055, -1.3132184568469e-27)
(10.27256075491152, -1.45763299397885)
(69.9460058299699, 9.93432901594521)
(70.68583470577035, 6.77618297499813e-29)
(-36.87671409434108, -5.23725594007668)
(-46.30034305653763, 6.57579015556219)
(54.238892641523954, -7.70336350275712)
(-5.493853707183429, -0.777532226748693)
(0.9978175406742009, 0.130960306067674)
(-51.83627878423159, 3.09398107171563e-30)
(58.119464091411174, 1.39112146798308e-29)
(73.08747220757594, -10.3805252333763)
(-73.82742735936014, -4.43565443427593e-28)
(4.018722933571741, -0.567362924067202)
(16.54833322463088, -2.34951143571411)
(-10.27256075491152, -1.45763299397885)
(-99.70501669503224, -14.1611083032433)
(-4.018722933571741, -0.567362924067202)
(27.453878484238032, 3.89877781647259)
(80.11061266653972, -1.92283264304371e-27)
(46.30034305653763, 6.57579015556219)
(-16.54833322463088, -2.34951143571411)
(-47.956202708183724, -6.81098836459494)
(90.28045569579949, 12.8225080937804)
(98.21949350761713, -13.9501156336138)
(76.2289489691309, 10.8267221900235)
(0, 0)
(-91.93645135237047, -13.0577154126865)
(33.73564776370796, 4.7910880047921)
(-7.853981633974483, 7.36192861774987e-31)
(-27.453878484238032, 3.89877781647259)
(-11.756160664943506, -1.66847511356391)
(-58.86575551695403, 8.36054305299913)
(-93.42197115634625, -13.2687078181799)
(-83.99744213110796, 11.9301098752818)
(-54.238892641523954, -7.70336350275712)
(-62.0071694687546, -8.80673558504463)
(-68.29004681399161, -9.69912415120835)
(32.2503175803598, 4.58011040647008)
(-69.9460058299699, 9.93432901594521)
(-33.73564776370796, 4.7910880047921)
(-55.72436177264862, -7.91435195205804)
(-19.687974476459267, 2.79557707373584)
(14.137166941154069, 4.29347676987172e-30)
(-71.43150584896037, 10.1453198768279)
(55.72436177264862, -7.91435195205804)
(-25.968662429745905, 3.68780913408032)
(62.0071694687546, -8.80673558504463)
(-63.66311035802902, 9.04193923563947)
(77.71445639547751, 11.0377136292074)
(45.553093477052, 1.74530768724744e-35)
(25.968662429745905, 3.68780913408032)
(-18.033090069858616, -2.56044421510836)
(-40.01786337973469, 5.68342974137886)
(-41.67366149888085, -5.91862382854916)
(92.6769832808989, -2.69152684487792e-27)
(82.51192891020227, 11.7191179837181)
(40.01786337973469, 5.68342974137886)
(-7.139419964373433, 1.012038154624)
(-49.441650363099725, -7.02197513700988)
(91.93645135237047, -13.0577154126865)
(47.956202708183724, -6.81098836459494)
(-77.71445639547751, 11.0377136292074)
(68.29004681399161, -9.69912415120835)
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:
$$x_{1} = 87.138945811754$$
$$x_{2} = 24.3132699931952$$
$$x_{3} = 18.0330900698586$$
$$x_{4} = -98.2194935076171$$
$$x_{5} = 1.5707963267949$$
$$x_{6} = -85.65343015591$$
$$x_{7} = 5.49385370718343$$
$$x_{8} = 60.5216851226385$$
$$x_{9} = -95.8185759344887$$
$$x_{10} = 11.7561606649435$$
$$x_{11} = 99.7050166950322$$
$$x_{12} = 10.2725607549115$$
$$x_{13} = 70.6858347057703$$
$$x_{14} = -36.8767140943411$$
$$x_{15} = 54.238892641524$$
$$x_{16} = -5.49385370718343$$
$$x_{17} = -51.8362787842316$$
$$x_{18} = 58.1194640914112$$
$$x_{19} = 73.0874722075759$$
$$x_{20} = 4.01872293357174$$
$$x_{21} = 16.5483332246309$$
$$x_{22} = -10.2725607549115$$
$$x_{23} = -99.7050166950322$$
$$x_{24} = -4.01872293357174$$
$$x_{25} = -16.5483332246309$$
$$x_{26} = -47.9562027081837$$
$$x_{27} = 98.2194935076171$$
$$x_{28} = 0$$
$$x_{29} = -91.9364513523705$$
$$x_{30} = -7.85398163397448$$
$$x_{31} = -11.7561606649435$$
$$x_{32} = -93.4219711563462$$
$$x_{33} = -54.238892641524$$
$$x_{34} = -62.0071694687546$$
$$x_{35} = -68.2900468139916$$
$$x_{36} = -55.7243617726486$$
$$x_{37} = 14.1371669411541$$
$$x_{38} = 55.7243617726486$$
$$x_{39} = 62.0071694687546$$
$$x_{40} = 45.553093477052$$
$$x_{41} = -18.0330900698586$$
$$x_{42} = -41.6736614988808$$
$$x_{43} = -49.4416503630997$$
$$x_{44} = 91.9364513523705$$
$$x_{45} = 47.9562027081837$$
$$x_{46} = 68.2900468139916$$
Puntos máximos de la función:
$$x_{46} = -90.2804556957995$$
$$x_{46} = -29.845130209103$$
$$x_{46} = 4.71238898038469$$
$$x_{46} = 36.1283155162826$$
$$x_{46} = 2.40467079662226$$
$$x_{46} = 83.997442131108$$
$$x_{46} = -32.2503175803598$$
$$x_{46} = -80.1106126665397$$
$$x_{46} = 38.5324692900873$$
$$x_{46} = 454.703366375065$$
$$x_{46} = -76.2289489691309$$
$$x_{46} = 67.5442420521806$$
$$x_{46} = 69.9460058299699$$
$$x_{46} = -46.3003430565376$$
$$x_{46} = 0.997817540674201$$
$$x_{46} = -73.8274273593601$$
$$x_{46} = 27.453878484238$$
$$x_{46} = 80.1106126665397$$
$$x_{46} = 46.3003430565376$$
$$x_{46} = 90.2804556957995$$
$$x_{46} = 76.2289489691309$$
$$x_{46} = 33.735647763708$$
$$x_{46} = -27.453878484238$$
$$x_{46} = -58.865755516954$$
$$x_{46} = -83.997442131108$$
$$x_{46} = 32.2503175803598$$
$$x_{46} = -69.9460058299699$$
$$x_{46} = -33.735647763708$$
$$x_{46} = -19.6879744764593$$
$$x_{46} = -71.4315058489604$$
$$x_{46} = -25.9686624297459$$
$$x_{46} = -63.663110358029$$
$$x_{46} = 77.7144563954775$$
$$x_{46} = 25.9686624297459$$
$$x_{46} = -40.0178633797347$$
$$x_{46} = 92.6769832808989$$
$$x_{46} = 82.5119289102023$$
$$x_{46} = 40.0178633797347$$
$$x_{46} = -7.13941996437343$$
$$x_{46} = -77.7144563954775$$
Decrece en los intervalos
$$\left[99.7050166950322, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -99.7050166950322\right]$$
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:
$$y = \lim_{x \to -\infty}\left(\frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}\right)$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \lim_{x \to \infty}\left(\frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \lim_{x \to -\infty}\left(\frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \lim_{x \to \infty}\left(\frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}\right)$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (x*sin(x))/(4 + tan(x)^2), dividida por x con x->+oo y x ->-oo
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = x \lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}\right)$$
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = x \lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = x \lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = x \lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}\right)$$
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:
$$\frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4} = \frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}$$
- Sí
$$\frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4} = - \frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}$$
- No
es decir, función
es
par
Pues, comprobamos:
$$\frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4} = \frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}$$
- Sí
$$\frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4} = - \frac{x \sin{\left(x \right)}}{\tan^{2}{\left(x \right)} + 4}$$
- No
es decir, función
es
par