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- Gráfico de la función implícita
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- Integrales paso a paso
- Gráfico de la función paramétrica
- Gráfico en coordenadas polares
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- Puntos de cruce de las funciones
-
¿Cómo usar?
- Gráfico de la función y =:
-
x^3+3*x^2+2
-
x*(-1-log(x))
-
e^3*x+10*e^2*x
-
x^2/(4-x^2)
-
Expresiones idénticas
- (uno /cos^2x)^((uno /x)ln(e))
- (1 dividir por coseno de al cuadrado x) en el grado ((1 dividir por x)ln(e))
- (uno dividir por coseno de al cuadrado x) en el grado ((uno dividir por x)ln(e))
- (1/cos2x)((1/x)ln(e))
- 1/cos2x1/xlne
- (1/cos²x)^((1/x)ln(e))
- (1/cos en el grado 2x) en el grado ((1/x)ln(e))
- 1/cos^2x^1/xlne
- (1 dividir por cos^2x)^((1 dividir por x)ln(e))
-
Expresiones con funciones
- Coseno cos
- cos(2*x)-sqrt(3)/2
- cos(3*π*x)/x
- cos(2*x*sqrt(2))+sin(2*x*sqrt(2))
- cos(2/x)-2*sin(1/x)+1/x
- cos(4*x)+sin(4*x)
- ln
- ln(1-1/x^2)
- ln*2x/(x-4)-x
- ln(2x)/(x-4)-x
- ln((3-2x-x))^2
- ln(x+4)^2+2x+7
Gráfico de la función y = (1/cos^2x)^((1/x)ln(e))
Solución
Ha introducido
[src]
log(E)
------
x
/ 1 \
f(x) = |-------|
| 2 |
\cos (x)/
$$f{\left(x \right)} = \left(\frac{1}{\cos^{2}{\left(x \right)}}\right)^{\frac{\log{\left(e \right)}}{x}}$$
f = (1/(cos(x)^2))^(log(E)/x)
Gráfico de la función
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
$$x_{1} = 0$$
$$x_{2} = 1.5707963267949$$
$$x_{3} = 4.71238898038469$$
$$x_{1} = 0$$
$$x_{2} = 1.5707963267949$$
$$x_{3} = 4.71238898038469$$
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:
$$\left(\frac{1}{\cos^{2}{\left(x \right)}}\right)^{\frac{\log{\left(e \right)}}{x}} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = -1.5707963267949$$
$$x_{2} = -1.57079632679485$$
o sea hay que resolver la ecuación:
$$\left(\frac{1}{\cos^{2}{\left(x \right)}}\right)^{\frac{\log{\left(e \right)}}{x}} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = -1.5707963267949$$
$$x_{2} = -1.57079632679485$$
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
$$\left(\frac{2 \log{\left(e \right)} \sin{\left(x \right)}}{x \cos{\left(x \right)}} - \frac{\log{\left(e \right)} \log{\left(\frac{1}{\cos^{2}{\left(x \right)}} \right)}}{x^{2}}\right) \left|{\cos{\left(x \right)}}\right|^{- \frac{2 \log{\left(e \right)}}{x}} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 72.2566310325652$$
$$x_{2} = -59.6902604182061$$
$$x_{3} = 3.14159265358979$$
$$x_{4} = -43.9822971502571$$
$$x_{5} = 81.6814089933346$$
$$x_{6} = -100.530964914873$$
$$x_{7} = 28.2743338823081$$
$$x_{8} = 65.9734457253857$$
$$x_{9} = -31.4159265358979$$
$$x_{10} = -9.42477796076938$$
$$x_{11} = 40.8407044966673$$
$$x_{12} = 56.5486677646163$$
$$x_{13} = -56.5486677646163$$
$$x_{14} = 12.5663706143592$$
$$x_{15} = 43.9822971502571$$
$$x_{16} = 100.530964914873$$
$$x_{17} = -3.14159265358979$$
$$x_{18} = -15.707963267949$$
$$x_{19} = 59.6902604182061$$
$$x_{20} = 6.28318530717959$$
$$x_{21} = 9.42477796076938$$
$$x_{22} = -53.4070751110265$$
$$x_{23} = -47.1238898038469$$
$$x_{24} = -87.9645943005142$$
$$x_{25} = 69.1150383789755$$
$$x_{26} = 21.9911485751286$$
$$x_{27} = 87.9645943005142$$
$$x_{28} = 18.8495559215388$$
$$x_{29} = -84.8230016469244$$
$$x_{30} = -72.2566310325652$$
$$x_{31} = 25.1327412287183$$
$$x_{32} = 37.6991118430775$$
$$x_{33} = -25.1327412287183$$
$$x_{34} = 50.2654824574367$$
$$x_{35} = 34.5575191894877$$
$$x_{36} = -6.28318530717959$$
$$x_{37} = -65.9734457253857$$
$$x_{38} = -21.9911485751286$$
$$x_{39} = -62.8318530717959$$
$$x_{40} = 75.398223686155$$
$$x_{41} = 84.8230016469244$$
$$x_{42} = 53.4070751110265$$
$$x_{43} = 15.707963267949$$
$$x_{44} = -28.2743338823081$$
$$x_{45} = -91.106186954104$$
$$x_{46} = 47.1238898038469$$
$$x_{47} = 97.3893722612836$$
$$x_{48} = -69.1150383789755$$
$$x_{49} = 94.2477796076938$$
$$x_{50} = -18.8495559215388$$
$$x_{51} = -50.2654824574367$$
$$x_{52} = -37.6991118430775$$
$$x_{53} = -81.6814089933346$$
$$x_{54} = 62.8318530717959$$
$$x_{55} = 78.5398163397448$$
$$x_{56} = 31.4159265358979$$
$$x_{57} = -78.5398163397448$$
$$x_{58} = -40.8407044966673$$
$$x_{59} = -97.3893722612836$$
$$x_{60} = -75.398223686155$$
$$x_{61} = 91.106186954104$$
$$x_{62} = -12.5663706143592$$
$$x_{63} = -94.2477796076938$$
$$x_{64} = -34.5575191894877$$
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:
$$x_{1} = 72.2566310325652$$
$$x_{2} = 3.14159265358979$$
$$x_{3} = 81.6814089933346$$
$$x_{4} = 28.2743338823081$$
$$x_{5} = 65.9734457253857$$
$$x_{6} = 40.8407044966673$$
$$x_{7} = 56.5486677646163$$
$$x_{8} = 12.5663706143592$$
$$x_{9} = 43.9822971502571$$
$$x_{10} = 100.530964914873$$
$$x_{11} = 59.6902604182061$$
$$x_{12} = 6.28318530717959$$
$$x_{13} = 9.42477796076938$$
$$x_{14} = 69.1150383789755$$
$$x_{15} = 21.9911485751286$$
$$x_{16} = 87.9645943005142$$
$$x_{17} = 18.8495559215388$$
$$x_{18} = 25.1327412287183$$
$$x_{19} = 37.6991118430775$$
$$x_{20} = 50.2654824574367$$
$$x_{21} = 34.5575191894877$$
$$x_{22} = 75.398223686155$$
$$x_{23} = 84.8230016469244$$
$$x_{24} = 53.4070751110265$$
$$x_{25} = 15.707963267949$$
$$x_{26} = 47.1238898038469$$
$$x_{27} = 97.3893722612836$$
$$x_{28} = 94.2477796076938$$
$$x_{29} = 62.8318530717959$$
$$x_{30} = 78.5398163397448$$
$$x_{31} = 31.4159265358979$$
$$x_{32} = 91.106186954104$$
Puntos máximos de la función:
$$x_{32} = -59.6902604182061$$
$$x_{32} = -43.9822971502571$$
$$x_{32} = -100.530964914873$$
$$x_{32} = -31.4159265358979$$
$$x_{32} = -9.42477796076938$$
$$x_{32} = -56.5486677646163$$
$$x_{32} = -3.14159265358979$$
$$x_{32} = -15.707963267949$$
$$x_{32} = -53.4070751110265$$
$$x_{32} = -47.1238898038469$$
$$x_{32} = -87.9645943005142$$
$$x_{32} = -84.8230016469244$$
$$x_{32} = -72.2566310325652$$
$$x_{32} = -25.1327412287183$$
$$x_{32} = -6.28318530717959$$
$$x_{32} = -65.9734457253857$$
$$x_{32} = -21.9911485751286$$
$$x_{32} = -62.8318530717959$$
$$x_{32} = -28.2743338823081$$
$$x_{32} = -91.106186954104$$
$$x_{32} = -69.1150383789755$$
$$x_{32} = -18.8495559215388$$
$$x_{32} = -50.2654824574367$$
$$x_{32} = -37.6991118430775$$
$$x_{32} = -81.6814089933346$$
$$x_{32} = -78.5398163397448$$
$$x_{32} = -40.8407044966673$$
$$x_{32} = -97.3893722612836$$
$$x_{32} = -75.398223686155$$
$$x_{32} = -12.5663706143592$$
$$x_{32} = -94.2477796076938$$
$$x_{32} = -34.5575191894877$$
Decrece en los intervalos
$$\left[100.530964914873, \infty\right)$$
Crece en los intervalos
$$\left[-3.14159265358979, 3.14159265358979\right]$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(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
$$\left(\frac{2 \log{\left(e \right)} \sin{\left(x \right)}}{x \cos{\left(x \right)}} - \frac{\log{\left(e \right)} \log{\left(\frac{1}{\cos^{2}{\left(x \right)}} \right)}}{x^{2}}\right) \left|{\cos{\left(x \right)}}\right|^{- \frac{2 \log{\left(e \right)}}{x}} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 72.2566310325652$$
$$x_{2} = -59.6902604182061$$
$$x_{3} = 3.14159265358979$$
$$x_{4} = -43.9822971502571$$
$$x_{5} = 81.6814089933346$$
$$x_{6} = -100.530964914873$$
$$x_{7} = 28.2743338823081$$
$$x_{8} = 65.9734457253857$$
$$x_{9} = -31.4159265358979$$
$$x_{10} = -9.42477796076938$$
$$x_{11} = 40.8407044966673$$
$$x_{12} = 56.5486677646163$$
$$x_{13} = -56.5486677646163$$
$$x_{14} = 12.5663706143592$$
$$x_{15} = 43.9822971502571$$
$$x_{16} = 100.530964914873$$
$$x_{17} = -3.14159265358979$$
$$x_{18} = -15.707963267949$$
$$x_{19} = 59.6902604182061$$
$$x_{20} = 6.28318530717959$$
$$x_{21} = 9.42477796076938$$
$$x_{22} = -53.4070751110265$$
$$x_{23} = -47.1238898038469$$
$$x_{24} = -87.9645943005142$$
$$x_{25} = 69.1150383789755$$
$$x_{26} = 21.9911485751286$$
$$x_{27} = 87.9645943005142$$
$$x_{28} = 18.8495559215388$$
$$x_{29} = -84.8230016469244$$
$$x_{30} = -72.2566310325652$$
$$x_{31} = 25.1327412287183$$
$$x_{32} = 37.6991118430775$$
$$x_{33} = -25.1327412287183$$
$$x_{34} = 50.2654824574367$$
$$x_{35} = 34.5575191894877$$
$$x_{36} = -6.28318530717959$$
$$x_{37} = -65.9734457253857$$
$$x_{38} = -21.9911485751286$$
$$x_{39} = -62.8318530717959$$
$$x_{40} = 75.398223686155$$
$$x_{41} = 84.8230016469244$$
$$x_{42} = 53.4070751110265$$
$$x_{43} = 15.707963267949$$
$$x_{44} = -28.2743338823081$$
$$x_{45} = -91.106186954104$$
$$x_{46} = 47.1238898038469$$
$$x_{47} = 97.3893722612836$$
$$x_{48} = -69.1150383789755$$
$$x_{49} = 94.2477796076938$$
$$x_{50} = -18.8495559215388$$
$$x_{51} = -50.2654824574367$$
$$x_{52} = -37.6991118430775$$
$$x_{53} = -81.6814089933346$$
$$x_{54} = 62.8318530717959$$
$$x_{55} = 78.5398163397448$$
$$x_{56} = 31.4159265358979$$
$$x_{57} = -78.5398163397448$$
$$x_{58} = -40.8407044966673$$
$$x_{59} = -97.3893722612836$$
$$x_{60} = -75.398223686155$$
$$x_{61} = 91.106186954104$$
$$x_{62} = -12.5663706143592$$
$$x_{63} = -94.2477796076938$$
$$x_{64} = -34.5575191894877$$
Signos de extremos en los puntos:
0.0138395602688605*log(E) (72.25663103256524, 1 )
-0.01675315190441*log(E) (-59.69026041820607, 1 )
0.318309886183791*log(E) (3.141592653589793, 1 )
-0.0227364204416993*log(E) (-43.982297150257104, 1 )
0.0122426879301458*log(E) (81.68140899333463, 1 )
-0.00994718394324346*log(E) (-100.53096491487338, 1 )
0.0353677651315323*log(E) (28.274333882308138, 1 )
0.0151576136277996*log(E) (65.97344572538566, 1 )
-0.0318309886183791*log(E) (-31.41592653589793, 1 )
-0.106103295394597*log(E) (-9.42477796076938, 1 )
0.0244853758602916*log(E) (40.840704496667314, 1 )
0.0176838825657662*log(E) (56.548667764616276, 1 )
-0.0176838825657662*log(E) (-56.548667764616276, 1 )
0.0795774715459477*log(E) (12.566370614359172, 1 )
0.0227364204416993*log(E) (43.982297150257104, 1 )
0.00994718394324346*log(E) (100.53096491487338, 1 )
-0.318309886183791*log(E) (-3.141592653589793, 1 )
-0.0636619772367581*log(E) (-15.707963267948966, 1 )
0.01675315190441*log(E) (59.69026041820607, 1 )
0.159154943091895*log(E) (6.283185307179586, 1 )
0.106103295394597*log(E) (9.42477796076938, 1 )
-0.0187241109519877*log(E) (-53.40707511102649, 1 )
-0.0212206590789194*log(E) (-47.1238898038469, 1 )
-0.0113682102208497*log(E) (-87.96459430051421, 1 )
0.0144686311901723*log(E) (69.11503837897546, 1 )
0.0454728408833987*log(E) (21.991148575128552, 1 )
0.0113682102208497*log(E) (87.96459430051421, 1 )
0.0530516476972984*log(E) (18.84955592153876, 1 )
-0.0117892550438441*log(E) (-84.82300164692441, 1 )
-0.0138395602688605*log(E) (-72.25663103256524, 1 )
0.0397887357729738*log(E) (25.132741228718345, 1 )
0.0265258238486492*log(E) (37.69911184307752, 1 )
-0.0397887357729738*log(E) (-25.132741228718345, 1 )
0.0198943678864869*log(E) (50.26548245743669, 1 )
0.0289372623803446*log(E) (34.55751918948773, 1 )
-0.159154943091895*log(E) (-6.283185307179586, 1 )
-0.0151576136277996*log(E) (-65.97344572538566, 1 )
-0.0454728408833987*log(E) (-21.991148575128552, 1 )
-0.0159154943091895*log(E) (-62.83185307179586, 1 )
0.0132629119243246*log(E) (75.39822368615503, 1 )
0.0117892550438441*log(E) (84.82300164692441, 1 )
0.0187241109519877*log(E) (53.40707511102649, 1 )
0.0636619772367581*log(E) (15.707963267948966, 1 )
-0.0353677651315323*log(E) (-28.274333882308138, 1 )
-0.0109762029718549*log(E) (-91.106186954104, 1 )
0.0212206590789194*log(E) (47.1238898038469, 1 )
0.0102680608446384*log(E) (97.3893722612836, 1 )
-0.0144686311901723*log(E) (-69.11503837897546, 1 )
0.0106103295394597*log(E) (94.2477796076938, 1 )
-0.0530516476972984*log(E) (-18.84955592153876, 1 )
-0.0198943678864869*log(E) (-50.26548245743669, 1 )
-0.0265258238486492*log(E) (-37.69911184307752, 1 )
-0.0122426879301458*log(E) (-81.68140899333463, 1 )
0.0159154943091895*log(E) (62.83185307179586, 1 )
0.0127323954473516*log(E) (78.53981633974483, 1 )
0.0318309886183791*log(E) (31.41592653589793, 1 )
-0.0127323954473516*log(E) (-78.53981633974483, 1 )
-0.0244853758602916*log(E) (-40.840704496667314, 1 )
-0.0102680608446384*log(E) (-97.3893722612836, 1 )
-0.0132629119243246*log(E) (-75.39822368615503, 1 )
0.0109762029718549*log(E) (91.106186954104, 1 )
-0.0795774715459477*log(E) (-12.566370614359172, 1 )
-0.0106103295394597*log(E) (-94.2477796076938, 1 )
-0.0289372623803446*log(E) (-34.55751918948773, 1 )
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:
$$x_{1} = 72.2566310325652$$
$$x_{2} = 3.14159265358979$$
$$x_{3} = 81.6814089933346$$
$$x_{4} = 28.2743338823081$$
$$x_{5} = 65.9734457253857$$
$$x_{6} = 40.8407044966673$$
$$x_{7} = 56.5486677646163$$
$$x_{8} = 12.5663706143592$$
$$x_{9} = 43.9822971502571$$
$$x_{10} = 100.530964914873$$
$$x_{11} = 59.6902604182061$$
$$x_{12} = 6.28318530717959$$
$$x_{13} = 9.42477796076938$$
$$x_{14} = 69.1150383789755$$
$$x_{15} = 21.9911485751286$$
$$x_{16} = 87.9645943005142$$
$$x_{17} = 18.8495559215388$$
$$x_{18} = 25.1327412287183$$
$$x_{19} = 37.6991118430775$$
$$x_{20} = 50.2654824574367$$
$$x_{21} = 34.5575191894877$$
$$x_{22} = 75.398223686155$$
$$x_{23} = 84.8230016469244$$
$$x_{24} = 53.4070751110265$$
$$x_{25} = 15.707963267949$$
$$x_{26} = 47.1238898038469$$
$$x_{27} = 97.3893722612836$$
$$x_{28} = 94.2477796076938$$
$$x_{29} = 62.8318530717959$$
$$x_{30} = 78.5398163397448$$
$$x_{31} = 31.4159265358979$$
$$x_{32} = 91.106186954104$$
Puntos máximos de la función:
$$x_{32} = -59.6902604182061$$
$$x_{32} = -43.9822971502571$$
$$x_{32} = -100.530964914873$$
$$x_{32} = -31.4159265358979$$
$$x_{32} = -9.42477796076938$$
$$x_{32} = -56.5486677646163$$
$$x_{32} = -3.14159265358979$$
$$x_{32} = -15.707963267949$$
$$x_{32} = -53.4070751110265$$
$$x_{32} = -47.1238898038469$$
$$x_{32} = -87.9645943005142$$
$$x_{32} = -84.8230016469244$$
$$x_{32} = -72.2566310325652$$
$$x_{32} = -25.1327412287183$$
$$x_{32} = -6.28318530717959$$
$$x_{32} = -65.9734457253857$$
$$x_{32} = -21.9911485751286$$
$$x_{32} = -62.8318530717959$$
$$x_{32} = -28.2743338823081$$
$$x_{32} = -91.106186954104$$
$$x_{32} = -69.1150383789755$$
$$x_{32} = -18.8495559215388$$
$$x_{32} = -50.2654824574367$$
$$x_{32} = -37.6991118430775$$
$$x_{32} = -81.6814089933346$$
$$x_{32} = -78.5398163397448$$
$$x_{32} = -40.8407044966673$$
$$x_{32} = -97.3893722612836$$
$$x_{32} = -75.398223686155$$
$$x_{32} = -12.5663706143592$$
$$x_{32} = -94.2477796076938$$
$$x_{32} = -34.5575191894877$$
Decrece en los intervalos
$$\left[100.530964914873, \infty\right)$$
Crece en los intervalos
$$\left[-3.14159265358979, 3.14159265358979\right]$$
Asíntotas verticales
Hay:
$$x_{1} = 0$$
$$x_{2} = 1.5707963267949$$
$$x_{3} = 4.71238898038469$$
$$x_{1} = 0$$
$$x_{2} = 1.5707963267949$$
$$x_{3} = 4.71238898038469$$
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
$$\lim_{x \to -\infty} \left(\frac{1}{\cos^{2}{\left(x \right)}}\right)^{\frac{\log{\left(e \right)}}{x}} = 1$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = 1$$
$$\lim_{x \to \infty} \left(\frac{1}{\cos^{2}{\left(x \right)}}\right)^{\frac{\log{\left(e \right)}}{x}} = 1$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = 1$$
$$\lim_{x \to -\infty} \left(\frac{1}{\cos^{2}{\left(x \right)}}\right)^{\frac{\log{\left(e \right)}}{x}} = 1$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = 1$$
$$\lim_{x \to \infty} \left(\frac{1}{\cos^{2}{\left(x \right)}}\right)^{\frac{\log{\left(e \right)}}{x}} = 1$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = 1$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (1/(cos(x)^2))^(log(E)/x), dividida por x con x->+oo y x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\left|{\cos{\left(x \right)}}\right|^{- \frac{2 \log{\left(e \right)}}{x}}}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{x \to \infty}\left(\frac{\left|{\cos{\left(x \right)}}\right|^{- \frac{2 \log{\left(e \right)}}{x}}}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
$$\lim_{x \to -\infty}\left(\frac{\left|{\cos{\left(x \right)}}\right|^{- \frac{2 \log{\left(e \right)}}{x}}}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{x \to \infty}\left(\frac{\left|{\cos{\left(x \right)}}\right|^{- \frac{2 \log{\left(e \right)}}{x}}}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
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:
$$\left(\frac{1}{\cos^{2}{\left(x \right)}}\right)^{\frac{\log{\left(e \right)}}{x}} = \left|{\cos{\left(x \right)}}\right|^{\frac{2 \log{\left(e \right)}}{x}}$$
- No
$$\left(\frac{1}{\cos^{2}{\left(x \right)}}\right)^{\frac{\log{\left(e \right)}}{x}} = - \left|{\cos{\left(x \right)}}\right|^{\frac{2 \log{\left(e \right)}}{x}}$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$\left(\frac{1}{\cos^{2}{\left(x \right)}}\right)^{\frac{\log{\left(e \right)}}{x}} = \left|{\cos{\left(x \right)}}\right|^{\frac{2 \log{\left(e \right)}}{x}}$$
- No
$$\left(\frac{1}{\cos^{2}{\left(x \right)}}\right)^{\frac{\log{\left(e \right)}}{x}} = - \left|{\cos{\left(x \right)}}\right|^{\frac{2 \log{\left(e \right)}}{x}}$$
- No
es decir, función
no es
par ni impar