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
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- 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
-
(1/3)^x
-
x/(x-3)
-
x/(x^2-9)
-
Expresiones idénticas
- exp(log(sin(x))+(cos(cero .1x)))
- exponente de ( logaritmo de ( seno de (x)) más ( coseno de (0.1x)))
- exponente de ( logaritmo de ( seno de (x)) más ( coseno de (cero .1x)))
- explogsinx+cos0.1x
-
Expresiones semejantes
- exp(log(sin(x))-(cos(0.1x)))
- exp(log(sinx)+(cos(0.1x)))
-
Expresiones con funciones
- Exponente exp
- exp
- exp(x)/(-1-x*exp(x))
- exp(5*x*(285+sqrt(81365))/7)+exp(5*x*(285-sqrt(81365))/7)
- exp(4-x-3x^2)
- exp(x)/(-1-x^2)
- Logaritmo log
- log(x^2-5*x+6)+3
- log(sin(sqrt(x)))
- log(x^2/(x-1))
- log((x-1)/(x-2))
- log(2*x+3)
- Seno sin
- sin(x)+x
- sin(x)/sin(x+pi/4)
- sin(x)+cos(x)^2
- sin(x)*cos(x)^(2)
- sin(x)+9
- Coseno cos
- cos(x)-sqrt(3)*sin(x)
- cos(x)-3
- cos(x)/8+cos(3*x)+sin(3*x)
- cos(x^2+5)^(3)
- cos(4*x)/sin(8*x)
Gráfico de la función y = exp(log(sin(x))+(cos(0.1x)))
Solución
Ha introducido
[src]
/x \
log(sin(x)) + cos|--|
\10/
f(x) = e
$$f{\left(x \right)} = e^{\log{\left(\sin{\left(x \right)} \right)} + \cos{\left(\frac{x}{10} \right)}}$$
f = exp(log(sin(x)) + cos(x/10))
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:
$$e^{\log{\left(\sin{\left(x \right)} \right)} + \cos{\left(\frac{x}{10} \right)}} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución analítica
$$x_{1} = 0$$
$$x_{2} = \pi$$
Solución numérica
$$x_{1} = 59.6902604182061$$
$$x_{2} = -100.530964914873$$
$$x_{3} = -15.707963267949$$
$$x_{4} = -25.1327412287183$$
$$x_{5} = 84.8230016469244$$
$$x_{6} = 0$$
$$x_{7} = -75.398223686155$$
$$x_{8} = 97.3893722612836$$
$$x_{9} = -50.2654824574367$$
$$x_{10} = 744.557458900781$$
$$x_{11} = 81.6814089933346$$
$$x_{12} = -72.2566310325652$$
$$x_{13} = 91.106186954104$$
$$x_{14} = 50.2654824574367$$
$$x_{15} = -43.9822971502571$$
$$x_{16} = -37.6991118430775$$
$$x_{17} = 25.1327412287183$$
$$x_{18} = -65.9734457253857$$
$$x_{19} = -53.4070751110265$$
$$x_{20} = -18.8495559215388$$
$$x_{21} = -59.6902604182061$$
$$x_{22} = 15.707963267949$$
$$x_{23} = 9.42477796076938$$
$$x_{24} = 18.8495559215388$$
$$x_{25} = -56.5486677646163$$
$$x_{26} = -6.28318530717959$$
$$x_{27} = -62.8318530717959$$
$$x_{28} = 12.5663706143592$$
$$x_{29} = -119.380520836412$$
$$x_{30} = 56.5486677646163$$
$$x_{31} = 40.8407044966673$$
$$x_{32} = 3.14159265358979$$
$$x_{33} = -21.9911485751286$$
$$x_{34} = -84.8230016469244$$
$$x_{35} = 6.28318530717959$$
$$x_{36} = 69.1150383789755$$
$$x_{37} = 72.2566310325652$$
$$x_{38} = -78.5398163397448$$
$$x_{39} = 37.6991118430775$$
$$x_{40} = 21.9911485751286$$
$$x_{41} = 47.1238898038469$$
$$x_{42} = 34.5575191894877$$
$$x_{43} = -97.3893722612836$$
$$x_{44} = -31.4159265358979$$
$$x_{45} = 100.530964914873$$
$$x_{46} = -47.1238898038469$$
$$x_{47} = 28.2743338823081$$
$$x_{48} = 94.2477796076938$$
$$x_{49} = -40.8407044966673$$
$$x_{50} = -12.5663706143592$$
$$x_{51} = -34.5575191894877$$
$$x_{52} = -28.2743338823081$$
$$x_{53} = 78.5398163397448$$
$$x_{54} = -94.2477796076938$$
$$x_{55} = -91.106186954104$$
$$x_{56} = 43.9822971502571$$
$$x_{57} = 75.398223686155$$
$$x_{58} = 62.8318530717959$$
$$x_{59} = -3.14159265358979$$
$$x_{60} = 87.9645943005142$$
$$x_{61} = 53.4070751110265$$
$$x_{62} = -81.6814089933346$$
$$x_{63} = -87.9645943005142$$
$$x_{64} = 65.9734457253857$$
$$x_{65} = -69.1150383789755$$
$$x_{66} = 31.4159265358979$$
$$x_{67} = -9.42477796076938$$
o sea hay que resolver la ecuación:
$$e^{\log{\left(\sin{\left(x \right)} \right)} + \cos{\left(\frac{x}{10} \right)}} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución analítica
$$x_{1} = 0$$
$$x_{2} = \pi$$
Solución numérica
$$x_{1} = 59.6902604182061$$
$$x_{2} = -100.530964914873$$
$$x_{3} = -15.707963267949$$
$$x_{4} = -25.1327412287183$$
$$x_{5} = 84.8230016469244$$
$$x_{6} = 0$$
$$x_{7} = -75.398223686155$$
$$x_{8} = 97.3893722612836$$
$$x_{9} = -50.2654824574367$$
$$x_{10} = 744.557458900781$$
$$x_{11} = 81.6814089933346$$
$$x_{12} = -72.2566310325652$$
$$x_{13} = 91.106186954104$$
$$x_{14} = 50.2654824574367$$
$$x_{15} = -43.9822971502571$$
$$x_{16} = -37.6991118430775$$
$$x_{17} = 25.1327412287183$$
$$x_{18} = -65.9734457253857$$
$$x_{19} = -53.4070751110265$$
$$x_{20} = -18.8495559215388$$
$$x_{21} = -59.6902604182061$$
$$x_{22} = 15.707963267949$$
$$x_{23} = 9.42477796076938$$
$$x_{24} = 18.8495559215388$$
$$x_{25} = -56.5486677646163$$
$$x_{26} = -6.28318530717959$$
$$x_{27} = -62.8318530717959$$
$$x_{28} = 12.5663706143592$$
$$x_{29} = -119.380520836412$$
$$x_{30} = 56.5486677646163$$
$$x_{31} = 40.8407044966673$$
$$x_{32} = 3.14159265358979$$
$$x_{33} = -21.9911485751286$$
$$x_{34} = -84.8230016469244$$
$$x_{35} = 6.28318530717959$$
$$x_{36} = 69.1150383789755$$
$$x_{37} = 72.2566310325652$$
$$x_{38} = -78.5398163397448$$
$$x_{39} = 37.6991118430775$$
$$x_{40} = 21.9911485751286$$
$$x_{41} = 47.1238898038469$$
$$x_{42} = 34.5575191894877$$
$$x_{43} = -97.3893722612836$$
$$x_{44} = -31.4159265358979$$
$$x_{45} = 100.530964914873$$
$$x_{46} = -47.1238898038469$$
$$x_{47} = 28.2743338823081$$
$$x_{48} = 94.2477796076938$$
$$x_{49} = -40.8407044966673$$
$$x_{50} = -12.5663706143592$$
$$x_{51} = -34.5575191894877$$
$$x_{52} = -28.2743338823081$$
$$x_{53} = 78.5398163397448$$
$$x_{54} = -94.2477796076938$$
$$x_{55} = -91.106186954104$$
$$x_{56} = 43.9822971502571$$
$$x_{57} = 75.398223686155$$
$$x_{58} = 62.8318530717959$$
$$x_{59} = -3.14159265358979$$
$$x_{60} = 87.9645943005142$$
$$x_{61} = 53.4070751110265$$
$$x_{62} = -81.6814089933346$$
$$x_{63} = -87.9645943005142$$
$$x_{64} = 65.9734457253857$$
$$x_{65} = -69.1150383789755$$
$$x_{66} = 31.4159265358979$$
$$x_{67} = -9.42477796076938$$
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
$$e^{\cos{\left(\frac{x}{10} \right)}} \sin{\left(x \right)} \left(- \frac{\sin{\left(\frac{x}{10} \right)}}{10} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = -17.1801620751675$$
$$x_{2} = 95.8343740834416$$
$$x_{3} = 26.657763126617$$
$$x_{4} = -86.3227064018565$$
$$x_{5} = 51.9247428423613$$
$$x_{6} = 61.2765459489209$$
$$x_{7} = -80.0120151469633$$
$$x_{8} = 42.5007653239139$$
$$x_{9} = -4.66742138622181$$
$$x_{10} = -45.6516909966284$$
$$x_{11} = 99.0059430169747$$
$$x_{12} = 48.7929786559929$$
$$x_{13} = 1.55530712287499$$
$$x_{14} = -70.6157364717051$$
$$x_{15} = -83.1629408196778$$
$$x_{16} = 4.66742138622181$$
$$x_{17} = 23.4908533300607$$
$$x_{18} = 20.3310877478819$$
$$x_{19} = -10.9071102294346$$
$$x_{20} = -36.1740899451789$$
$$x_{21} = -89.4896161984129$$
$$x_{22} = 29.8293320601501$$
$$x_{23} = -29.8293320601501$$
$$x_{24} = -23.4908533300607$$
$$x_{25} = 7.78388339990927$$
$$x_{26} = 45.6516909966284$$
$$x_{27} = -20.3310877478819$$
$$x_{28} = -48.7929786559929$$
$$x_{29} = -14.0388744158029$$
$$x_{30} = -99.0059430169747$$
$$x_{31} = -26.657763126617$$
$$x_{32} = 14.0388744158029$$
$$x_{33} = -42.5007653239139$$
$$x_{34} = 17.1801620751675$$
$$x_{35} = -7.78388339990927$$
$$x_{36} = -92.661185131946$$
$$x_{37} = -102.172852813531$$
$$x_{38} = 80.0120151469633$$
$$x_{39} = 86.3227064018565$$
$$x_{40} = -51.9247428423613$$
$$x_{41} = -61.2765459489209$$
$$x_{42} = -95.8343740834416$$
$$x_{43} = 33.0025210116458$$
$$x_{44} = 55.0479696718866$$
$$x_{45} = 73.7389633012305$$
$$x_{46} = 10.9071102294346$$
$$x_{47} = -58.1644316855741$$
$$x_{48} = -76.8707274875988$$
$$x_{49} = 92.661185131946$$
$$x_{50} = -39.3409997417352$$
$$x_{51} = 105.33261839571$$
$$x_{52} = -1.55530712287499$$
$$x_{53} = 76.8707274875988$$
$$x_{54} = 67.4992744580177$$
$$x_{55} = -33.0025210116458$$
$$x_{56} = 39.3409997417352$$
$$x_{57} = -64.3871601946709$$
$$x_{58} = -73.7389633012305$$
$$x_{59} = 58.1644316855741$$
$$x_{60} = 64.3871601946709$$
$$x_{61} = -67.4992744580177$$
$$x_{62} = 70.6157364717051$$
$$x_{63} = -55.0479696718866$$
$$x_{64} = 89.4896161984129$$
$$x_{65} = 83.1629408196778$$
$$x_{66} = 36.1740899451789$$
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:
$$x_{1} = 61.2765459489209$$
$$x_{2} = 42.5007653239139$$
$$x_{3} = -45.6516909966284$$
$$x_{4} = 99.0059430169747$$
$$x_{5} = 48.7929786559929$$
$$x_{6} = -70.6157364717051$$
$$x_{7} = -83.1629408196778$$
$$x_{8} = 4.66742138622181$$
$$x_{9} = 23.4908533300607$$
$$x_{10} = -89.4896161984129$$
$$x_{11} = 29.8293320601501$$
$$x_{12} = -20.3310877478819$$
$$x_{13} = -14.0388744158029$$
$$x_{14} = -26.657763126617$$
$$x_{15} = 17.1801620751675$$
$$x_{16} = -7.78388339990927$$
$$x_{17} = -102.172852813531$$
$$x_{18} = 80.0120151469633$$
$$x_{19} = 86.3227064018565$$
$$x_{20} = -51.9247428423613$$
$$x_{21} = -95.8343740834416$$
$$x_{22} = 55.0479696718866$$
$$x_{23} = 73.7389633012305$$
$$x_{24} = 10.9071102294346$$
$$x_{25} = -58.1644316855741$$
$$x_{26} = -76.8707274875988$$
$$x_{27} = 92.661185131946$$
$$x_{28} = -39.3409997417352$$
$$x_{29} = 105.33261839571$$
$$x_{30} = -1.55530712287499$$
$$x_{31} = 67.4992744580177$$
$$x_{32} = -33.0025210116458$$
$$x_{33} = -64.3871601946709$$
$$x_{34} = 36.1740899451789$$
Puntos máximos de la función:
$$x_{34} = -17.1801620751675$$
$$x_{34} = 95.8343740834416$$
$$x_{34} = 26.657763126617$$
$$x_{34} = -86.3227064018565$$
$$x_{34} = 51.9247428423613$$
$$x_{34} = -80.0120151469633$$
$$x_{34} = -4.66742138622181$$
$$x_{34} = 1.55530712287499$$
$$x_{34} = 20.3310877478819$$
$$x_{34} = -10.9071102294346$$
$$x_{34} = -36.1740899451789$$
$$x_{34} = -29.8293320601501$$
$$x_{34} = -23.4908533300607$$
$$x_{34} = 7.78388339990927$$
$$x_{34} = 45.6516909966284$$
$$x_{34} = -48.7929786559929$$
$$x_{34} = -99.0059430169747$$
$$x_{34} = 14.0388744158029$$
$$x_{34} = -42.5007653239139$$
$$x_{34} = -92.661185131946$$
$$x_{34} = -61.2765459489209$$
$$x_{34} = 33.0025210116458$$
$$x_{34} = 76.8707274875988$$
$$x_{34} = 39.3409997417352$$
$$x_{34} = -73.7389633012305$$
$$x_{34} = 58.1644316855741$$
$$x_{34} = 64.3871601946709$$
$$x_{34} = -67.4992744580177$$
$$x_{34} = 70.6157364717051$$
$$x_{34} = -55.0479696718866$$
$$x_{34} = 89.4896161984129$$
$$x_{34} = 83.1629408196778$$
Decrece en los intervalos
$$\left[105.33261839571, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -102.172852813531\right]$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(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
$$e^{\cos{\left(\frac{x}{10} \right)}} \sin{\left(x \right)} \left(- \frac{\sin{\left(\frac{x}{10} \right)}}{10} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = -17.1801620751675$$
$$x_{2} = 95.8343740834416$$
$$x_{3} = 26.657763126617$$
$$x_{4} = -86.3227064018565$$
$$x_{5} = 51.9247428423613$$
$$x_{6} = 61.2765459489209$$
$$x_{7} = -80.0120151469633$$
$$x_{8} = 42.5007653239139$$
$$x_{9} = -4.66742138622181$$
$$x_{10} = -45.6516909966284$$
$$x_{11} = 99.0059430169747$$
$$x_{12} = 48.7929786559929$$
$$x_{13} = 1.55530712287499$$
$$x_{14} = -70.6157364717051$$
$$x_{15} = -83.1629408196778$$
$$x_{16} = 4.66742138622181$$
$$x_{17} = 23.4908533300607$$
$$x_{18} = 20.3310877478819$$
$$x_{19} = -10.9071102294346$$
$$x_{20} = -36.1740899451789$$
$$x_{21} = -89.4896161984129$$
$$x_{22} = 29.8293320601501$$
$$x_{23} = -29.8293320601501$$
$$x_{24} = -23.4908533300607$$
$$x_{25} = 7.78388339990927$$
$$x_{26} = 45.6516909966284$$
$$x_{27} = -20.3310877478819$$
$$x_{28} = -48.7929786559929$$
$$x_{29} = -14.0388744158029$$
$$x_{30} = -99.0059430169747$$
$$x_{31} = -26.657763126617$$
$$x_{32} = 14.0388744158029$$
$$x_{33} = -42.5007653239139$$
$$x_{34} = 17.1801620751675$$
$$x_{35} = -7.78388339990927$$
$$x_{36} = -92.661185131946$$
$$x_{37} = -102.172852813531$$
$$x_{38} = 80.0120151469633$$
$$x_{39} = 86.3227064018565$$
$$x_{40} = -51.9247428423613$$
$$x_{41} = -61.2765459489209$$
$$x_{42} = -95.8343740834416$$
$$x_{43} = 33.0025210116458$$
$$x_{44} = 55.0479696718866$$
$$x_{45} = 73.7389633012305$$
$$x_{46} = 10.9071102294346$$
$$x_{47} = -58.1644316855741$$
$$x_{48} = -76.8707274875988$$
$$x_{49} = 92.661185131946$$
$$x_{50} = -39.3409997417352$$
$$x_{51} = 105.33261839571$$
$$x_{52} = -1.55530712287499$$
$$x_{53} = 76.8707274875988$$
$$x_{54} = 67.4992744580177$$
$$x_{55} = -33.0025210116458$$
$$x_{56} = 39.3409997417352$$
$$x_{57} = -64.3871601946709$$
$$x_{58} = -73.7389633012305$$
$$x_{59} = 58.1644316855741$$
$$x_{60} = 64.3871601946709$$
$$x_{61} = -67.4992744580177$$
$$x_{62} = 70.6157364717051$$
$$x_{63} = -55.0479696718866$$
$$x_{64} = 89.4896161984129$$
$$x_{65} = 83.1629408196778$$
$$x_{66} = 36.1740899451789$$
Signos de extremos en los puntos:
(-17.180162075167463, 0.859368648952312)
(95.83437408344163, 0.372482669676623)
(26.657763126617002, 0.410669264992146)
(-86.32270640185654, 0.494310627412953)
(51.924742842361276, 1.58080905920172)
(61.27654594892088, -2.68534576903038)
(-80.01201514696332, 0.859368648952312)
(42.500765323913924, -0.63762281426652)
(-4.667421386221807, 2.44007215781738)
(-45.6516909966284, -0.859368648952312)
(99.00594301697473, -0.410669264992147)
(48.792978655992925, -1.17503329227924)
(1.5553071228749864, 2.68534576903038)
(-70.61573647170513, -2.03315173042758)
(-83.1629408196778, -0.63762281426652)
(4.667421386221807, -2.44007215781738)
(23.49085333006067, -0.494310627412953)
(20.331087747881938, 0.63762281426652)
(-10.90711022943459, 1.58080905920172)
(-36.174089945178864, 0.410669264992147)
(-89.48961619841286, -0.410669264992146)
(29.8293320601501, -0.372482669676622)
(-29.8293320601501, 0.372482669676622)
(-23.49085333006067, 0.494310627412953)
(7.783883399909268, 2.03315173042758)
(45.6516909966284, 0.859368648952312)
(-20.331087747881938, -0.63762281426652)
(-48.792978655992925, 1.17503329227924)
(-14.038874415802939, -1.17503329227924)
(-99.00594301697473, 0.410669264992147)
(-26.657763126617002, -0.410669264992146)
(14.038874415802939, 1.17503329227924)
(-42.500765323913924, 0.63762281426652)
(17.180162075167463, -0.859368648952312)
(-7.783883399909268, -2.03315173042758)
(-92.66118513194597, 0.372482669676623)
(-102.17285281353107, -0.494310627412953)
(80.01201514696332, -0.859368648952312)
(86.32270640185654, -0.494310627412953)
(-51.924742842361276, -1.58080905920172)
(-61.27654594892088, 2.68534576903038)
(-95.83437408344163, -0.372482669676623)
(33.00252101164576, 0.372482669676622)
(55.0479696718866, -2.03315173042758)
(73.73896330123046, -1.58080905920172)
(10.90711022943459, -1.58080905920172)
(-58.16443168557406, -2.44007215781738)
(-76.8707274875988, -1.17503329227924)
(92.66118513194597, -0.372482669676623)
(-39.340999741735196, -0.494310627412953)
(105.33261839570979, -0.637622814266521)
(-1.5553071228749864, -2.68534576903038)
(76.8707274875988, 1.17503329227924)
(67.49927445801767, -2.44007215781738)
(-33.00252101164576, -0.372482669676622)
(39.340999741735196, 0.494310627412953)
(-64.38716019467086, -2.68534576903037)
(-73.73896330123046, 1.58080905920172)
(58.16443168557406, 2.44007215781738)
(64.38716019467086, 2.68534576903037)
(-67.49927445801767, 2.44007215781738)
(70.61573647170513, 2.03315173042758)
(-55.0479696718866, 2.03315173042758)
(89.48961619841286, 0.410669264992146)
(83.1629408196778, 0.63762281426652)
(36.174089945178864, -0.410669264992147)
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:
$$x_{1} = 61.2765459489209$$
$$x_{2} = 42.5007653239139$$
$$x_{3} = -45.6516909966284$$
$$x_{4} = 99.0059430169747$$
$$x_{5} = 48.7929786559929$$
$$x_{6} = -70.6157364717051$$
$$x_{7} = -83.1629408196778$$
$$x_{8} = 4.66742138622181$$
$$x_{9} = 23.4908533300607$$
$$x_{10} = -89.4896161984129$$
$$x_{11} = 29.8293320601501$$
$$x_{12} = -20.3310877478819$$
$$x_{13} = -14.0388744158029$$
$$x_{14} = -26.657763126617$$
$$x_{15} = 17.1801620751675$$
$$x_{16} = -7.78388339990927$$
$$x_{17} = -102.172852813531$$
$$x_{18} = 80.0120151469633$$
$$x_{19} = 86.3227064018565$$
$$x_{20} = -51.9247428423613$$
$$x_{21} = -95.8343740834416$$
$$x_{22} = 55.0479696718866$$
$$x_{23} = 73.7389633012305$$
$$x_{24} = 10.9071102294346$$
$$x_{25} = -58.1644316855741$$
$$x_{26} = -76.8707274875988$$
$$x_{27} = 92.661185131946$$
$$x_{28} = -39.3409997417352$$
$$x_{29} = 105.33261839571$$
$$x_{30} = -1.55530712287499$$
$$x_{31} = 67.4992744580177$$
$$x_{32} = -33.0025210116458$$
$$x_{33} = -64.3871601946709$$
$$x_{34} = 36.1740899451789$$
Puntos máximos de la función:
$$x_{34} = -17.1801620751675$$
$$x_{34} = 95.8343740834416$$
$$x_{34} = 26.657763126617$$
$$x_{34} = -86.3227064018565$$
$$x_{34} = 51.9247428423613$$
$$x_{34} = -80.0120151469633$$
$$x_{34} = -4.66742138622181$$
$$x_{34} = 1.55530712287499$$
$$x_{34} = 20.3310877478819$$
$$x_{34} = -10.9071102294346$$
$$x_{34} = -36.1740899451789$$
$$x_{34} = -29.8293320601501$$
$$x_{34} = -23.4908533300607$$
$$x_{34} = 7.78388339990927$$
$$x_{34} = 45.6516909966284$$
$$x_{34} = -48.7929786559929$$
$$x_{34} = -99.0059430169747$$
$$x_{34} = 14.0388744158029$$
$$x_{34} = -42.5007653239139$$
$$x_{34} = -92.661185131946$$
$$x_{34} = -61.2765459489209$$
$$x_{34} = 33.0025210116458$$
$$x_{34} = 76.8707274875988$$
$$x_{34} = 39.3409997417352$$
$$x_{34} = -73.7389633012305$$
$$x_{34} = 58.1644316855741$$
$$x_{34} = 64.3871601946709$$
$$x_{34} = -67.4992744580177$$
$$x_{34} = 70.6157364717051$$
$$x_{34} = -55.0479696718866$$
$$x_{34} = 89.4896161984129$$
$$x_{34} = 83.1629408196778$$
Decrece en los intervalos
$$\left[105.33261839571, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -102.172852813531\right]$$
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
$$\lim_{x \to -\infty} e^{\log{\left(\sin{\left(x \right)} \right)} + \cos{\left(\frac{x}{10} \right)}} = \left\langle - e, e\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \left\langle - e, e\right\rangle$$
$$\lim_{x \to \infty} e^{\log{\left(\sin{\left(x \right)} \right)} + \cos{\left(\frac{x}{10} \right)}} = \left\langle - e, e\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \left\langle - e, e\right\rangle$$
$$\lim_{x \to -\infty} e^{\log{\left(\sin{\left(x \right)} \right)} + \cos{\left(\frac{x}{10} \right)}} = \left\langle - e, e\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \left\langle - e, e\right\rangle$$
$$\lim_{x \to \infty} e^{\log{\left(\sin{\left(x \right)} \right)} + \cos{\left(\frac{x}{10} \right)}} = \left\langle - e, e\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \left\langle - e, e\right\rangle$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función exp(log(sin(x)) + cos(x/10)), dividida por x con x->+oo y x ->-oo
$$\lim_{x \to -\infty}\left(\frac{e^{\cos{\left(\frac{x}{10} \right)}} \sin{\left(x \right)}}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{x \to \infty}\left(\frac{e^{\cos{\left(\frac{x}{10} \right)}} \sin{\left(x \right)}}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
$$\lim_{x \to -\infty}\left(\frac{e^{\cos{\left(\frac{x}{10} \right)}} \sin{\left(x \right)}}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{x \to \infty}\left(\frac{e^{\cos{\left(\frac{x}{10} \right)}} \sin{\left(x \right)}}{x}\right) = 0$$
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:
$$e^{\log{\left(\sin{\left(x \right)} \right)} + \cos{\left(\frac{x}{10} \right)}} = - e^{\cos{\left(\frac{x}{10} \right)}} \sin{\left(x \right)}$$
- No
$$e^{\log{\left(\sin{\left(x \right)} \right)} + \cos{\left(\frac{x}{10} \right)}} = e^{\cos{\left(\frac{x}{10} \right)}} \sin{\left(x \right)}$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$e^{\log{\left(\sin{\left(x \right)} \right)} + \cos{\left(\frac{x}{10} \right)}} = - e^{\cos{\left(\frac{x}{10} \right)}} \sin{\left(x \right)}$$
- No
$$e^{\log{\left(\sin{\left(x \right)} \right)} + \cos{\left(\frac{x}{10} \right)}} = e^{\cos{\left(\frac{x}{10} \right)}} \sin{\left(x \right)}$$
- No
es decir, función
no es
par ni impar