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- Puntos de cruce de las funciones
-
¿Cómo usar?
- Gráfico de la función y =:
-
(x^3)/
-
x^3-cos(x)-sin(x)-6*x
-
x^3-9*x^2+24*x
-
x^3*(cos(log(x))+sin(log(x)))
-
Expresiones idénticas
- uno / dos *(e^(sin(dos *x))+cos(dos *x)-log(sqrt(tres)))
- 1 dividir por 2 multiplicar por (e en el grado ( seno de (2 multiplicar por x)) más coseno de (2 multiplicar por x) menos logaritmo de ( raíz cuadrada de (3)))
- uno dividir por dos multiplicar por (e en el grado ( seno de (dos multiplicar por x)) más coseno de (dos multiplicar por x) menos logaritmo de ( raíz cuadrada de (tres)))
- 1/2*(e^(sin(2*x))+cos(2*x)-log(√(3)))
- 1/2*(e(sin(2*x))+cos(2*x)-log(sqrt(3)))
- 1/2*esin2*x+cos2*x-logsqrt3
- 1/2(e^(sin(2x))+cos(2x)-log(sqrt(3)))
- 1/2(e(sin(2x))+cos(2x)-log(sqrt(3)))
- 1/2esin2x+cos2x-logsqrt3
- 1/2e^sin2x+cos2x-logsqrt3
- 1 dividir por 2*(e^(sin(2*x))+cos(2*x)-log(sqrt(3)))
-
Expresiones semejantes
- 1/2*(e^(sin(2*x))-cos(2*x)-log(sqrt(3)))
- 1/2*(e^(sin(2*x))+cos(2*x)+log(sqrt(3)))
Gráfico de la función y = 1/2*(e^(sin(2*x))+cos(2*x)-log(sqrt(3)))
Solución
Ha introducido
[src]
sin(2*x) / ___\
E + cos(2*x) - log\\/ 3 /
f(x) = ---------------------------------
2
$$f{\left(x \right)} = \frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2}$$
f = (E^sin(2*x) + cos(2*x) - log(sqrt(3)))/2
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:
$$\frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = 71.559521804308$$
$$x_{2} = 64.2042970386951$$
$$x_{3} = -19.546665149796$$
$$x_{4} = -82.3785182215919$$
$$x_{5} = 49.5683732291795$$
$$x_{6} = -23.7602972618191$$
$$x_{7} = 2.44448342533256$$
$$x_{8} = 33.8604099612305$$
$$x_{9} = 26.5051851956176$$
$$x_{10} = 42.2131484635666$$
$$x_{11} = -94.944888835951$$
$$x_{12} = -25.8298504569756$$
$$x_{13} = -98.0864814895408$$
$$x_{14} = 92.4786309210033$$
$$x_{15} = 70.4874823458747$$
$$x_{16} = 13.9388145812584$$
$$x_{17} = -85.5201108751817$$
$$x_{18} = -89.7337429872047$$
$$x_{19} = -32.1130357641552$$
$$x_{20} = 90.4090777258468$$
$$x_{21} = 79.9122603066441$$
$$x_{22} = 65.2763364971284$$
$$x_{23} = 21.2940393468713$$
$$x_{24} = 43.2851879219999$$
$$x_{25} = 27.5772246540509$$
$$x_{26} = 37.0020026148203$$
$$x_{27} = 93.5506703794366$$
$$x_{28} = -47.8209990321041$$
$$x_{29} = -76.0953329144123$$
$$x_{30} = 101.903408881773$$
$$x_{31} = -42.6098531833578$$
$$x_{32} = -1.76914868669053$$
$$x_{33} = -28.9714431105654$$
$$x_{34} = -30.0434825689987$$
$$x_{35} = -6104.81163515323$$
$$x_{36} = -74.0257797192558$$
$$x_{37} = -91.8032961823612$$
$$x_{38} = -44.6794063785143$$
$$x_{39} = 68.4179291507182$$
$$x_{40} = 4.51403662048906$$
$$x_{41} = 46.4267805755897$$
$$x_{42} = -41.5378137249245$$
$$x_{43} = 87.267485072257$$
$$x_{44} = -99.1585209479741$$
$$x_{45} = -39.468260529768$$
$$x_{46} = -54.1041843392837$$
$$x_{47} = 20.221999888438$$
$$x_{48} = 24.4356320004611$$
$$x_{49} = 84.1258924186672$$
$$x_{50} = 55.851558536359$$
$$x_{51} = -38.3962210713348$$
$$x_{52} = -69.8121476072327$$
$$x_{53} = -88.6617035287715$$
$$x_{54} = 5.58607607892235$$
$$x_{55} = 48.4963337707462$$
$$x_{56} = 15.0108540396917$$
$$x_{57} = -60.3873696464633$$
$$x_{58} = -0.697109228257237$$
$$x_{59} = 99.8338556866161$$
$$x_{60} = -96.0169282943843$$
$$x_{61} = -17.4771119546395$$
$$x_{62} = -66.6705549536429$$
$$x_{63} = 11.8692613861019$$
$$x_{64} = -16.4050724962062$$
$$x_{65} = 86.1954456138237$$
$$x_{66} = -72.9537402608225$$
$$x_{67} = -50.9625916856939$$
$$x_{68} = -52.0346311441272$$
$$x_{69} = 35.929963156387$$
$$x_{70} = -67.7425944120762$$
$$x_{71} = 18.1524466932815$$
$$x_{72} = -63.5289623000531$$
$$x_{73} = -10.1218871890266$$
$$x_{74} = -3.83870188184703$$
$$x_{75} = -22.6882578033858$$
$$x_{76} = -45.7514458369476$$
$$x_{77} = -83.4505576800252$$
$$x_{78} = 40.1435952684101$$
$$x_{79} = 57.9211117315155$$
$$x_{80} = -8.05233399387011$$
$$x_{81} = -6.98029453543682$$
$$x_{82} = -469.86645407157$$
$$x_{83} = 58.9931511899488$$
$$x_{84} = 77.8427071114876$$
$$x_{85} = 62.1347438435386$$
$$x_{86} = 54.7795190779257$$
$$x_{87} = -61.4594091048966$$
o sea hay que resolver la ecuación:
$$\frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = 71.559521804308$$
$$x_{2} = 64.2042970386951$$
$$x_{3} = -19.546665149796$$
$$x_{4} = -82.3785182215919$$
$$x_{5} = 49.5683732291795$$
$$x_{6} = -23.7602972618191$$
$$x_{7} = 2.44448342533256$$
$$x_{8} = 33.8604099612305$$
$$x_{9} = 26.5051851956176$$
$$x_{10} = 42.2131484635666$$
$$x_{11} = -94.944888835951$$
$$x_{12} = -25.8298504569756$$
$$x_{13} = -98.0864814895408$$
$$x_{14} = 92.4786309210033$$
$$x_{15} = 70.4874823458747$$
$$x_{16} = 13.9388145812584$$
$$x_{17} = -85.5201108751817$$
$$x_{18} = -89.7337429872047$$
$$x_{19} = -32.1130357641552$$
$$x_{20} = 90.4090777258468$$
$$x_{21} = 79.9122603066441$$
$$x_{22} = 65.2763364971284$$
$$x_{23} = 21.2940393468713$$
$$x_{24} = 43.2851879219999$$
$$x_{25} = 27.5772246540509$$
$$x_{26} = 37.0020026148203$$
$$x_{27} = 93.5506703794366$$
$$x_{28} = -47.8209990321041$$
$$x_{29} = -76.0953329144123$$
$$x_{30} = 101.903408881773$$
$$x_{31} = -42.6098531833578$$
$$x_{32} = -1.76914868669053$$
$$x_{33} = -28.9714431105654$$
$$x_{34} = -30.0434825689987$$
$$x_{35} = -6104.81163515323$$
$$x_{36} = -74.0257797192558$$
$$x_{37} = -91.8032961823612$$
$$x_{38} = -44.6794063785143$$
$$x_{39} = 68.4179291507182$$
$$x_{40} = 4.51403662048906$$
$$x_{41} = 46.4267805755897$$
$$x_{42} = -41.5378137249245$$
$$x_{43} = 87.267485072257$$
$$x_{44} = -99.1585209479741$$
$$x_{45} = -39.468260529768$$
$$x_{46} = -54.1041843392837$$
$$x_{47} = 20.221999888438$$
$$x_{48} = 24.4356320004611$$
$$x_{49} = 84.1258924186672$$
$$x_{50} = 55.851558536359$$
$$x_{51} = -38.3962210713348$$
$$x_{52} = -69.8121476072327$$
$$x_{53} = -88.6617035287715$$
$$x_{54} = 5.58607607892235$$
$$x_{55} = 48.4963337707462$$
$$x_{56} = 15.0108540396917$$
$$x_{57} = -60.3873696464633$$
$$x_{58} = -0.697109228257237$$
$$x_{59} = 99.8338556866161$$
$$x_{60} = -96.0169282943843$$
$$x_{61} = -17.4771119546395$$
$$x_{62} = -66.6705549536429$$
$$x_{63} = 11.8692613861019$$
$$x_{64} = -16.4050724962062$$
$$x_{65} = 86.1954456138237$$
$$x_{66} = -72.9537402608225$$
$$x_{67} = -50.9625916856939$$
$$x_{68} = -52.0346311441272$$
$$x_{69} = 35.929963156387$$
$$x_{70} = -67.7425944120762$$
$$x_{71} = 18.1524466932815$$
$$x_{72} = -63.5289623000531$$
$$x_{73} = -10.1218871890266$$
$$x_{74} = -3.83870188184703$$
$$x_{75} = -22.6882578033858$$
$$x_{76} = -45.7514458369476$$
$$x_{77} = -83.4505576800252$$
$$x_{78} = 40.1435952684101$$
$$x_{79} = 57.9211117315155$$
$$x_{80} = -8.05233399387011$$
$$x_{81} = -6.98029453543682$$
$$x_{82} = -469.86645407157$$
$$x_{83} = 58.9931511899488$$
$$x_{84} = 77.8427071114876$$
$$x_{85} = 62.1347438435386$$
$$x_{86} = 54.7795190779257$$
$$x_{87} = -61.4594091048966$$
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
$$e^{\sin{\left(2 x \right)}} \cos{\left(2 x \right)} - \sin{\left(2 x \right)} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 25.7302797812042$$
$$x_{2} = 107.411688774539$$
$$x_{3} = -51.5666560890822$$
$$x_{4} = -64.1330267034414$$
$$x_{5} = -49.6679439049508$$
$$x_{6} = 96.0881986296381$$
$$x_{7} = -57.8498413962618$$
$$x_{8} = 67.81386474733$$
$$x_{9} = 60.2877989706919$$
$$x_{10} = -87.3670557480283$$
$$x_{11} = -11.9688320618733$$
$$x_{12} = 47.7214283563328$$
$$x_{13} = 74.0970500545096$$
$$x_{14} = 32.0134650883838$$
$$x_{15} = 64.6722720937402$$
$$x_{16} = -2008.77887927552$$
$$x_{17} = -84.2254630944386$$
$$x_{18} = 54.0046136635124$$
$$x_{19} = 0.597538552485871$$
$$x_{20} = 91.7037255065899$$
$$x_{21} = -13.8675442460047$$
$$x_{22} = 3.73913120607566$$
$$x_{23} = -48.4250634354924$$
$$x_{24} = 23.8315675970729$$
$$x_{25} = -92.4073605857495$$
$$x_{26} = -73.5578046642107$$
$$x_{27} = 1.8404190219443$$
$$x_{28} = -39.000285474723$$
$$x_{29} = -79.8409899713903$$
$$x_{30} = -7.58435893882508$$
$$x_{31} = -33.9599806370019$$
$$x_{32} = -20.1507295531843$$
$$x_{33} = 75.9957622386409$$
$$x_{34} = -70.4162120106209$$
$$x_{35} = -77.942277787259$$
$$x_{36} = 89.8050133224585$$
$$x_{37} = -5.68564675469371$$
$$x_{38} = -18.2520173690529$$
$$x_{39} = 52.105901479381$$
$$x_{40} = -42.1418781283128$$
$$x_{41} = -1.30117363164549$$
$$x_{42} = 30.1147529042524$$
$$x_{43} = 86.6634206688687$$
$$x_{44} = -23.292322206774$$
$$x_{45} = 82.2789475458205$$
$$x_{46} = 104.270096120949$$
$$x_{47} = -90.5086484016181$$
$$x_{48} = 42.6811235186116$$
$$x_{49} = 20.6899749434831$$
$$x_{50} = -99.9334263623875$$
$$x_{51} = -35.8586928211332$$
$$x_{52} = -95.5489532393393$$
$$x_{53} = -67.2746193570312$$
$$x_{54} = -93.6502410552079$$
$$x_{55} = 14.4067896363035$$
$$x_{56} = -111.256916507288$$
$$x_{57} = 58.3890867865606$$
$$x_{58} = 97.9869108137695$$
$$x_{59} = -40.2431659441814$$
$$x_{60} = -29.5755075139536$$
$$x_{61} = 16.3055018204348$$
$$x_{62} = -54.708248742672$$
$$x_{63} = -55.9511292121304$$
$$x_{64} = 8.12360432912389$$
$$x_{65} = -27.6767953298223$$
$$x_{66} = -71.6590924800794$$
$$x_{67} = -62.23431451931$$
$$x_{68} = -86.1241752785699$$
$$x_{69} = 36.397938211432$$
$$x_{70} = 38.2966503955634$$
$$x_{71} = 45.8227161722014$$
$$x_{72} = 80.3802353616891$$
$$x_{73} = 10.0223165132553$$
$$x_{74} = -45.2834707819026$$
$$x_{75} = 69.7125769314613$$
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:
$$x_{1} = -51.5666560890822$$
$$x_{2} = -64.1330267034414$$
$$x_{3} = 96.0881986296381$$
$$x_{4} = -57.8498413962618$$
$$x_{5} = 67.81386474733$$
$$x_{6} = 74.0970500545096$$
$$x_{7} = 64.6722720937402$$
$$x_{8} = -2008.77887927552$$
$$x_{9} = -13.8675442460047$$
$$x_{10} = -48.4250634354924$$
$$x_{11} = 23.8315675970729$$
$$x_{12} = -92.4073605857495$$
$$x_{13} = -73.5578046642107$$
$$x_{14} = 1.8404190219443$$
$$x_{15} = -39.000285474723$$
$$x_{16} = -79.8409899713903$$
$$x_{17} = -7.58435893882508$$
$$x_{18} = -20.1507295531843$$
$$x_{19} = -70.4162120106209$$
$$x_{20} = 89.8050133224585$$
$$x_{21} = 52.105901479381$$
$$x_{22} = -42.1418781283128$$
$$x_{23} = -1.30117363164549$$
$$x_{24} = 30.1147529042524$$
$$x_{25} = 86.6634206688687$$
$$x_{26} = -23.292322206774$$
$$x_{27} = 42.6811235186116$$
$$x_{28} = 20.6899749434831$$
$$x_{29} = -35.8586928211332$$
$$x_{30} = -95.5489532393393$$
$$x_{31} = -67.2746193570312$$
$$x_{32} = 14.4067896363035$$
$$x_{33} = -111.256916507288$$
$$x_{34} = 58.3890867865606$$
$$x_{35} = -29.5755075139536$$
$$x_{36} = -54.708248742672$$
$$x_{37} = 8.12360432912389$$
$$x_{38} = -86.1241752785699$$
$$x_{39} = 36.397938211432$$
$$x_{40} = 45.8227161722014$$
$$x_{41} = 80.3802353616891$$
$$x_{42} = -45.2834707819026$$
Puntos máximos de la función:
$$x_{42} = 25.7302797812042$$
$$x_{42} = 107.411688774539$$
$$x_{42} = -49.6679439049508$$
$$x_{42} = 60.2877989706919$$
$$x_{42} = -87.3670557480283$$
$$x_{42} = -11.9688320618733$$
$$x_{42} = 47.7214283563328$$
$$x_{42} = 32.0134650883838$$
$$x_{42} = -84.2254630944386$$
$$x_{42} = 54.0046136635124$$
$$x_{42} = 0.597538552485871$$
$$x_{42} = 91.7037255065899$$
$$x_{42} = 3.73913120607566$$
$$x_{42} = -33.9599806370019$$
$$x_{42} = 75.9957622386409$$
$$x_{42} = -77.942277787259$$
$$x_{42} = -5.68564675469371$$
$$x_{42} = -18.2520173690529$$
$$x_{42} = 82.2789475458205$$
$$x_{42} = 104.270096120949$$
$$x_{42} = -90.5086484016181$$
$$x_{42} = -99.9334263623875$$
$$x_{42} = -93.6502410552079$$
$$x_{42} = 97.9869108137695$$
$$x_{42} = -40.2431659441814$$
$$x_{42} = 16.3055018204348$$
$$x_{42} = -55.9511292121304$$
$$x_{42} = -27.6767953298223$$
$$x_{42} = -71.6590924800794$$
$$x_{42} = -62.23431451931$$
$$x_{42} = 38.2966503955634$$
$$x_{42} = 10.0223165132553$$
$$x_{42} = 69.7125769314613$$
Decrece en los intervalos
$$\left[96.0881986296381, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -2008.77887927552\right]$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(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
$$e^{\sin{\left(2 x \right)}} \cos{\left(2 x \right)} - \sin{\left(2 x \right)} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 25.7302797812042$$
$$x_{2} = 107.411688774539$$
$$x_{3} = -51.5666560890822$$
$$x_{4} = -64.1330267034414$$
$$x_{5} = -49.6679439049508$$
$$x_{6} = 96.0881986296381$$
$$x_{7} = -57.8498413962618$$
$$x_{8} = 67.81386474733$$
$$x_{9} = 60.2877989706919$$
$$x_{10} = -87.3670557480283$$
$$x_{11} = -11.9688320618733$$
$$x_{12} = 47.7214283563328$$
$$x_{13} = 74.0970500545096$$
$$x_{14} = 32.0134650883838$$
$$x_{15} = 64.6722720937402$$
$$x_{16} = -2008.77887927552$$
$$x_{17} = -84.2254630944386$$
$$x_{18} = 54.0046136635124$$
$$x_{19} = 0.597538552485871$$
$$x_{20} = 91.7037255065899$$
$$x_{21} = -13.8675442460047$$
$$x_{22} = 3.73913120607566$$
$$x_{23} = -48.4250634354924$$
$$x_{24} = 23.8315675970729$$
$$x_{25} = -92.4073605857495$$
$$x_{26} = -73.5578046642107$$
$$x_{27} = 1.8404190219443$$
$$x_{28} = -39.000285474723$$
$$x_{29} = -79.8409899713903$$
$$x_{30} = -7.58435893882508$$
$$x_{31} = -33.9599806370019$$
$$x_{32} = -20.1507295531843$$
$$x_{33} = 75.9957622386409$$
$$x_{34} = -70.4162120106209$$
$$x_{35} = -77.942277787259$$
$$x_{36} = 89.8050133224585$$
$$x_{37} = -5.68564675469371$$
$$x_{38} = -18.2520173690529$$
$$x_{39} = 52.105901479381$$
$$x_{40} = -42.1418781283128$$
$$x_{41} = -1.30117363164549$$
$$x_{42} = 30.1147529042524$$
$$x_{43} = 86.6634206688687$$
$$x_{44} = -23.292322206774$$
$$x_{45} = 82.2789475458205$$
$$x_{46} = 104.270096120949$$
$$x_{47} = -90.5086484016181$$
$$x_{48} = 42.6811235186116$$
$$x_{49} = 20.6899749434831$$
$$x_{50} = -99.9334263623875$$
$$x_{51} = -35.8586928211332$$
$$x_{52} = -95.5489532393393$$
$$x_{53} = -67.2746193570312$$
$$x_{54} = -93.6502410552079$$
$$x_{55} = 14.4067896363035$$
$$x_{56} = -111.256916507288$$
$$x_{57} = 58.3890867865606$$
$$x_{58} = 97.9869108137695$$
$$x_{59} = -40.2431659441814$$
$$x_{60} = -29.5755075139536$$
$$x_{61} = 16.3055018204348$$
$$x_{62} = -54.708248742672$$
$$x_{63} = -55.9511292121304$$
$$x_{64} = 8.12360432912389$$
$$x_{65} = -27.6767953298223$$
$$x_{66} = -71.6590924800794$$
$$x_{67} = -62.23431451931$$
$$x_{68} = -86.1241752785699$$
$$x_{69} = 36.397938211432$$
$$x_{70} = 38.2966503955634$$
$$x_{71} = 45.8227161722014$$
$$x_{72} = 80.3802353616891$$
$$x_{73} = 10.0223165132553$$
$$x_{74} = -45.2834707819026$$
$$x_{75} = 69.7125769314613$$
Signos de extremos en los puntos:
/ ___\
log\\/ 3 /
(25.730279781204217, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(107.41168877453885, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-51.56665608908219, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-64.13302670344136, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-49.66794390495082, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(96.0881986296381, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-57.84984139626177, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(67.81386474732996, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(60.287798970691945, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-87.36705574802833, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-11.968832061873302, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(47.72142835633277, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(74.09705005450955, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(32.0134650883838, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(64.67227209374016, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-2008.7788792755234, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-84.22546309443855, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(54.00461366351236, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(0.5975385524858713, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(91.70372550658988, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-13.867544246004664, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(3.7391312060756645, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-48.42506343549239, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(23.831567597072855, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-92.4073605857495, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-73.55780466421074, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(1.840419021944301, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-39.000285474723015, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-79.84098997139033, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-7.584358938825079, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-33.959980637001856, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-20.150729553184252, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(75.9957622386409, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-70.41621201062094, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-77.94227778725896, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(89.8050133224585, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-5.685646754693715, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-18.252017369052886, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(52.10590147938099, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-42.141878128312804, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-1.3011736316454923, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(30.11475290425244, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(86.66342066886872, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-23.292322206774045, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(82.2789475458205, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(104.27009612094905, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-90.50864840161813, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(42.681123518611614, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(20.68997494348306, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-99.93342636238751, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-35.85869282113322, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-95.54895323933928, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-67.27461935703116, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-93.65024105520793, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(14.406789636303474, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-111.25691650728825, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(58.38908678656058, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(97.98691081376946, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-40.24316594418144, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-29.57550751395363, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(16.305501820434838, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-54.70824874267198, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-55.951129212130404, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(8.123604329123888, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(-27.67679532982227, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-71.65909248007938, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-62.23431451930999, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-86.12417527856991, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(36.39793821143203, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(38.29665039556339, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(45.8227161722014, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(80.38023536168913, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(10.022316513255252, 1.45103461121082 - ----------)
2 / ___\
log\\/ 3 /
(-45.2834707819026, -0.129846037665657 - ----------)
2 / ___\
log\\/ 3 /
(69.71257693146133, 1.45103461121082 - ----------)
2 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:
$$x_{1} = -51.5666560890822$$
$$x_{2} = -64.1330267034414$$
$$x_{3} = 96.0881986296381$$
$$x_{4} = -57.8498413962618$$
$$x_{5} = 67.81386474733$$
$$x_{6} = 74.0970500545096$$
$$x_{7} = 64.6722720937402$$
$$x_{8} = -2008.77887927552$$
$$x_{9} = -13.8675442460047$$
$$x_{10} = -48.4250634354924$$
$$x_{11} = 23.8315675970729$$
$$x_{12} = -92.4073605857495$$
$$x_{13} = -73.5578046642107$$
$$x_{14} = 1.8404190219443$$
$$x_{15} = -39.000285474723$$
$$x_{16} = -79.8409899713903$$
$$x_{17} = -7.58435893882508$$
$$x_{18} = -20.1507295531843$$
$$x_{19} = -70.4162120106209$$
$$x_{20} = 89.8050133224585$$
$$x_{21} = 52.105901479381$$
$$x_{22} = -42.1418781283128$$
$$x_{23} = -1.30117363164549$$
$$x_{24} = 30.1147529042524$$
$$x_{25} = 86.6634206688687$$
$$x_{26} = -23.292322206774$$
$$x_{27} = 42.6811235186116$$
$$x_{28} = 20.6899749434831$$
$$x_{29} = -35.8586928211332$$
$$x_{30} = -95.5489532393393$$
$$x_{31} = -67.2746193570312$$
$$x_{32} = 14.4067896363035$$
$$x_{33} = -111.256916507288$$
$$x_{34} = 58.3890867865606$$
$$x_{35} = -29.5755075139536$$
$$x_{36} = -54.708248742672$$
$$x_{37} = 8.12360432912389$$
$$x_{38} = -86.1241752785699$$
$$x_{39} = 36.397938211432$$
$$x_{40} = 45.8227161722014$$
$$x_{41} = 80.3802353616891$$
$$x_{42} = -45.2834707819026$$
Puntos máximos de la función:
$$x_{42} = 25.7302797812042$$
$$x_{42} = 107.411688774539$$
$$x_{42} = -49.6679439049508$$
$$x_{42} = 60.2877989706919$$
$$x_{42} = -87.3670557480283$$
$$x_{42} = -11.9688320618733$$
$$x_{42} = 47.7214283563328$$
$$x_{42} = 32.0134650883838$$
$$x_{42} = -84.2254630944386$$
$$x_{42} = 54.0046136635124$$
$$x_{42} = 0.597538552485871$$
$$x_{42} = 91.7037255065899$$
$$x_{42} = 3.73913120607566$$
$$x_{42} = -33.9599806370019$$
$$x_{42} = 75.9957622386409$$
$$x_{42} = -77.942277787259$$
$$x_{42} = -5.68564675469371$$
$$x_{42} = -18.2520173690529$$
$$x_{42} = 82.2789475458205$$
$$x_{42} = 104.270096120949$$
$$x_{42} = -90.5086484016181$$
$$x_{42} = -99.9334263623875$$
$$x_{42} = -93.6502410552079$$
$$x_{42} = 97.9869108137695$$
$$x_{42} = -40.2431659441814$$
$$x_{42} = 16.3055018204348$$
$$x_{42} = -55.9511292121304$$
$$x_{42} = -27.6767953298223$$
$$x_{42} = -71.6590924800794$$
$$x_{42} = -62.23431451931$$
$$x_{42} = 38.2966503955634$$
$$x_{42} = 10.0223165132553$$
$$x_{42} = 69.7125769314613$$
Decrece en los intervalos
$$\left[96.0881986296381, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -2008.77887927552\right]$$
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
segunda derivada
$$2 \left(- e^{\sin{\left(2 x \right)}} \sin{\left(2 x \right)} + e^{\sin{\left(2 x \right)}} \cos^{2}{\left(2 x \right)} - \cos{\left(2 x \right)}\right) = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 96.8360106018888$$
$$x_{2} = 81.6814092797807$$
$$x_{3} = 28.2743338676393$$
$$x_{4} = 49.7121207980419$$
$$x_{5} = -79.0931779991396$$
$$x_{6} = -41.3940661560621$$
$$x_{7} = -28.2743336158059$$
$$x_{8} = 15.7079635439569$$
$$x_{9} = 19.9963345057749$$
$$x_{10} = 4.28837123782592$$
$$x_{11} = -83.6762230626883$$
$$x_{12} = -23.9859626444822$$
$$x_{13} = -47.6772514632417$$
$$x_{14} = -67.9682597947393$$
$$x_{15} = -25.6861028881131$$
$$x_{16} = 87.9645943415359$$
$$x_{17} = 63.978631656032$$
$$x_{18} = 74.8448620267603$$
$$x_{19} = 70.2618169632116$$
$$x_{20} = -69.6684000383702$$
$$x_{21} = 55.9953061052215$$
$$x_{22} = -87.9645943455885$$
$$x_{23} = 2.58823099419503$$
$$x_{24} = -94.247779358601$$
$$x_{25} = -100.530965007034$$
$$x_{26} = 48.270668388083$$
$$x_{27} = -352.411738861452$$
$$x_{28} = -40.8407044595488$$
$$x_{29} = 59.6902607017326$$
$$x_{30} = 12.0130089549644$$
$$x_{31} = -53.9604367704212$$
$$x_{32} = -91.6595486134988$$
$$x_{33} = 50.2654824473634$$
$$x_{34} = -59.6902604436943$$
$$x_{35} = 24.5793795693236$$
$$x_{36} = 40.2873428372725$$
$$x_{37} = -45.9771112196108$$
$$x_{38} = 85.9697802311605$$
$$x_{39} = 30.8625648765032$$
$$x_{40} = -6.28318503569359$$
$$x_{41} = 94.247779609375$$
$$x_{42} = 26.2795198129545$$
$$x_{43} = -97.389372310019$$
$$x_{44} = 62.2784914124011$$
$$x_{45} = -19.4029175809335$$
$$x_{46} = -78.5398167377463$$
$$x_{47} = 99.9776032554786$$
$$x_{48} = -37.6991118670078$$
$$x_{49} = 69.1150383073985$$
$$x_{50} = -13.1197322737539$$
$$x_{51} = -65.9734457586377$$
$$x_{52} = -31.9692881952927$$
$$x_{53} = 52.8537134516317$$
$$x_{54} = 84.2696399875297$$
$$x_{55} = 72.256631027912$$
$$x_{56} = -35.1108808488825$$
$$x_{57} = -17.7027773373026$$
$$x_{58} = 90.5528252947092$$
$$x_{59} = -72.2566307772889$$
$$x_{60} = -21.9911485858974$$
$$x_{61} = 0$$
$$x_{62} = 92.2529655383401$$
$$x_{63} = -81.6814090194997$$
$$x_{64} = -57.102029424011$$
$$x_{65} = 25.1327414331326$$
$$x_{66} = 37.6991121231114$$
$$x_{67} = -61.6850744875597$$
$$x_{68} = 6.28318528868238$$
$$x_{69} = -43.9822971720912$$
$$x_{70} = -9.97813962016414$$
$$x_{71} = -39.6939259124312$$
$$x_{72} = 8.87141630137462$$
$$x_{73} = 34.004157530093$$
$$x_{74} = -1.99481406935366$$
$$x_{75} = -50.2654821963477$$
$$x_{76} = 43.9822971711027$$
$$x_{77} = -3.69495431298456$$
$$x_{78} = 77.9864546803501$$
$$x_{79} = -63.3852147311906$$
$$x_{80} = -89.9594083698679$$
$$x_{81} = -75.9515853455498$$
$$x_{82} = -85.3763633063192$$
$$x_{83} = 21.9911485856521$$
$$x_{84} = -15.7079632895347$$
$$x_{85} = -97.9427339206784$$
$$x_{86} = 46.5705281444521$$
$$x_{87} = 68.5616767195807$$
$$x_{88} = 41.9874830809034$$
$$x_{89} = 65.9734457563877$$
$$x_{90} = 18.296194262144$$
$$x_{91} = 93.694417948299$$
Intervalos de convexidad y concavidad:
Hallemos los intervales donde la función es convexa o cóncava, para eso veamos cómo se comporta la función en los puntos de flexiones:
Cóncava en los intervalos
$$\left[92.2529655383401, \infty\right)$$
Convexa en los intervalos
$$\left(-\infty, -89.9594083698679\right]$$
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
segunda derivada
$$2 \left(- e^{\sin{\left(2 x \right)}} \sin{\left(2 x \right)} + e^{\sin{\left(2 x \right)}} \cos^{2}{\left(2 x \right)} - \cos{\left(2 x \right)}\right) = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 96.8360106018888$$
$$x_{2} = 81.6814092797807$$
$$x_{3} = 28.2743338676393$$
$$x_{4} = 49.7121207980419$$
$$x_{5} = -79.0931779991396$$
$$x_{6} = -41.3940661560621$$
$$x_{7} = -28.2743336158059$$
$$x_{8} = 15.7079635439569$$
$$x_{9} = 19.9963345057749$$
$$x_{10} = 4.28837123782592$$
$$x_{11} = -83.6762230626883$$
$$x_{12} = -23.9859626444822$$
$$x_{13} = -47.6772514632417$$
$$x_{14} = -67.9682597947393$$
$$x_{15} = -25.6861028881131$$
$$x_{16} = 87.9645943415359$$
$$x_{17} = 63.978631656032$$
$$x_{18} = 74.8448620267603$$
$$x_{19} = 70.2618169632116$$
$$x_{20} = -69.6684000383702$$
$$x_{21} = 55.9953061052215$$
$$x_{22} = -87.9645943455885$$
$$x_{23} = 2.58823099419503$$
$$x_{24} = -94.247779358601$$
$$x_{25} = -100.530965007034$$
$$x_{26} = 48.270668388083$$
$$x_{27} = -352.411738861452$$
$$x_{28} = -40.8407044595488$$
$$x_{29} = 59.6902607017326$$
$$x_{30} = 12.0130089549644$$
$$x_{31} = -53.9604367704212$$
$$x_{32} = -91.6595486134988$$
$$x_{33} = 50.2654824473634$$
$$x_{34} = -59.6902604436943$$
$$x_{35} = 24.5793795693236$$
$$x_{36} = 40.2873428372725$$
$$x_{37} = -45.9771112196108$$
$$x_{38} = 85.9697802311605$$
$$x_{39} = 30.8625648765032$$
$$x_{40} = -6.28318503569359$$
$$x_{41} = 94.247779609375$$
$$x_{42} = 26.2795198129545$$
$$x_{43} = -97.389372310019$$
$$x_{44} = 62.2784914124011$$
$$x_{45} = -19.4029175809335$$
$$x_{46} = -78.5398167377463$$
$$x_{47} = 99.9776032554786$$
$$x_{48} = -37.6991118670078$$
$$x_{49} = 69.1150383073985$$
$$x_{50} = -13.1197322737539$$
$$x_{51} = -65.9734457586377$$
$$x_{52} = -31.9692881952927$$
$$x_{53} = 52.8537134516317$$
$$x_{54} = 84.2696399875297$$
$$x_{55} = 72.256631027912$$
$$x_{56} = -35.1108808488825$$
$$x_{57} = -17.7027773373026$$
$$x_{58} = 90.5528252947092$$
$$x_{59} = -72.2566307772889$$
$$x_{60} = -21.9911485858974$$
$$x_{61} = 0$$
$$x_{62} = 92.2529655383401$$
$$x_{63} = -81.6814090194997$$
$$x_{64} = -57.102029424011$$
$$x_{65} = 25.1327414331326$$
$$x_{66} = 37.6991121231114$$
$$x_{67} = -61.6850744875597$$
$$x_{68} = 6.28318528868238$$
$$x_{69} = -43.9822971720912$$
$$x_{70} = -9.97813962016414$$
$$x_{71} = -39.6939259124312$$
$$x_{72} = 8.87141630137462$$
$$x_{73} = 34.004157530093$$
$$x_{74} = -1.99481406935366$$
$$x_{75} = -50.2654821963477$$
$$x_{76} = 43.9822971711027$$
$$x_{77} = -3.69495431298456$$
$$x_{78} = 77.9864546803501$$
$$x_{79} = -63.3852147311906$$
$$x_{80} = -89.9594083698679$$
$$x_{81} = -75.9515853455498$$
$$x_{82} = -85.3763633063192$$
$$x_{83} = 21.9911485856521$$
$$x_{84} = -15.7079632895347$$
$$x_{85} = -97.9427339206784$$
$$x_{86} = 46.5705281444521$$
$$x_{87} = 68.5616767195807$$
$$x_{88} = 41.9874830809034$$
$$x_{89} = 65.9734457563877$$
$$x_{90} = 18.296194262144$$
$$x_{91} = 93.694417948299$$
Intervalos de convexidad y concavidad:
Hallemos los intervales donde la función es convexa o cóncava, para eso veamos cómo se comporta la función en los puntos de flexiones:
Cóncava en los intervalos
$$\left[92.2529655383401, \infty\right)$$
Convexa en los intervalos
$$\left(-\infty, -89.9594083698679\right]$$
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
$$\lim_{x \to -\infty}\left(\frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2}\right) = \left\langle - \frac{1}{2} + \frac{1}{2 e}, \frac{1}{2} + \frac{e}{2}\right\rangle - \frac{\log{\left(\sqrt{3} \right)}}{2}$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \left\langle - \frac{1}{2} + \frac{1}{2 e}, \frac{1}{2} + \frac{e}{2}\right\rangle - \frac{\log{\left(\sqrt{3} \right)}}{2}$$
$$\lim_{x \to \infty}\left(\frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2}\right) = \left\langle - \frac{1}{2} + \frac{1}{2 e}, \frac{1}{2} + \frac{e}{2}\right\rangle - \frac{\log{\left(\sqrt{3} \right)}}{2}$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \left\langle - \frac{1}{2} + \frac{1}{2 e}, \frac{1}{2} + \frac{e}{2}\right\rangle - \frac{\log{\left(\sqrt{3} \right)}}{2}$$
$$\lim_{x \to -\infty}\left(\frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2}\right) = \left\langle - \frac{1}{2} + \frac{1}{2 e}, \frac{1}{2} + \frac{e}{2}\right\rangle - \frac{\log{\left(\sqrt{3} \right)}}{2}$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \left\langle - \frac{1}{2} + \frac{1}{2 e}, \frac{1}{2} + \frac{e}{2}\right\rangle - \frac{\log{\left(\sqrt{3} \right)}}{2}$$
$$\lim_{x \to \infty}\left(\frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2}\right) = \left\langle - \frac{1}{2} + \frac{1}{2 e}, \frac{1}{2} + \frac{e}{2}\right\rangle - \frac{\log{\left(\sqrt{3} \right)}}{2}$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \left\langle - \frac{1}{2} + \frac{1}{2 e}, \frac{1}{2} + \frac{e}{2}\right\rangle - \frac{\log{\left(\sqrt{3} \right)}}{2}$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (E^sin(2*x) + cos(2*x) - log(sqrt(3)))/2, dividida por x con x->+oo y x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2 x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{x \to \infty}\left(\frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2 x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
$$\lim_{x \to -\infty}\left(\frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2 x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{x \to \infty}\left(\frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2 x}\right) = 0$$
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:
$$\frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2} = \frac{\cos{\left(2 x \right)}}{2} - \frac{\log{\left(\sqrt{3} \right)}}{2} + \frac{e^{- \sin{\left(2 x \right)}}}{2}$$
- No
$$\frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2} = - \frac{\cos{\left(2 x \right)}}{2} + \frac{\log{\left(\sqrt{3} \right)}}{2} - \frac{e^{- \sin{\left(2 x \right)}}}{2}$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$\frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2} = \frac{\cos{\left(2 x \right)}}{2} - \frac{\log{\left(\sqrt{3} \right)}}{2} + \frac{e^{- \sin{\left(2 x \right)}}}{2}$$
- No
$$\frac{\left(e^{\sin{\left(2 x \right)}} + \cos{\left(2 x \right)}\right) - \log{\left(\sqrt{3} \right)}}{2} = - \frac{\cos{\left(2 x \right)}}{2} + \frac{\log{\left(\sqrt{3} \right)}}{2} - \frac{e^{- \sin{\left(2 x \right)}}}{2}$$
- No
es decir, función
no es
par ni impar