Sr Examen
Otras calculadoras
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- Integrales paso a paso
- Gráfico de la función paramétrica
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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
-
sin(2*x)
-
x*atan(x)
-
4x-x^2
-
Expresiones idénticas
- abs(cos(x)+sin(x))
- abs( coseno de (x) más seno de (x))
- abscosx+sinx
-
Expresiones semejantes
- abs(cos(x)-sin(x))
- abs(cosx+sinx)
-
Expresiones con funciones
- abs
- abs(-0.25x^2-2x-3)
- abs(x+1)
- abs(x+1)+abs(x-2)
- abs(x)/abs(abs(x)+1)
- absx
- Coseno cos
- cos(1/x)*sin(x)
- cos(x)/cos(2x)
- cos(x)*sin(x)
- cos(3*x)^2
- cos(3*x)
- Seno sin
- sin(2*x)
- sin^-1(2x)
- sin(x)/x
- sinh(2*x)
- sinx
Gráfico de la función y = abs(cos(x)+sin(x))
Solución
Ha introducido
[src]
f(x) = |cos(x) + sin(x)|
$$f{\left(x \right)} = \left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right|$$
f = Abs(sin(x) + cos(x))
Gráfico de la función
Puntos de cruce con el eje de coordenadas X
El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right| = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución analítica
$$x_{1} = - \frac{\pi}{4}$$
Solución numérica
$$x_{1} = 93.4623814442964$$
$$x_{2} = 21.2057504117311$$
$$x_{3} = 43.1968989868597$$
$$x_{4} = 90.3207887907066$$
$$x_{5} = -10.2101761241668$$
$$x_{6} = -19.6349540849362$$
$$x_{7} = 71.4712328691678$$
$$x_{8} = -44.7676953136546$$
$$x_{9} = -41.6261026600648$$
$$x_{10} = 11.7809724509617$$
$$x_{11} = 8.63937979737193$$
$$x_{12} = -66.7588438887831$$
$$x_{13} = -60.4756585816035$$
$$x_{14} = 27.4889357189107$$
$$x_{15} = -63618.0366333567$$
$$x_{16} = 74.6128255227576$$
$$x_{17} = -29.0597320457056$$
$$x_{18} = 40.0553063332699$$
$$x_{19} = -85.6083998103219$$
$$x_{20} = 33.7721210260903$$
$$x_{21} = 84.037603483527$$
$$x_{22} = -57.3340659280137$$
$$x_{23} = -73.0420291959627$$
$$x_{24} = -54.1924732744239$$
$$x_{25} = -76.1836218495525$$
$$x_{26} = -32.2013246992954$$
$$x_{27} = 30.6305283725005$$
$$x_{28} = -82.4668071567321$$
$$x_{29} = -38.484510006475$$
$$x_{30} = 96.6039740978861$$
$$x_{31} = -22.776546738526$$
$$x_{32} = -79.3252145031423$$
$$x_{33} = 2.35619449019234$$
$$x_{34} = 68.329640215578$$
$$x_{35} = -13.3517687777566$$
$$x_{36} = -88.7499924639117$$
$$x_{37} = 80.8960108299372$$
$$x_{38} = -51.0508806208341$$
$$x_{39} = 137.444678594553$$
$$x_{40} = 36.9137136796801$$
$$x_{41} = -7.06858347057703$$
$$x_{42} = -16.4933614313464$$
$$x_{43} = 49.4800842940392$$
$$x_{44} = 62.0464549083984$$
$$x_{45} = -98.174770424681$$
$$x_{46} = 46.3384916404494$$
$$x_{47} = 52.621676947629$$
$$x_{48} = 24.3473430653209$$
$$x_{49} = -107.59954838545$$
$$x_{50} = -0.785398163397448$$
$$x_{51} = 5.49778714378214$$
$$x_{52} = 285.099533313274$$
$$x_{53} = -63.6172512351933$$
$$x_{54} = 99.7455667514759$$
$$x_{55} = 58.9048622548086$$
$$x_{56} = 14.9225651045515$$
$$x_{57} = -91.8915851175014$$
$$x_{58} = 55.7632696012188$$
$$x_{59} = -95.0331777710912$$
$$x_{60} = -35.3429173528852$$
$$x_{61} = 77.7544181763474$$
o sea hay que resolver la ecuación:
$$\left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right| = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución analítica
$$x_{1} = - \frac{\pi}{4}$$
Solución numérica
$$x_{1} = 93.4623814442964$$
$$x_{2} = 21.2057504117311$$
$$x_{3} = 43.1968989868597$$
$$x_{4} = 90.3207887907066$$
$$x_{5} = -10.2101761241668$$
$$x_{6} = -19.6349540849362$$
$$x_{7} = 71.4712328691678$$
$$x_{8} = -44.7676953136546$$
$$x_{9} = -41.6261026600648$$
$$x_{10} = 11.7809724509617$$
$$x_{11} = 8.63937979737193$$
$$x_{12} = -66.7588438887831$$
$$x_{13} = -60.4756585816035$$
$$x_{14} = 27.4889357189107$$
$$x_{15} = -63618.0366333567$$
$$x_{16} = 74.6128255227576$$
$$x_{17} = -29.0597320457056$$
$$x_{18} = 40.0553063332699$$
$$x_{19} = -85.6083998103219$$
$$x_{20} = 33.7721210260903$$
$$x_{21} = 84.037603483527$$
$$x_{22} = -57.3340659280137$$
$$x_{23} = -73.0420291959627$$
$$x_{24} = -54.1924732744239$$
$$x_{25} = -76.1836218495525$$
$$x_{26} = -32.2013246992954$$
$$x_{27} = 30.6305283725005$$
$$x_{28} = -82.4668071567321$$
$$x_{29} = -38.484510006475$$
$$x_{30} = 96.6039740978861$$
$$x_{31} = -22.776546738526$$
$$x_{32} = -79.3252145031423$$
$$x_{33} = 2.35619449019234$$
$$x_{34} = 68.329640215578$$
$$x_{35} = -13.3517687777566$$
$$x_{36} = -88.7499924639117$$
$$x_{37} = 80.8960108299372$$
$$x_{38} = -51.0508806208341$$
$$x_{39} = 137.444678594553$$
$$x_{40} = 36.9137136796801$$
$$x_{41} = -7.06858347057703$$
$$x_{42} = -16.4933614313464$$
$$x_{43} = 49.4800842940392$$
$$x_{44} = 62.0464549083984$$
$$x_{45} = -98.174770424681$$
$$x_{46} = 46.3384916404494$$
$$x_{47} = 52.621676947629$$
$$x_{48} = 24.3473430653209$$
$$x_{49} = -107.59954838545$$
$$x_{50} = -0.785398163397448$$
$$x_{51} = 5.49778714378214$$
$$x_{52} = 285.099533313274$$
$$x_{53} = -63.6172512351933$$
$$x_{54} = 99.7455667514759$$
$$x_{55} = 58.9048622548086$$
$$x_{56} = 14.9225651045515$$
$$x_{57} = -91.8915851175014$$
$$x_{58} = 55.7632696012188$$
$$x_{59} = -95.0331777710912$$
$$x_{60} = -35.3429173528852$$
$$x_{61} = 77.7544181763474$$
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
$$\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) \operatorname{sign}{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = -52.621676947629$$
$$x_{2} = -33.7721210260903$$
$$x_{3} = 60.4756585816035$$
$$x_{4} = -55.7632696012188$$
$$x_{5} = -96.6039740978861$$
$$x_{6} = 13.3517687777566$$
$$x_{7} = -106.028752058656$$
$$x_{8} = 95.0331777710912$$
$$x_{9} = 32.2013246992954$$
$$x_{10} = 25.9181393921158$$
$$x_{11} = 66.7588438887831$$
$$x_{12} = -6646.8246568326$$
$$x_{13} = 51.0508806208341$$
$$x_{14} = -71.4712328691678$$
$$x_{15} = 41.6261026600648$$
$$x_{16} = 63.6172512351933$$
$$x_{17} = -8.63937979737193$$
$$x_{18} = 88.7499924639117$$
$$x_{19} = -99.7455667514759$$
$$x_{20} = -58.9048622548086$$
$$x_{21} = -18.0641577581413$$
$$x_{22} = -354.214571692249$$
$$x_{23} = -1881.02860133689$$
$$x_{24} = 3.92699081698724$$
$$x_{25} = -941.692397913541$$
$$x_{26} = 73.0420291959627$$
$$x_{27} = -14.9225651045515$$
$$x_{28} = 38.484510006475$$
$$x_{29} = -77.7544181763474$$
$$x_{30} = 22.776546738526$$
$$x_{31} = -36.9137136796801$$
$$x_{32} = 79.3252145031423$$
$$x_{33} = 82.4668071567321$$
$$x_{34} = -62.0464549083984$$
$$x_{35} = 16.4933614313464$$
$$x_{36} = 10.2101761241668$$
$$x_{37} = 76.1836218495525$$
$$x_{38} = 85.6083998103219$$
$$x_{39} = -2.35619449019234$$
$$x_{40} = -21.2057504117311$$
$$x_{41} = 7.06858347057703$$
$$x_{42} = 57.3340659280137$$
$$x_{43} = 35.3429173528852$$
$$x_{44} = -68.329640215578$$
$$x_{45} = 98.174770424681$$
$$x_{46} = 0.785398163397448$$
$$x_{47} = -24.3473430653209$$
$$x_{48} = -11.7809724509617$$
$$x_{49} = -90.3207887907066$$
$$x_{50} = -74.6128255227576$$
$$x_{51} = -46.3384916404494$$
$$x_{52} = 19.6349540849362$$
$$x_{53} = 69.9004365423729$$
$$x_{54} = -27.4889357189107$$
$$x_{55} = 44.7676953136546$$
$$x_{56} = -30.6305283725005$$
$$x_{57} = -259.966792084555$$
$$x_{58} = -84.037603483527$$
$$x_{59} = -49.4800842940392$$
$$x_{60} = -40.0553063332699$$
$$x_{61} = -65.1880475619882$$
$$x_{62} = -5.49778714378214$$
$$x_{63} = 47.9092879672443$$
$$x_{64} = -43.1968989868597$$
$$x_{65} = 7760.51925253019$$
$$x_{66} = -80.8960108299372$$
$$x_{67} = 54.1924732744239$$
$$x_{68} = 101.316363078271$$
$$x_{69} = -93.4623814442964$$
$$x_{70} = 29.0597320457056$$
$$x_{71} = 91.8915851175014$$
$$x_{72} = -87.1791961371168$$
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:
La función no tiene puntos mínimos
Puntos máximos de la función:
$$x_{72} = -52.621676947629$$
$$x_{72} = -33.7721210260903$$
$$x_{72} = 60.4756585816035$$
$$x_{72} = -55.7632696012188$$
$$x_{72} = -96.6039740978861$$
$$x_{72} = 13.3517687777566$$
$$x_{72} = -106.028752058656$$
$$x_{72} = 95.0331777710912$$
$$x_{72} = 32.2013246992954$$
$$x_{72} = 25.9181393921158$$
$$x_{72} = 66.7588438887831$$
$$x_{72} = -6646.8246568326$$
$$x_{72} = 51.0508806208341$$
$$x_{72} = -71.4712328691678$$
$$x_{72} = 41.6261026600648$$
$$x_{72} = 63.6172512351933$$
$$x_{72} = -8.63937979737193$$
$$x_{72} = 88.7499924639117$$
$$x_{72} = -99.7455667514759$$
$$x_{72} = -58.9048622548086$$
$$x_{72} = -18.0641577581413$$
$$x_{72} = -354.214571692249$$
$$x_{72} = -1881.02860133689$$
$$x_{72} = 3.92699081698724$$
$$x_{72} = -941.692397913541$$
$$x_{72} = 73.0420291959627$$
$$x_{72} = -14.9225651045515$$
$$x_{72} = 38.484510006475$$
$$x_{72} = -77.7544181763474$$
$$x_{72} = 22.776546738526$$
$$x_{72} = -36.9137136796801$$
$$x_{72} = 79.3252145031423$$
$$x_{72} = 82.4668071567321$$
$$x_{72} = -62.0464549083984$$
$$x_{72} = 16.4933614313464$$
$$x_{72} = 10.2101761241668$$
$$x_{72} = 76.1836218495525$$
$$x_{72} = 85.6083998103219$$
$$x_{72} = -2.35619449019234$$
$$x_{72} = -21.2057504117311$$
$$x_{72} = 7.06858347057703$$
$$x_{72} = 57.3340659280137$$
$$x_{72} = 35.3429173528852$$
$$x_{72} = -68.329640215578$$
$$x_{72} = 98.174770424681$$
$$x_{72} = 0.785398163397448$$
$$x_{72} = -24.3473430653209$$
$$x_{72} = -11.7809724509617$$
$$x_{72} = -90.3207887907066$$
$$x_{72} = -74.6128255227576$$
$$x_{72} = -46.3384916404494$$
$$x_{72} = 19.6349540849362$$
$$x_{72} = 69.9004365423729$$
$$x_{72} = -27.4889357189107$$
$$x_{72} = 44.7676953136546$$
$$x_{72} = -30.6305283725005$$
$$x_{72} = -259.966792084555$$
$$x_{72} = -84.037603483527$$
$$x_{72} = -49.4800842940392$$
$$x_{72} = -40.0553063332699$$
$$x_{72} = -65.1880475619882$$
$$x_{72} = -5.49778714378214$$
$$x_{72} = 47.9092879672443$$
$$x_{72} = -43.1968989868597$$
$$x_{72} = 7760.51925253019$$
$$x_{72} = -80.8960108299372$$
$$x_{72} = 54.1924732744239$$
$$x_{72} = 101.316363078271$$
$$x_{72} = -93.4623814442964$$
$$x_{72} = 29.0597320457056$$
$$x_{72} = 91.8915851175014$$
$$x_{72} = -87.1791961371168$$
Decrece en los intervalos
$$\left(-\infty, -6646.8246568326\right]$$
Crece en los intervalos
$$\left[7760.51925253019, \infty\right)$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(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
$$\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) \operatorname{sign}{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = -52.621676947629$$
$$x_{2} = -33.7721210260903$$
$$x_{3} = 60.4756585816035$$
$$x_{4} = -55.7632696012188$$
$$x_{5} = -96.6039740978861$$
$$x_{6} = 13.3517687777566$$
$$x_{7} = -106.028752058656$$
$$x_{8} = 95.0331777710912$$
$$x_{9} = 32.2013246992954$$
$$x_{10} = 25.9181393921158$$
$$x_{11} = 66.7588438887831$$
$$x_{12} = -6646.8246568326$$
$$x_{13} = 51.0508806208341$$
$$x_{14} = -71.4712328691678$$
$$x_{15} = 41.6261026600648$$
$$x_{16} = 63.6172512351933$$
$$x_{17} = -8.63937979737193$$
$$x_{18} = 88.7499924639117$$
$$x_{19} = -99.7455667514759$$
$$x_{20} = -58.9048622548086$$
$$x_{21} = -18.0641577581413$$
$$x_{22} = -354.214571692249$$
$$x_{23} = -1881.02860133689$$
$$x_{24} = 3.92699081698724$$
$$x_{25} = -941.692397913541$$
$$x_{26} = 73.0420291959627$$
$$x_{27} = -14.9225651045515$$
$$x_{28} = 38.484510006475$$
$$x_{29} = -77.7544181763474$$
$$x_{30} = 22.776546738526$$
$$x_{31} = -36.9137136796801$$
$$x_{32} = 79.3252145031423$$
$$x_{33} = 82.4668071567321$$
$$x_{34} = -62.0464549083984$$
$$x_{35} = 16.4933614313464$$
$$x_{36} = 10.2101761241668$$
$$x_{37} = 76.1836218495525$$
$$x_{38} = 85.6083998103219$$
$$x_{39} = -2.35619449019234$$
$$x_{40} = -21.2057504117311$$
$$x_{41} = 7.06858347057703$$
$$x_{42} = 57.3340659280137$$
$$x_{43} = 35.3429173528852$$
$$x_{44} = -68.329640215578$$
$$x_{45} = 98.174770424681$$
$$x_{46} = 0.785398163397448$$
$$x_{47} = -24.3473430653209$$
$$x_{48} = -11.7809724509617$$
$$x_{49} = -90.3207887907066$$
$$x_{50} = -74.6128255227576$$
$$x_{51} = -46.3384916404494$$
$$x_{52} = 19.6349540849362$$
$$x_{53} = 69.9004365423729$$
$$x_{54} = -27.4889357189107$$
$$x_{55} = 44.7676953136546$$
$$x_{56} = -30.6305283725005$$
$$x_{57} = -259.966792084555$$
$$x_{58} = -84.037603483527$$
$$x_{59} = -49.4800842940392$$
$$x_{60} = -40.0553063332699$$
$$x_{61} = -65.1880475619882$$
$$x_{62} = -5.49778714378214$$
$$x_{63} = 47.9092879672443$$
$$x_{64} = -43.1968989868597$$
$$x_{65} = 7760.51925253019$$
$$x_{66} = -80.8960108299372$$
$$x_{67} = 54.1924732744239$$
$$x_{68} = 101.316363078271$$
$$x_{69} = -93.4623814442964$$
$$x_{70} = 29.0597320457056$$
$$x_{71} = 91.8915851175014$$
$$x_{72} = -87.1791961371168$$
Signos de extremos en los puntos:
(-52.621676947629034, 1.41421356237309)
(-33.772121026090275, 1.41421356237309)
(60.47565858160352, 1.41421356237309)
(-55.76326960121883, 1.41421356237309)
(-96.60397409788614, 1.41421356237309)
(13.351768777756622, 1.41421356237309)
(-106.02875205865553, 1.41421356237309)
(95.03317777109125, 1.41421356237309)
(32.201324699295384, 1.41421356237309)
(25.918139392115794, 1.41421356237309)
(66.7588438887831, 1.4142135623731)
(-6646.824656832605, 1.41421356237309)
(51.05088062083414, 1.41421356237309)
(-71.47123286916779, 1.41421356237309)
(41.62610266006476, 1.41421356237309)
(63.617251235193315, 1.41421356237309)
(-8.639379797371932, 1.41421356237309)
(88.74999246391165, 1.4142135623731)
(-99.74556675147593, 1.41421356237309)
(-58.90486225480862, 1.41421356237309)
(-18.06415775814131, 1.41421356237309)
(-354.2145716922492, 1.41421356237309)
(-1881.0286013368886, 1.41421356237309)
(3.9269908169872414, 1.4142135623731)
(-941.6923979135405, 1.41421356237309)
(73.0420291959627, 1.41421356237309)
(-14.922565104551518, 1.41421356237309)
(38.48451000647497, 1.41421356237309)
(-77.75441817634739, 1.41421356237309)
(22.776546738526, 1.4142135623731)
(-36.91371367968007, 1.41421356237309)
(79.32521450314228, 1.41421356237309)
(82.46680715673207, 1.41421356237309)
(-62.04645490839842, 1.41421356237309)
(16.493361431346415, 1.41421356237309)
(10.210176124166829, 1.41421356237309)
(76.18362184955248, 1.41421356237309)
(85.60839981032187, 1.41421356237309)
(-2.356194490192345, 1.41421356237309)
(-21.205750411731103, 1.4142135623731)
(7.0685834705770345, 1.41421356237309)
(57.33406592801373, 1.41421356237309)
(35.34291735288517, 1.41421356237309)
(-68.329640215578, 1.41421356237309)
(98.17477042468104, 1.41421356237309)
(0.7853981633974483, 1.41421356237309)
(-24.3473430653209, 1.4142135623731)
(-11.780972450961725, 1.41421356237309)
(-90.32078879070656, 1.41421356237309)
(-74.61282552275759, 1.41421356237309)
(-46.33849164044945, 1.41421356237309)
(19.634954084936208, 1.41421356237309)
(69.9004365423729, 1.4142135623731)
(-27.488935718910692, 1.41421356237309)
(44.767695313654556, 1.41421356237309)
(-30.630528372500486, 1.41421356237309)
(-259.9667920845554, 1.41421356237309)
(-84.03760348352696, 1.41421356237309)
(-49.480084294039244, 1.41421356237309)
(-40.05530633326986, 1.41421356237309)
(-65.18804756198821, 1.41421356237309)
(-5.497787143782138, 1.41421356237309)
(47.909287967244346, 1.41421356237309)
(-43.19689898685966, 1.41421356237309)
(7760.519252530186, 1.41421356237309)
(-80.89601082993718, 1.41421356237309)
(54.19247327442393, 1.41421356237309)
(101.31636307827083, 1.41421356237309)
(-93.46238144429635, 1.4142135623731)
(29.059732045705587, 1.41421356237309)
(91.89158511750145, 1.41421356237309)
(-87.17919613711676, 1.41421356237309)
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:
La función no tiene puntos mínimos
Puntos máximos de la función:
$$x_{72} = -52.621676947629$$
$$x_{72} = -33.7721210260903$$
$$x_{72} = 60.4756585816035$$
$$x_{72} = -55.7632696012188$$
$$x_{72} = -96.6039740978861$$
$$x_{72} = 13.3517687777566$$
$$x_{72} = -106.028752058656$$
$$x_{72} = 95.0331777710912$$
$$x_{72} = 32.2013246992954$$
$$x_{72} = 25.9181393921158$$
$$x_{72} = 66.7588438887831$$
$$x_{72} = -6646.8246568326$$
$$x_{72} = 51.0508806208341$$
$$x_{72} = -71.4712328691678$$
$$x_{72} = 41.6261026600648$$
$$x_{72} = 63.6172512351933$$
$$x_{72} = -8.63937979737193$$
$$x_{72} = 88.7499924639117$$
$$x_{72} = -99.7455667514759$$
$$x_{72} = -58.9048622548086$$
$$x_{72} = -18.0641577581413$$
$$x_{72} = -354.214571692249$$
$$x_{72} = -1881.02860133689$$
$$x_{72} = 3.92699081698724$$
$$x_{72} = -941.692397913541$$
$$x_{72} = 73.0420291959627$$
$$x_{72} = -14.9225651045515$$
$$x_{72} = 38.484510006475$$
$$x_{72} = -77.7544181763474$$
$$x_{72} = 22.776546738526$$
$$x_{72} = -36.9137136796801$$
$$x_{72} = 79.3252145031423$$
$$x_{72} = 82.4668071567321$$
$$x_{72} = -62.0464549083984$$
$$x_{72} = 16.4933614313464$$
$$x_{72} = 10.2101761241668$$
$$x_{72} = 76.1836218495525$$
$$x_{72} = 85.6083998103219$$
$$x_{72} = -2.35619449019234$$
$$x_{72} = -21.2057504117311$$
$$x_{72} = 7.06858347057703$$
$$x_{72} = 57.3340659280137$$
$$x_{72} = 35.3429173528852$$
$$x_{72} = -68.329640215578$$
$$x_{72} = 98.174770424681$$
$$x_{72} = 0.785398163397448$$
$$x_{72} = -24.3473430653209$$
$$x_{72} = -11.7809724509617$$
$$x_{72} = -90.3207887907066$$
$$x_{72} = -74.6128255227576$$
$$x_{72} = -46.3384916404494$$
$$x_{72} = 19.6349540849362$$
$$x_{72} = 69.9004365423729$$
$$x_{72} = -27.4889357189107$$
$$x_{72} = 44.7676953136546$$
$$x_{72} = -30.6305283725005$$
$$x_{72} = -259.966792084555$$
$$x_{72} = -84.037603483527$$
$$x_{72} = -49.4800842940392$$
$$x_{72} = -40.0553063332699$$
$$x_{72} = -65.1880475619882$$
$$x_{72} = -5.49778714378214$$
$$x_{72} = 47.9092879672443$$
$$x_{72} = -43.1968989868597$$
$$x_{72} = 7760.51925253019$$
$$x_{72} = -80.8960108299372$$
$$x_{72} = 54.1924732744239$$
$$x_{72} = 101.316363078271$$
$$x_{72} = -93.4623814442964$$
$$x_{72} = 29.0597320457056$$
$$x_{72} = 91.8915851175014$$
$$x_{72} = -87.1791961371168$$
Decrece en los intervalos
$$\left(-\infty, -6646.8246568326\right]$$
Crece en los intervalos
$$\left[7760.51925253019, \infty\right)$$
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
$$2 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} \delta\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) - \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) \operatorname{sign}{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)} = 0$$
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga flexiones
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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
$$2 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} \delta\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) - \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) \operatorname{sign}{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)} = 0$$
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga flexiones
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
$$\lim_{x \to -\infty} \left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right| = \left|{\left\langle -2, 2\right\rangle}\right|$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \left|{\left\langle -2, 2\right\rangle}\right|$$
$$\lim_{x \to \infty} \left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right| = \left|{\left\langle -2, 2\right\rangle}\right|$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \left|{\left\langle -2, 2\right\rangle}\right|$$
$$\lim_{x \to -\infty} \left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right| = \left|{\left\langle -2, 2\right\rangle}\right|$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \left|{\left\langle -2, 2\right\rangle}\right|$$
$$\lim_{x \to \infty} \left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right| = \left|{\left\langle -2, 2\right\rangle}\right|$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \left|{\left\langle -2, 2\right\rangle}\right|$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función Abs(cos(x) + sin(x)), dividida por x con x->+oo y x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right|}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{x \to \infty}\left(\frac{\left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right|}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
$$\lim_{x \to -\infty}\left(\frac{\left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right|}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{x \to \infty}\left(\frac{\left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right|}{x}\right) = 0$$
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:
$$\left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right| = \left|{\sin{\left(x \right)} - \cos{\left(x \right)}}\right|$$
- No
$$\left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right| = - \left|{\sin{\left(x \right)} - \cos{\left(x \right)}}\right|$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$\left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right| = \left|{\sin{\left(x \right)} - \cos{\left(x \right)}}\right|$$
- No
$$\left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right| = - \left|{\sin{\left(x \right)} - \cos{\left(x \right)}}\right|$$
- No
es decir, función
no es
par ni impar