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Otras calculadoras
- Gráfico de la función implícita
- Derivadas paso a paso
- Integrales paso a paso
- Gráfico de la función paramétrica
- Gráfico en coordenadas polares
- Superficie especificada paramétricamente
- Superficie dada por la ecuación
- Curva en el espacio especificada paramétricamente
- Superficie de una figura limitada con líneas
- Puntos de cruce de las funciones
-
¿Cómo usar?
- Gráfico de la función y =:
-
7-x-2*x^2
-
y=x^3
-
(3*x-4)^40/(x^2-2)^36
-
y=x^2-x
-
Expresiones idénticas
- (exp((-x)/ dos)/ dos -cos(x)*sin(sin(x)))/x-(cos(sin(x))-e^((-x)/ dos))/x^ dos
- ( exponente de (( menos x) dividir por 2) dividir por 2 menos coseno de (x) multiplicar por seno de ( seno de (x))) dividir por x menos ( coseno de ( seno de (x)) menos e en el grado (( menos x) dividir por 2)) dividir por x al cuadrado
- ( exponente de (( menos x) dividir por dos) dividir por dos menos coseno de (x) multiplicar por seno de ( seno de (x))) dividir por x menos ( coseno de ( seno de (x)) menos e en el grado (( menos x) dividir por dos)) dividir por x en el grado dos
- (exp((-x)/2)/2-cos(x)*sin(sin(x)))/x-(cos(sin(x))-e((-x)/2))/x2
- exp-x/2/2-cosx*sinsinx/x-cossinx-e-x/2/x2
- (exp((-x)/2)/2-cos(x)*sin(sin(x)))/x-(cos(sin(x))-e^((-x)/2))/x²
- (exp((-x)/2)/2-cos(x)*sin(sin(x)))/x-(cos(sin(x))-e en el grado ((-x)/2))/x en el grado 2
- (exp((-x)/2)/2-cos(x)sin(sin(x)))/x-(cos(sin(x))-e^((-x)/2))/x^2
- (exp((-x)/2)/2-cos(x)sin(sin(x)))/x-(cos(sin(x))-e((-x)/2))/x2
- exp-x/2/2-cosxsinsinx/x-cossinx-e-x/2/x2
- exp-x/2/2-cosxsinsinx/x-cossinx-e^-x/2/x^2
- (exp((-x) dividir por 2) dividir por 2-cos(x)*sin(sin(x))) dividir por x-(cos(sin(x))-e^((-x) dividir por 2)) dividir por x^2
-
Expresiones semejantes
- (exp((-x)/2)/2-cos(x)*sin(sin(x)))/x+(cos(sin(x))-e^((-x)/2))/x^2
- (exp((x)/2)/2-cos(x)*sin(sin(x)))/x-(cos(sin(x))-e^((-x)/2))/x^2
- (exp((-x)/2)/2-cos(x)*sin(sin(x)))/x-(cos(sin(x))-e^((x)/2))/x^2
- (exp((-x)/2)/2-cos(x)*sin(sin(x)))/x-(cos(sin(x))+e^((-x)/2))/x^2
- (exp((-x)/2)/2+cos(x)*sin(sin(x)))/x-(cos(sin(x))-e^((-x)/2))/x^2
- (exp((-x)/2)/2-cosx*sin(sinx))/x-(cos(sinx)-e^((-x)/2))/x^2
-
Expresiones con funciones
- Exponente exp
- exp(-2*x)*(x+1)
- exp(x*(2+x))
- exp(-7*x/10)-3*sqrt(x)/10-1
- exp^(1/(x-4))
- exp(1/(3-x))
- Coseno cos
- cos(log(x))+sin(log(x))
- cos(3)/x
- cos((x+pi)/6)-1
- cos(x)*sqrt(x^2+1)
- cos(x^3)+x^3
- Seno sin
- sin(x)^2/(x^2*cos(x)^2)
- sin(pi*x)/sin(pi*x)
- sin((pi*x^2)/(1+x^2))
- sin(2*x-pi/4)
- sin(3*x)+3
- Seno sin
- sin(x)^2/(x^2*cos(x)^2)
- sin(pi*x)/sin(pi*x)
- sin((pi*x^2)/(1+x^2))
- sin(2*x-pi/4)
- sin(3*x)+3
- Coseno cos
- cos(log(x))+sin(log(x))
- cos(3)/x
- cos((x+pi)/6)-1
- cos(x)*sqrt(x^2+1)
- cos(x^3)+x^3
- Seno sin
- sin(x)^2/(x^2*cos(x)^2)
- sin(pi*x)/sin(pi*x)
- sin((pi*x^2)/(1+x^2))
- sin(2*x-pi/4)
- sin(3*x)+3
Gráfico de la función y = (exp((-x)/2)/2-cos(x)*sin(sin(x)))/x-(cos(sin(x))-e^((-x)/2))/x^2
Solución
Ha introducido
[src]
-x
---
2 -x
e ---
---- - cos(x)*sin(sin(x)) 2
2 cos(sin(x)) - E
f(x) = ------------------------- - ------------------
x 2
x
$$f{\left(x \right)} = - \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x}$$
f = -(-E^((-x)/2) + cos(sin(x)))/x^2 + (exp((-x)/2)/2 - sin(sin(x))*cos(x))/x
Gráfico de la función
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
$$x_{1} = 0$$
$$x_{1} = 0$$
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:
$$- \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = 20.4517633182518$$
$$x_{2} = 37.6725610881152$$
$$x_{3} = 59.6735009919361$$
$$x_{4} = 1.2935145217858$$
$$x_{5} = 105.249454856867$$
$$x_{6} = 92.6839114698133$$
$$x_{7} = 45.5671881401567$$
$$x_{8} = 226.190249972607$$
$$x_{9} = 86.401230015273$$
$$x_{10} = 15.6441816493174$$
$$x_{11} = 34.5285495599042$$
$$x_{12} = 80.1186275923176$$
$$x_{13} = 48.707871555818$$
$$x_{14} = 29.8666412571427$$
$$x_{15} = 12.4872541864278$$
$$x_{16} = 51.8486651663544$$
$$x_{17} = 14.1819924110663$$
$$x_{18} = 78.5270811909166$$
$$x_{19} = 73.8361243776383$$
$$x_{20} = 67.5537480546902$$
$$x_{21} = 42.426639401039$$
$$x_{22} = -1.73371630155173$$
$$x_{23} = 83.2599178065512$$
$$x_{24} = 4.76977107733803$$
$$x_{25} = 26.7275777377294$$
$$x_{26} = 28.2389073182524$$
$$x_{27} = 23.5891854106957$$
$$x_{28} = 21.9455590447597$$
$$x_{29} = 81.6691638577428$$
$$x_{30} = 50.2455775793592$$
$$x_{31} = 95.8252769757041$$
$$x_{32} = -2.12466883462839$$
$$x_{33} = 58.1305115060264$$
$$x_{34} = 89.5425619034202$$
$$x_{35} = 70.6949182400329$$
$$x_{36} = 36.1460864338985$$
$$x_{37} = 43.9595450359395$$
$$x_{38} = 64.4126190823488$$
$$x_{39} = 94.2371676849837$$
$$x_{40} = 87.9532241306717$$
$$x_{41} = 56.5309765021226$$
$$x_{42} = 65.9582834654203$$
$$x_{43} = 72.2427879360818$$
$$x_{44} = 6.15068665036262$$
$$x_{45} = 7.92129717826965$$
$$x_{46} = 100.521016418248$$
o sea hay que resolver la ecuación:
$$- \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = 20.4517633182518$$
$$x_{2} = 37.6725610881152$$
$$x_{3} = 59.6735009919361$$
$$x_{4} = 1.2935145217858$$
$$x_{5} = 105.249454856867$$
$$x_{6} = 92.6839114698133$$
$$x_{7} = 45.5671881401567$$
$$x_{8} = 226.190249972607$$
$$x_{9} = 86.401230015273$$
$$x_{10} = 15.6441816493174$$
$$x_{11} = 34.5285495599042$$
$$x_{12} = 80.1186275923176$$
$$x_{13} = 48.707871555818$$
$$x_{14} = 29.8666412571427$$
$$x_{15} = 12.4872541864278$$
$$x_{16} = 51.8486651663544$$
$$x_{17} = 14.1819924110663$$
$$x_{18} = 78.5270811909166$$
$$x_{19} = 73.8361243776383$$
$$x_{20} = 67.5537480546902$$
$$x_{21} = 42.426639401039$$
$$x_{22} = -1.73371630155173$$
$$x_{23} = 83.2599178065512$$
$$x_{24} = 4.76977107733803$$
$$x_{25} = 26.7275777377294$$
$$x_{26} = 28.2389073182524$$
$$x_{27} = 23.5891854106957$$
$$x_{28} = 21.9455590447597$$
$$x_{29} = 81.6691638577428$$
$$x_{30} = 50.2455775793592$$
$$x_{31} = 95.8252769757041$$
$$x_{32} = -2.12466883462839$$
$$x_{33} = 58.1305115060264$$
$$x_{34} = 89.5425619034202$$
$$x_{35} = 70.6949182400329$$
$$x_{36} = 36.1460864338985$$
$$x_{37} = 43.9595450359395$$
$$x_{38} = 64.4126190823488$$
$$x_{39} = 94.2371676849837$$
$$x_{40} = 87.9532241306717$$
$$x_{41} = 56.5309765021226$$
$$x_{42} = 65.9582834654203$$
$$x_{43} = 72.2427879360818$$
$$x_{44} = 6.15068665036262$$
$$x_{45} = 7.92129717826965$$
$$x_{46} = 100.521016418248$$
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
$$\frac{d}{d x} f{\left(x \right)} = $$
primera derivada
$$\frac{- \frac{e^{\frac{\left(-1\right) x}{2}}}{4} + \sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)} - \cos^{2}{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)}}{x} - \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x^{2}} + \frac{- \frac{e^{\frac{\left(-1\right) x}{2}}}{2} + \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x^{2}} - \frac{2 \left(e^{\frac{\left(-1\right) x}{2}} - \cos{\left(\sin{\left(x \right)} \right)}\right)}{x^{3}} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = -1.93007408048574$$
$$x_{2} = 63.5665984080535$$
$$x_{3} = 60.42458359052$$
$$x_{4} = 33.8009961986888$$
$$x_{5} = 82.4179991548889$$
$$x_{6} = 38.428471870656$$
$$x_{7} = 30.6580596186008$$
$$x_{8} = 25.8552584606865$$
$$x_{9} = 88.7016222038868$$
$$x_{10} = 69.850511674875$$
$$x_{11} = -0.033790285342516$$
$$x_{12} = 66.708572569087$$
$$x_{13} = 19.5651215987813$$
$$x_{14} = 93.4999487345468$$
$$x_{15} = 84.074602601828$$
$$x_{16} = 21.2270546596334$$
$$x_{17} = 71.5072467334144$$
$$x_{18} = 40.0862646696593$$
$$x_{19} = 49.5132102460951$$
$$x_{20} = 99.7834541642334$$
$$x_{21} = 68.3653525223029$$
$$x_{22} = 76.1343024153111$$
$$x_{23} = 41.571106470485$$
$$x_{24} = 18.0820731824244$$
$$x_{25} = 62.0814749554559$$
$$x_{26} = 44.7135898561596$$
$$x_{27} = 8.63282034357175$$
$$x_{28} = 11.787104732733$$
$$x_{29} = 32.1425638107126$$
$$x_{30} = 80.9327917405466$$
$$x_{31} = 54.1404029068618$$
$$x_{32} = 3.75092855882849$$
$$x_{33} = 27.5148353953567$$
$$x_{34} = 52.6553585097603$$
$$x_{35} = 46.3709894042637$$
$$x_{36} = 22.7106982434412$$
$$x_{37} = 77.7909636231305$$
$$x_{38} = 2.10531699821158$$
$$x_{39} = 16.4179171000477$$
$$x_{40} = 55.7974460756187$$
$$x_{41} = 24.3712203656572$$
$$x_{42} = 5.45882698165754$$
$$x_{43} = 98.1269500433719$$
$$x_{44} = 90.358179623441$$
$$x_{45} = 47.8559526964791$$
$$x_{46} = 74.6491161193322$$
$$x_{47} = 85.5598188583576$$
$$x_{48} = 10.1126591305442$$
$$x_{49} = 96.6417065655218$$
$$x_{50} = 91.8434108974037$$
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:
$$x_{1} = 63.5665984080535$$
$$x_{2} = 60.42458359052$$
$$x_{3} = 82.4179991548889$$
$$x_{4} = 38.428471870656$$
$$x_{5} = 25.8552584606865$$
$$x_{6} = 88.7016222038868$$
$$x_{7} = 69.850511674875$$
$$x_{8} = -0.033790285342516$$
$$x_{9} = 66.708572569087$$
$$x_{10} = 19.5651215987813$$
$$x_{11} = 76.1343024153111$$
$$x_{12} = 41.571106470485$$
$$x_{13} = 44.7135898561596$$
$$x_{14} = 32.1425638107126$$
$$x_{15} = 54.1404029068618$$
$$x_{16} = 3.75092855882849$$
$$x_{17} = 22.7106982434412$$
$$x_{18} = 16.4179171000477$$
$$x_{19} = 98.1269500433719$$
$$x_{20} = 47.8559526964791$$
$$x_{21} = 85.5598188583576$$
$$x_{22} = 10.1126591305442$$
$$x_{23} = 91.8434108974037$$
Puntos máximos de la función:
$$x_{23} = -1.93007408048574$$
$$x_{23} = 33.8009961986888$$
$$x_{23} = 30.6580596186008$$
$$x_{23} = 93.4999487345468$$
$$x_{23} = 84.074602601828$$
$$x_{23} = 21.2270546596334$$
$$x_{23} = 71.5072467334144$$
$$x_{23} = 40.0862646696593$$
$$x_{23} = 49.5132102460951$$
$$x_{23} = 99.7834541642334$$
$$x_{23} = 68.3653525223029$$
$$x_{23} = 18.0820731824244$$
$$x_{23} = 62.0814749554559$$
$$x_{23} = 8.63282034357175$$
$$x_{23} = 11.787104732733$$
$$x_{23} = 80.9327917405466$$
$$x_{23} = 27.5148353953567$$
$$x_{23} = 52.6553585097603$$
$$x_{23} = 46.3709894042637$$
$$x_{23} = 77.7909636231305$$
$$x_{23} = 2.10531699821158$$
$$x_{23} = 55.7974460756187$$
$$x_{23} = 24.3712203656572$$
$$x_{23} = 5.45882698165754$$
$$x_{23} = 90.358179623441$$
$$x_{23} = 74.6491161193322$$
$$x_{23} = 96.6417065655218$$
Decrece en los intervalos
$$\left[98.1269500433719, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -0.033790285342516\right]$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
$$\frac{d}{d x} f{\left(x \right)} = $$
primera derivada
$$\frac{- \frac{e^{\frac{\left(-1\right) x}{2}}}{4} + \sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)} - \cos^{2}{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)}}{x} - \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x^{2}} + \frac{- \frac{e^{\frac{\left(-1\right) x}{2}}}{2} + \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x^{2}} - \frac{2 \left(e^{\frac{\left(-1\right) x}{2}} - \cos{\left(\sin{\left(x \right)} \right)}\right)}{x^{3}} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = -1.93007408048574$$
$$x_{2} = 63.5665984080535$$
$$x_{3} = 60.42458359052$$
$$x_{4} = 33.8009961986888$$
$$x_{5} = 82.4179991548889$$
$$x_{6} = 38.428471870656$$
$$x_{7} = 30.6580596186008$$
$$x_{8} = 25.8552584606865$$
$$x_{9} = 88.7016222038868$$
$$x_{10} = 69.850511674875$$
$$x_{11} = -0.033790285342516$$
$$x_{12} = 66.708572569087$$
$$x_{13} = 19.5651215987813$$
$$x_{14} = 93.4999487345468$$
$$x_{15} = 84.074602601828$$
$$x_{16} = 21.2270546596334$$
$$x_{17} = 71.5072467334144$$
$$x_{18} = 40.0862646696593$$
$$x_{19} = 49.5132102460951$$
$$x_{20} = 99.7834541642334$$
$$x_{21} = 68.3653525223029$$
$$x_{22} = 76.1343024153111$$
$$x_{23} = 41.571106470485$$
$$x_{24} = 18.0820731824244$$
$$x_{25} = 62.0814749554559$$
$$x_{26} = 44.7135898561596$$
$$x_{27} = 8.63282034357175$$
$$x_{28} = 11.787104732733$$
$$x_{29} = 32.1425638107126$$
$$x_{30} = 80.9327917405466$$
$$x_{31} = 54.1404029068618$$
$$x_{32} = 3.75092855882849$$
$$x_{33} = 27.5148353953567$$
$$x_{34} = 52.6553585097603$$
$$x_{35} = 46.3709894042637$$
$$x_{36} = 22.7106982434412$$
$$x_{37} = 77.7909636231305$$
$$x_{38} = 2.10531699821158$$
$$x_{39} = 16.4179171000477$$
$$x_{40} = 55.7974460756187$$
$$x_{41} = 24.3712203656572$$
$$x_{42} = 5.45882698165754$$
$$x_{43} = 98.1269500433719$$
$$x_{44} = 90.358179623441$$
$$x_{45} = 47.8559526964791$$
$$x_{46} = 74.6491161193322$$
$$x_{47} = 85.5598188583576$$
$$x_{48} = 10.1126591305442$$
$$x_{49} = 96.6417065655218$$
$$x_{50} = 91.8434108974037$$
Signos de extremos en los puntos:
(-1.930074080485738, 0.0121751516814136)
(63.5665984080535, -0.00744622077607571)
(60.42458359051995, -0.00784397087030914)
(33.80099619868885, 0.0129581474369869)
(82.41799915488893, -0.00570901229687562)
(38.42847187065602, -0.0125259108790993)
(30.65805961860079, 0.0142095100231356)
(25.8552584606865, -0.0189982130888589)
(88.70162220388683, -0.0052970299080708)
(69.850511674875, -0.00676054480107385)
(-0.033790285342516, -0.625703609307118)
(66.70857256908701, -0.00708684389380194)
(19.56512159878134, -0.0255986674849128)
(93.49994873454683, 0.00484194971729688)
(84.07460260182802, 0.00537364521121259)
(21.22705465963345, 0.0199919644163597)
(71.50724673341442, 0.00629526569944311)
(40.086264669659336, 0.0110165534044349)
(49.51321024609514, 0.00899384597663131)
(99.78345416423338, 0.00454230860768394)
(68.36535252230293, 0.0065772498871008)
(76.13430241531114, -0.00619045812313403)
(41.57110647048502, -0.0115421226076137)
(18.082073182424363, 0.0231197755627614)
(62.08147495545586, 0.00722440396103394)
(44.71358985615962, -0.0107014744736439)
(8.632820343571748, 0.0439379011930541)
(11.787104732733045, 0.0336545377659331)
(32.14256381071264, -0.0150988467750716)
(80.93279174054663, 0.0055778014565613)
(54.14040290686175, -0.00878209518815057)
(3.750928558828491, -0.146823697689196)
(27.514835395356723, 0.0157273307719214)
(52.65535850976031, 0.00847499047606231)
(46.370989404263696, 0.00958028815515183)
(22.71069824344117, -0.0218119300888545)
(77.79096362313051, 0.00579807605090685)
(2.1053169982115834, 0.197975479737667)
(16.41791710004775, -0.0309615043409198)
(55.797446075618666, 0.00801268502117623)
(24.37122036565722, 0.017606342342308)
(5.458826981657544, 0.066585519095165)
(98.12695004337189, -0.00477963222892754)
(90.35817962344102, 0.00500709584366417)
(47.85595269647905, -0.0099748680247489)
(74.64911611933218, 0.00603645530716869)
(85.55981885835757, -0.00549531264268704)
(10.11265913054425, -0.0528076153572385)
(96.64170656552182, 0.00468734668104291)
(91.84341089740369, -0.00511255424090387)
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:
$$x_{1} = 63.5665984080535$$
$$x_{2} = 60.42458359052$$
$$x_{3} = 82.4179991548889$$
$$x_{4} = 38.428471870656$$
$$x_{5} = 25.8552584606865$$
$$x_{6} = 88.7016222038868$$
$$x_{7} = 69.850511674875$$
$$x_{8} = -0.033790285342516$$
$$x_{9} = 66.708572569087$$
$$x_{10} = 19.5651215987813$$
$$x_{11} = 76.1343024153111$$
$$x_{12} = 41.571106470485$$
$$x_{13} = 44.7135898561596$$
$$x_{14} = 32.1425638107126$$
$$x_{15} = 54.1404029068618$$
$$x_{16} = 3.75092855882849$$
$$x_{17} = 22.7106982434412$$
$$x_{18} = 16.4179171000477$$
$$x_{19} = 98.1269500433719$$
$$x_{20} = 47.8559526964791$$
$$x_{21} = 85.5598188583576$$
$$x_{22} = 10.1126591305442$$
$$x_{23} = 91.8434108974037$$
Puntos máximos de la función:
$$x_{23} = -1.93007408048574$$
$$x_{23} = 33.8009961986888$$
$$x_{23} = 30.6580596186008$$
$$x_{23} = 93.4999487345468$$
$$x_{23} = 84.074602601828$$
$$x_{23} = 21.2270546596334$$
$$x_{23} = 71.5072467334144$$
$$x_{23} = 40.0862646696593$$
$$x_{23} = 49.5132102460951$$
$$x_{23} = 99.7834541642334$$
$$x_{23} = 68.3653525223029$$
$$x_{23} = 18.0820731824244$$
$$x_{23} = 62.0814749554559$$
$$x_{23} = 8.63282034357175$$
$$x_{23} = 11.787104732733$$
$$x_{23} = 80.9327917405466$$
$$x_{23} = 27.5148353953567$$
$$x_{23} = 52.6553585097603$$
$$x_{23} = 46.3709894042637$$
$$x_{23} = 77.7909636231305$$
$$x_{23} = 2.10531699821158$$
$$x_{23} = 55.7974460756187$$
$$x_{23} = 24.3712203656572$$
$$x_{23} = 5.45882698165754$$
$$x_{23} = 90.358179623441$$
$$x_{23} = 74.6491161193322$$
$$x_{23} = 96.6417065655218$$
Decrece en los intervalos
$$\left[98.1269500433719, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -0.033790285342516\right]$$
Asíntotas verticales
Hay:
$$x_{1} = 0$$
$$x_{1} = 0$$
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
$$\lim_{x \to -\infty}\left(- \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x}\right) = -\infty$$
Tomamos como el límite
es decir,
no hay asíntota horizontal a la izquierda
$$\lim_{x \to \infty}\left(- \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x}\right) = 0$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = 0$$
$$\lim_{x \to -\infty}\left(- \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x}\right) = -\infty$$
Tomamos como el límite
es decir,
no hay asíntota horizontal a la izquierda
$$\lim_{x \to \infty}\left(- \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x}\right) = 0$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = 0$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (exp((-x)/2)/2 - cos(x)*sin(sin(x)))/x - (cos(sin(x)) - E^((-x)/2))/x^2, dividida por x con x->+oo y x ->-oo
$$\lim_{x \to -\infty}\left(\frac{- \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x}}{x}\right) = \infty$$
Tomamos como el límite
es decir,
no hay asíntota inclinada a la izquierda
$$\lim_{x \to \infty}\left(\frac{- \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x}}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
$$\lim_{x \to -\infty}\left(\frac{- \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x}}{x}\right) = \infty$$
Tomamos como el límite
es decir,
no hay asíntota inclinada a la izquierda
$$\lim_{x \to \infty}\left(\frac{- \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x}}{x}\right) = 0$$
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:
$$- \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x} = - \frac{\frac{e^{\frac{x}{2}}}{2} + \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x} - \frac{- e^{\frac{x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}}$$
- No
$$- \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x} = \frac{\frac{e^{\frac{x}{2}}}{2} + \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x} + \frac{- e^{\frac{x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}}$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$- \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x} = - \frac{\frac{e^{\frac{x}{2}}}{2} + \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x} - \frac{- e^{\frac{x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}}$$
- No
$$- \frac{- e^{\frac{\left(-1\right) x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}} + \frac{\frac{e^{\frac{\left(-1\right) x}{2}}}{2} - \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x} = \frac{\frac{e^{\frac{x}{2}}}{2} + \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x} + \frac{- e^{\frac{x}{2}} + \cos{\left(\sin{\left(x \right)} \right)}}{x^{2}}$$
- No
es decir, función
no es
par ni impar