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- 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 =:
-
x-x^3
-
x^4-2x^2
-
1-x^3
-
x^2/(x-3)
-
Expresiones idénticas
- (- cuatro *cos(dos *x)+ tres *sin(dos *x)- diez *x*cos(dos *x)- cinco *x*sin(dos *x))*exp(dos)/ veinticinco
- ( menos 4 multiplicar por coseno de (2 multiplicar por x) más 3 multiplicar por seno de (2 multiplicar por x) menos 10 multiplicar por x multiplicar por coseno de (2 multiplicar por x) menos 5 multiplicar por x multiplicar por seno de (2 multiplicar por x)) multiplicar por exponente de (2) dividir por 25
- ( menos cuatro multiplicar por coseno de (dos multiplicar por x) más tres multiplicar por seno de (dos multiplicar por x) menos diez multiplicar por x multiplicar por coseno de (dos multiplicar por x) menos cinco multiplicar por x multiplicar por seno de (dos multiplicar por x)) multiplicar por exponente de (dos) dividir por veinticinco
- (-4cos(2x)+3sin(2x)-10xcos(2x)-5xsin(2x))exp(2)/25
- -4cos2x+3sin2x-10xcos2x-5xsin2xexp2/25
- (-4*cos(2*x)+3*sin(2*x)-10*x*cos(2*x)-5*x*sin(2*x))*exp(2) dividir por 25
-
Expresiones semejantes
- (4*cos(2*x)+3*sin(2*x)-10*x*cos(2*x)-5*x*sin(2*x))*exp(2)/25
- (-4*cos(2*x)+3*sin(2*x)-10*x*cos(2*x)+5*x*sin(2*x))*exp(2)/25
- (-4*cos(2*x)+3*sin(2*x)+10*x*cos(2*x)-5*x*sin(2*x))*exp(2)/25
- (-4*cos(2*x)-3*sin(2*x)-10*x*cos(2*x)-5*x*sin(2*x))*exp(2)/25
-
Expresiones con funciones
- Coseno cos
- cos^2(x)-cos(x)
- cos(0.5x)-1
- cosx-x
- cos(x)*2
- cos(x)/9
- Seno sin
- sin(x)-3
- sinx/(2+cosx)
- sin(x)*cos(x)+x
- sin(x)+(x/2)
- sin(x^6)
- Coseno cos
- cos^2(x)-cos(x)
- cos(0.5x)-1
- cosx-x
- cos(x)*2
- cos(x)/9
- Seno sin
- sin(x)-3
- sinx/(2+cosx)
- sin(x)*cos(x)+x
- sin(x)+(x/2)
- sin(x^6)
- Exponente exp
- exp(x)/3
- exp((-1)/x^2)
- exp(1/(x-2))
- exp(y)
- exp(x)*x
Gráfico de la función y = (-4*cos(2*x)+3*sin(2*x)-10*x*cos(2*x)-5*x*sin(2*x))*exp(2)/25
Solución
Ha introducido
[src]
2
(-4*cos(2*x) + 3*sin(2*x) - 10*x*cos(2*x) - 5*x*sin(2*x))*e
f(x) = ------------------------------------------------------------
25
$$f{\left(x \right)} = \frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25}$$
f = ((-5*x*sin(2*x) - 10*x*cos(2*x) + 3*sin(2*x) - 4*cos(2*x))*exp(2))/25
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:
$$\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = -82.2325453148142$$
$$x_{2} = 48.1369742468376$$
$$x_{3} = 92.1212425868993$$
$$x_{4} = 71.7002750718382$$
$$x_{5} = -97.9409004053142$$
$$x_{6} = -63.3822620275935$$
$$x_{7} = -53.9569290879675$$
$$x_{8} = -96.3700706562873$$
$$x_{9} = -90.0867399786036$$
$$x_{10} = -49.2441826243389$$
$$x_{11} = -83.8033874497159$$
$$x_{12} = -77.52000774231$$
$$x_{13} = 38.711194082931$$
$$x_{14} = 27.7135950463327$$
$$x_{15} = 10.4231820678823$$
$$x_{16} = 13.5690713585147$$
$$x_{17} = -30.392080701905$$
$$x_{18} = 33.998096818604$$
$$x_{19} = 35.5691499799686$$
$$x_{20} = 77.9836839246782$$
$$x_{21} = 24.5710936445514$$
$$x_{22} = -25.6784664664367$$
$$x_{23} = -6.80652346886145$$
$$x_{24} = -5.22625597509219$$
$$x_{25} = -75.9491577762104$$
$$x_{26} = -69.6657336523285$$
$$x_{27} = -2.01596760929877$$
$$x_{28} = -11.5315060675231$$
$$x_{29} = -31.9632046337359$$
$$x_{30} = 85.8378990745764$$
$$x_{31} = -61.8113849962171$$
$$x_{32} = -47.6732513637146$$
$$x_{33} = 57.562427329489$$
$$x_{34} = -68.0948707145325$$
$$x_{35} = 70.1294166172771$$
$$x_{36} = -19.3927111661874$$
$$x_{37} = -88.5159040771196$$
$$x_{38} = 93.692075156457$$
$$x_{39} = 16.7133624699783$$
$$x_{40} = -17.8209857998202$$
$$x_{41} = 84.2670595187915$$
$$x_{42} = -9.95786750711371$$
$$x_{43} = 76.4128351491376$$
$$x_{44} = 2.51487634015187$$
$$x_{45} = -27.2497186610371$$
$$x_{46} = 40.2821898543443$$
$$x_{47} = -16.2490784315059$$
$$x_{48} = 54.4206355245892$$
$$x_{49} = -55.5278310424106$$
$$x_{50} = 82.6962183246632$$
$$x_{51} = 90.5504087626561$$
$$x_{52} = 11.9964038547978$$
$$x_{53} = 22.9997506147888$$
$$x_{54} = 19.8568075344756$$
$$x_{55} = 62.2750774800987$$
$$x_{56} = 99.9753940683265$$
$$x_{57} = 0.832403564977084$$
$$x_{58} = -60.2405037417412$$
$$x_{59} = -39.8184345452483$$
$$x_{60} = 68.5585553239472$$
$$x_{61} = 32.4270189220146$$
$$x_{62} = 63.8459523224512$$
$$x_{63} = 4.11257088016$$
$$x_{64} = -71.2365936441077$$
$$x_{65} = -74.3783055382886$$
$$x_{66} = -38.2474297987677$$
$$x_{67} = 98.4045659366674$$
$$x_{68} = -33.5342976831179$$
$$x_{69} = 18.2851637632985$$
$$x_{70} = -8.38313491957301$$
$$x_{71} = -91.6575745206459$$
$$x_{72} = 79.5545306341413$$
$$x_{73} = -99.5117290970474$$
$$x_{74} = -93.2284077721128$$
$$x_{75} = 60.7041985874648$$
$$x_{76} = 41.8531707240276$$
$$x_{77} = 46.5660389415817$$
$$x_{78} = -46.1023108671164$$
$$x_{79} = -85.3742278949593$$
$$x_{80} = -24.1071543447115$$
$$x_{81} = 5.69574005599237$$
$$x_{82} = -52.3860207742208$$
$$x_{83} = 49.7079008028105$$
$$x_{84} = 26.1423714491946$$
$$x_{85} = 55.9915342108209$$
$$x_{86} = -41.3894233927615$$
$$x_{87} = -3.63724136542249$$
o sea hay que resolver la ecuación:
$$\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = -82.2325453148142$$
$$x_{2} = 48.1369742468376$$
$$x_{3} = 92.1212425868993$$
$$x_{4} = 71.7002750718382$$
$$x_{5} = -97.9409004053142$$
$$x_{6} = -63.3822620275935$$
$$x_{7} = -53.9569290879675$$
$$x_{8} = -96.3700706562873$$
$$x_{9} = -90.0867399786036$$
$$x_{10} = -49.2441826243389$$
$$x_{11} = -83.8033874497159$$
$$x_{12} = -77.52000774231$$
$$x_{13} = 38.711194082931$$
$$x_{14} = 27.7135950463327$$
$$x_{15} = 10.4231820678823$$
$$x_{16} = 13.5690713585147$$
$$x_{17} = -30.392080701905$$
$$x_{18} = 33.998096818604$$
$$x_{19} = 35.5691499799686$$
$$x_{20} = 77.9836839246782$$
$$x_{21} = 24.5710936445514$$
$$x_{22} = -25.6784664664367$$
$$x_{23} = -6.80652346886145$$
$$x_{24} = -5.22625597509219$$
$$x_{25} = -75.9491577762104$$
$$x_{26} = -69.6657336523285$$
$$x_{27} = -2.01596760929877$$
$$x_{28} = -11.5315060675231$$
$$x_{29} = -31.9632046337359$$
$$x_{30} = 85.8378990745764$$
$$x_{31} = -61.8113849962171$$
$$x_{32} = -47.6732513637146$$
$$x_{33} = 57.562427329489$$
$$x_{34} = -68.0948707145325$$
$$x_{35} = 70.1294166172771$$
$$x_{36} = -19.3927111661874$$
$$x_{37} = -88.5159040771196$$
$$x_{38} = 93.692075156457$$
$$x_{39} = 16.7133624699783$$
$$x_{40} = -17.8209857998202$$
$$x_{41} = 84.2670595187915$$
$$x_{42} = -9.95786750711371$$
$$x_{43} = 76.4128351491376$$
$$x_{44} = 2.51487634015187$$
$$x_{45} = -27.2497186610371$$
$$x_{46} = 40.2821898543443$$
$$x_{47} = -16.2490784315059$$
$$x_{48} = 54.4206355245892$$
$$x_{49} = -55.5278310424106$$
$$x_{50} = 82.6962183246632$$
$$x_{51} = 90.5504087626561$$
$$x_{52} = 11.9964038547978$$
$$x_{53} = 22.9997506147888$$
$$x_{54} = 19.8568075344756$$
$$x_{55} = 62.2750774800987$$
$$x_{56} = 99.9753940683265$$
$$x_{57} = 0.832403564977084$$
$$x_{58} = -60.2405037417412$$
$$x_{59} = -39.8184345452483$$
$$x_{60} = 68.5585553239472$$
$$x_{61} = 32.4270189220146$$
$$x_{62} = 63.8459523224512$$
$$x_{63} = 4.11257088016$$
$$x_{64} = -71.2365936441077$$
$$x_{65} = -74.3783055382886$$
$$x_{66} = -38.2474297987677$$
$$x_{67} = 98.4045659366674$$
$$x_{68} = -33.5342976831179$$
$$x_{69} = 18.2851637632985$$
$$x_{70} = -8.38313491957301$$
$$x_{71} = -91.6575745206459$$
$$x_{72} = 79.5545306341413$$
$$x_{73} = -99.5117290970474$$
$$x_{74} = -93.2284077721128$$
$$x_{75} = 60.7041985874648$$
$$x_{76} = 41.8531707240276$$
$$x_{77} = 46.5660389415817$$
$$x_{78} = -46.1023108671164$$
$$x_{79} = -85.3742278949593$$
$$x_{80} = -24.1071543447115$$
$$x_{81} = 5.69574005599237$$
$$x_{82} = -52.3860207742208$$
$$x_{83} = 49.7079008028105$$
$$x_{84} = 26.1423714491946$$
$$x_{85} = 55.9915342108209$$
$$x_{86} = -41.3894233927615$$
$$x_{87} = -3.63724136542249$$
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
$$\frac{\left(20 x \sin{\left(2 x \right)} - 10 x \cos{\left(2 x \right)} + 3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right) e^{2}}{25} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 64.6352443879741$$
$$x_{2} = -72.0255033591792$$
$$x_{3} = -35.8978923510335$$
$$x_{4} = -67.3131632574602$$
$$x_{5} = -94.0164887583458$$
$$x_{6} = -100.2996406125$$
$$x_{7} = -79.8794163763463$$
$$x_{8} = -51.6054276384411$$
$$x_{9} = 45.7860045671659$$
$$x_{10} = 37.9322468707416$$
$$x_{11} = 52.06905917643$$
$$x_{12} = -23.3322825654232$$
$$x_{13} = 100.763283948745$$
$$x_{14} = -70.4547225967174$$
$$x_{15} = 20.6545735900731$$
$$x_{16} = -57.8885070098078$$
$$x_{17} = -64.1716071901995$$
$$x_{18} = -1.38120160239195$$
$$x_{19} = 9.66167172579424$$
$$x_{20} = -7.62888790549685$$
$$x_{21} = -21.7616436866734$$
$$x_{22} = 39.5029913226638$$
$$x_{23} = -26.4736167915785$$
$$x_{24} = -89.3041279638035$$
$$x_{25} = 58.3521418348081$$
$$x_{26} = 86.6261976410267$$
$$x_{27} = 1.82726394043287$$
$$x_{28} = 44.2152466924093$$
$$x_{29} = -78.308632669004$$
$$x_{30} = -45.3223777683704$$
$$x_{31} = 88.1969837349327$$
$$x_{32} = 67.7768014012035$$
$$x_{33} = 80.3430572566921$$
$$x_{34} = -86.1625558175537$$
$$x_{35} = 30.0786053386116$$
$$x_{36} = 31.6493202274584$$
$$x_{37} = 14.3724218304636$$
$$x_{38} = 83.4846266056516$$
$$x_{39} = 61.4936910044344$$
$$x_{40} = 66.2060224730732$$
$$x_{41} = 50.4982924871669$$
$$x_{42} = 53.6398275949959$$
$$x_{43} = 42.6444916370061$$
$$x_{44} = 17.5134060900679$$
$$x_{45} = -50.0346619693212$$
$$x_{46} = -81.4502005716198$$
$$x_{47} = -95.5872763087217$$
$$x_{48} = 0.325795503797285$$
$$x_{49} = -59.4592803626043$$
$$x_{50} = 75.6307068537696$$
$$x_{51} = -28.0443057693738$$
$$x_{52} = -12.33866578552$$
$$x_{53} = -20.1910295447822$$
$$x_{54} = 81.9138417082726$$
$$x_{55} = -37.4686296462638$$
$$x_{56} = 72.4891426972687$$
$$x_{57} = -6.05989325317838$$
$$x_{58} = -42.180868035436$$
$$x_{59} = 6.52244633170316$$
$$x_{60} = 23.7958523877927$$
$$x_{61} = -34.3271604895018$$
$$x_{62} = 96.0509192143605$$
$$x_{63} = 8.09183517436296$$
$$x_{64} = -73.5962847878296$$
$$x_{65} = -15.4794117940065$$
$$x_{66} = 22.2252019991699$$
$$x_{67} = -43.7516214066214$$
$$x_{68} = -92.4457015068628$$
$$x_{69} = -56.3177349431024$$
$$x_{70} = -65.742384785425$$
$$x_{71} = -48.46389829568$$
$$x_{72} = 89.7677701861569$$
$$x_{73} = 36.3615068758865$$
$$x_{74} = 85.0554119241887$$
$$x_{75} = 28.5078993606643$$
$$x_{76} = 15.9428843727392$$
$$x_{77} = -29.6150062107158$$
$$x_{78} = -87.7333417066779$$
$$x_{79} = 74.0599244741303$$
$$x_{80} = -122.290699217015$$
$$x_{81} = -13.9089903135835$$
$$x_{82} = 97.621707199601$$
$$x_{83} = 94.4801315058989$$
$$x_{84} = 59.9229158515985$$
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:
$$x_{1} = -35.8978923510335$$
$$x_{2} = -67.3131632574602$$
$$x_{3} = -79.8794163763463$$
$$x_{4} = -51.6054276384411$$
$$x_{5} = 37.9322468707416$$
$$x_{6} = -23.3322825654232$$
$$x_{7} = 100.763283948745$$
$$x_{8} = -70.4547225967174$$
$$x_{9} = -57.8885070098078$$
$$x_{10} = -64.1716071901995$$
$$x_{11} = -1.38120160239195$$
$$x_{12} = 9.66167172579424$$
$$x_{13} = -7.62888790549685$$
$$x_{14} = -26.4736167915785$$
$$x_{15} = -89.3041279638035$$
$$x_{16} = 44.2152466924093$$
$$x_{17} = -45.3223777683704$$
$$x_{18} = 88.1969837349327$$
$$x_{19} = -86.1625558175537$$
$$x_{20} = 31.6493202274584$$
$$x_{21} = 66.2060224730732$$
$$x_{22} = 50.4982924871669$$
$$x_{23} = 53.6398275949959$$
$$x_{24} = -95.5872763087217$$
$$x_{25} = 0.325795503797285$$
$$x_{26} = 75.6307068537696$$
$$x_{27} = -20.1910295447822$$
$$x_{28} = 81.9138417082726$$
$$x_{29} = 72.4891426972687$$
$$x_{30} = -42.180868035436$$
$$x_{31} = 6.52244633170316$$
$$x_{32} = -73.5962847878296$$
$$x_{33} = 22.2252019991699$$
$$x_{34} = -92.4457015068628$$
$$x_{35} = -48.46389829568$$
$$x_{36} = 85.0554119241887$$
$$x_{37} = 28.5078993606643$$
$$x_{38} = 15.9428843727392$$
$$x_{39} = -29.6150062107158$$
$$x_{40} = -13.9089903135835$$
$$x_{41} = 97.621707199601$$
$$x_{42} = 94.4801315058989$$
$$x_{43} = 59.9229158515985$$
Puntos máximos de la función:
$$x_{43} = 64.6352443879741$$
$$x_{43} = -72.0255033591792$$
$$x_{43} = -94.0164887583458$$
$$x_{43} = -100.2996406125$$
$$x_{43} = 45.7860045671659$$
$$x_{43} = 52.06905917643$$
$$x_{43} = 20.6545735900731$$
$$x_{43} = -21.7616436866734$$
$$x_{43} = 39.5029913226638$$
$$x_{43} = 58.3521418348081$$
$$x_{43} = 86.6261976410267$$
$$x_{43} = 1.82726394043287$$
$$x_{43} = -78.308632669004$$
$$x_{43} = 67.7768014012035$$
$$x_{43} = 80.3430572566921$$
$$x_{43} = 30.0786053386116$$
$$x_{43} = 14.3724218304636$$
$$x_{43} = 83.4846266056516$$
$$x_{43} = 61.4936910044344$$
$$x_{43} = 42.6444916370061$$
$$x_{43} = 17.5134060900679$$
$$x_{43} = -50.0346619693212$$
$$x_{43} = -81.4502005716198$$
$$x_{43} = -59.4592803626043$$
$$x_{43} = -28.0443057693738$$
$$x_{43} = -12.33866578552$$
$$x_{43} = -37.4686296462638$$
$$x_{43} = -6.05989325317838$$
$$x_{43} = 23.7958523877927$$
$$x_{43} = -34.3271604895018$$
$$x_{43} = 96.0509192143605$$
$$x_{43} = 8.09183517436296$$
$$x_{43} = -15.4794117940065$$
$$x_{43} = -43.7516214066214$$
$$x_{43} = -56.3177349431024$$
$$x_{43} = -65.742384785425$$
$$x_{43} = 89.7677701861569$$
$$x_{43} = 36.3615068758865$$
$$x_{43} = -87.7333417066779$$
$$x_{43} = 74.0599244741303$$
$$x_{43} = -122.290699217015$$
Decrece en los intervalos
$$\left[100.763283948745, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -95.5872763087217\right]$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(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
$$\frac{\left(20 x \sin{\left(2 x \right)} - 10 x \cos{\left(2 x \right)} + 3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right) e^{2}}{25} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 64.6352443879741$$
$$x_{2} = -72.0255033591792$$
$$x_{3} = -35.8978923510335$$
$$x_{4} = -67.3131632574602$$
$$x_{5} = -94.0164887583458$$
$$x_{6} = -100.2996406125$$
$$x_{7} = -79.8794163763463$$
$$x_{8} = -51.6054276384411$$
$$x_{9} = 45.7860045671659$$
$$x_{10} = 37.9322468707416$$
$$x_{11} = 52.06905917643$$
$$x_{12} = -23.3322825654232$$
$$x_{13} = 100.763283948745$$
$$x_{14} = -70.4547225967174$$
$$x_{15} = 20.6545735900731$$
$$x_{16} = -57.8885070098078$$
$$x_{17} = -64.1716071901995$$
$$x_{18} = -1.38120160239195$$
$$x_{19} = 9.66167172579424$$
$$x_{20} = -7.62888790549685$$
$$x_{21} = -21.7616436866734$$
$$x_{22} = 39.5029913226638$$
$$x_{23} = -26.4736167915785$$
$$x_{24} = -89.3041279638035$$
$$x_{25} = 58.3521418348081$$
$$x_{26} = 86.6261976410267$$
$$x_{27} = 1.82726394043287$$
$$x_{28} = 44.2152466924093$$
$$x_{29} = -78.308632669004$$
$$x_{30} = -45.3223777683704$$
$$x_{31} = 88.1969837349327$$
$$x_{32} = 67.7768014012035$$
$$x_{33} = 80.3430572566921$$
$$x_{34} = -86.1625558175537$$
$$x_{35} = 30.0786053386116$$
$$x_{36} = 31.6493202274584$$
$$x_{37} = 14.3724218304636$$
$$x_{38} = 83.4846266056516$$
$$x_{39} = 61.4936910044344$$
$$x_{40} = 66.2060224730732$$
$$x_{41} = 50.4982924871669$$
$$x_{42} = 53.6398275949959$$
$$x_{43} = 42.6444916370061$$
$$x_{44} = 17.5134060900679$$
$$x_{45} = -50.0346619693212$$
$$x_{46} = -81.4502005716198$$
$$x_{47} = -95.5872763087217$$
$$x_{48} = 0.325795503797285$$
$$x_{49} = -59.4592803626043$$
$$x_{50} = 75.6307068537696$$
$$x_{51} = -28.0443057693738$$
$$x_{52} = -12.33866578552$$
$$x_{53} = -20.1910295447822$$
$$x_{54} = 81.9138417082726$$
$$x_{55} = -37.4686296462638$$
$$x_{56} = 72.4891426972687$$
$$x_{57} = -6.05989325317838$$
$$x_{58} = -42.180868035436$$
$$x_{59} = 6.52244633170316$$
$$x_{60} = 23.7958523877927$$
$$x_{61} = -34.3271604895018$$
$$x_{62} = 96.0509192143605$$
$$x_{63} = 8.09183517436296$$
$$x_{64} = -73.5962847878296$$
$$x_{65} = -15.4794117940065$$
$$x_{66} = 22.2252019991699$$
$$x_{67} = -43.7516214066214$$
$$x_{68} = -92.4457015068628$$
$$x_{69} = -56.3177349431024$$
$$x_{70} = -65.742384785425$$
$$x_{71} = -48.46389829568$$
$$x_{72} = 89.7677701861569$$
$$x_{73} = 36.3615068758865$$
$$x_{74} = 85.0554119241887$$
$$x_{75} = 28.5078993606643$$
$$x_{76} = 15.9428843727392$$
$$x_{77} = -29.6150062107158$$
$$x_{78} = -87.7333417066779$$
$$x_{79} = 74.0599244741303$$
$$x_{80} = -122.290699217015$$
$$x_{81} = -13.9089903135835$$
$$x_{82} = 97.621707199601$$
$$x_{83} = 94.4801315058989$$
$$x_{84} = 59.9229158515985$$
Signos de extremos en los puntos:
2 (64.63524438797407, 28.9948923620801*e )
2 (-72.02550335917921, 32.1210614185897*e )
2 (-35.89789235103348, -15.9640190445123*e )
2 (-67.3131632574602, -30.0136191852217*e )
2 (-94.0164887583458, 41.9557947445377*e )
2 (-100.29964061249967, 44.7657191408808*e )
2 (-79.87941637634631, -35.6334657154449*e )
2 (-51.60542763844109, -22.9888146351093*e )
2 (45.78600456716588, 20.5651288215444*e )
2 (37.93224687074159, -17.0527314711191*e )
2 (52.069059176430024, 23.3750488688439*e )
2 (-23.332282565423245, -10.3442012872768*e )
2 (100.76328394874524, -45.1519539022625*e )
2 (-70.45472259671737, -31.418580641551*e )
2 (20.654573590073127, 9.32548385202523*e )
2 (-57.888507009807775, -25.7987357898477*e )
2 (-64.17160719019948, -28.608657875224*e )
2 (-1.3812016023919491, -0.511276106334118*e )
2 (9.66167172579424, -4.40823309118173*e )
2 (-7.6288879054968515, -3.31959096286351*e )
2 (-21.761643686673448, 9.64172685620577*e )
2 (39.50299132266381, 17.7552106242279*e )
2 (-26.473616791578547, -11.749152675255*e )
2 (-89.30412796380352, -39.8483515857425*e )
2 (58.35214183480807, 26.1849701705871*e )
2 (86.62619764102669, 38.8296242503845*e )
2 (1.8272639404328703, 0.896705738789304*e )
2 (44.21524669240928, -19.862649068112*e )
2 (-78.30863266900396, 34.9309848067047*e )
2 (-45.322377768370444, -20.1788947997625*e )
2 (88.19698373493272, -39.5321052658568*e )
2 (67.77680140120351, 30.3998537143839*e )
2 (80.34305725669208, 36.019700366994*e )
2 (-86.1625558175537, -38.4433895566568*e )
2 (30.078605338611613, 13.5403393161195*e )
2 (31.649320227458396, -14.2428171470094*e )
2 (14.372421830463598, 6.51560418959179*e )
2 (83.48462660565158, 37.4246622709793*e )
2 (61.493691004434396, 27.589931172105*e )
2 (66.20602247307319, -29.6973730193808*e )
2 (50.49829248716687, -22.6725687211968*e )
2 (53.63982759499592, -24.0775290938307*e )
2 (42.64449163700615, 19.1601694407716*e )
2 (17.51340609006795, 7.9205399219896*e )
2 (-50.0346619693212, 22.2863345330862*e )
2 (-81.45020057161976, 36.3359466460064*e )
2 (-95.58727630872174, -42.658275825146*e )
2 (0.3257955037972845, -0.197579404789642*e )
2 (-59.45928036260429, 26.5012162355076*e )
2 (75.63070685376955, -33.9122576729332*e )
2 (-28.044305769373786, 12.451629347221*e )
2 (-12.33866578552004, 5.42691853666759*e )
2 (-20.191029544782236, -8.93925353165252*e )
2 (81.91384170827256, -36.7221813090182*e )
2 (-37.46862964626381, 16.6664978775403*e )
2 (72.48914269726872, -32.5072960011658*e )
2 (-6.059893253178378, 2.61719016207641*e )
2 (-42.18086803543602, -18.7739355619817*e )
2 (6.52244633170316, -3.00337610001784*e )
2 (23.795852387792745, 10.73043276069*e )
2 (-34.32716048950175, 15.2615404545068*e )
2 (96.05091921436053, 43.0445105672703*e )
2 (8.09183517436296, 3.70579456836871*e )
2 (-73.59628478782957, -32.8235422254219*e )
2 (-15.479411794006543, 6.8318436088485*e )
2 (22.225201999169858, -10.0279578147771*e )
2 (-43.75162140662138, 19.4764151139974*e )
2 (-92.44570150686276, -41.2533136772963*e )
2 (-56.3177349431024, 25.0962554017054*e )
2 (-65.74238478542499, 29.3111385106163*e )
2 (-48.463898295680046, -21.5838545203074*e )
2 (89.76777018615694, 40.234586297309*e )
2 (36.36150687588652, 16.3502525173509*e )
2 (85.05541192418873, -38.1271432517755*e )
2 (28.50789936066434, -12.837861883783*e )
2 (15.942884372739243, -7.21807073205542*e )
2 (-29.615006210715844, -13.1541065319221*e )
2 (-87.73334170667792, 39.1458705629708*e )
2 (74.05992447413026, 33.2097768235707*e )
2 (-122.2906992170149, 54.6004557407121*e )
2 (-13.908990313583539, -6.12937890360175*e )
2 (97.62170719960096, -43.7469916673266*e )
2 (94.4801315058989, -42.342029479592*e )
2 (59.92291585159847, -26.8874506459426*e )
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:
$$x_{1} = -35.8978923510335$$
$$x_{2} = -67.3131632574602$$
$$x_{3} = -79.8794163763463$$
$$x_{4} = -51.6054276384411$$
$$x_{5} = 37.9322468707416$$
$$x_{6} = -23.3322825654232$$
$$x_{7} = 100.763283948745$$
$$x_{8} = -70.4547225967174$$
$$x_{9} = -57.8885070098078$$
$$x_{10} = -64.1716071901995$$
$$x_{11} = -1.38120160239195$$
$$x_{12} = 9.66167172579424$$
$$x_{13} = -7.62888790549685$$
$$x_{14} = -26.4736167915785$$
$$x_{15} = -89.3041279638035$$
$$x_{16} = 44.2152466924093$$
$$x_{17} = -45.3223777683704$$
$$x_{18} = 88.1969837349327$$
$$x_{19} = -86.1625558175537$$
$$x_{20} = 31.6493202274584$$
$$x_{21} = 66.2060224730732$$
$$x_{22} = 50.4982924871669$$
$$x_{23} = 53.6398275949959$$
$$x_{24} = -95.5872763087217$$
$$x_{25} = 0.325795503797285$$
$$x_{26} = 75.6307068537696$$
$$x_{27} = -20.1910295447822$$
$$x_{28} = 81.9138417082726$$
$$x_{29} = 72.4891426972687$$
$$x_{30} = -42.180868035436$$
$$x_{31} = 6.52244633170316$$
$$x_{32} = -73.5962847878296$$
$$x_{33} = 22.2252019991699$$
$$x_{34} = -92.4457015068628$$
$$x_{35} = -48.46389829568$$
$$x_{36} = 85.0554119241887$$
$$x_{37} = 28.5078993606643$$
$$x_{38} = 15.9428843727392$$
$$x_{39} = -29.6150062107158$$
$$x_{40} = -13.9089903135835$$
$$x_{41} = 97.621707199601$$
$$x_{42} = 94.4801315058989$$
$$x_{43} = 59.9229158515985$$
Puntos máximos de la función:
$$x_{43} = 64.6352443879741$$
$$x_{43} = -72.0255033591792$$
$$x_{43} = -94.0164887583458$$
$$x_{43} = -100.2996406125$$
$$x_{43} = 45.7860045671659$$
$$x_{43} = 52.06905917643$$
$$x_{43} = 20.6545735900731$$
$$x_{43} = -21.7616436866734$$
$$x_{43} = 39.5029913226638$$
$$x_{43} = 58.3521418348081$$
$$x_{43} = 86.6261976410267$$
$$x_{43} = 1.82726394043287$$
$$x_{43} = -78.308632669004$$
$$x_{43} = 67.7768014012035$$
$$x_{43} = 80.3430572566921$$
$$x_{43} = 30.0786053386116$$
$$x_{43} = 14.3724218304636$$
$$x_{43} = 83.4846266056516$$
$$x_{43} = 61.4936910044344$$
$$x_{43} = 42.6444916370061$$
$$x_{43} = 17.5134060900679$$
$$x_{43} = -50.0346619693212$$
$$x_{43} = -81.4502005716198$$
$$x_{43} = -59.4592803626043$$
$$x_{43} = -28.0443057693738$$
$$x_{43} = -12.33866578552$$
$$x_{43} = -37.4686296462638$$
$$x_{43} = -6.05989325317838$$
$$x_{43} = 23.7958523877927$$
$$x_{43} = -34.3271604895018$$
$$x_{43} = 96.0509192143605$$
$$x_{43} = 8.09183517436296$$
$$x_{43} = -15.4794117940065$$
$$x_{43} = -43.7516214066214$$
$$x_{43} = -56.3177349431024$$
$$x_{43} = -65.742384785425$$
$$x_{43} = 89.7677701861569$$
$$x_{43} = 36.3615068758865$$
$$x_{43} = -87.7333417066779$$
$$x_{43} = 74.0599244741303$$
$$x_{43} = -122.290699217015$$
Decrece en los intervalos
$$\left[100.763283948745, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -95.5872763087217\right]$$
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
$$\frac{4 \left(5 x \sin{\left(2 x \right)} + 10 x \cos{\left(2 x \right)} + 7 \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) e^{2}}{25} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = -52.39560050084$$
$$x_{2} = 7.34011082755754$$
$$x_{3} = 90.5559181166057$$
$$x_{4} = 79.5607994828484$$
$$x_{5} = -3.77823446654156$$
$$x_{6} = 76.4193610334537$$
$$x_{7} = 60.712407331793$$
$$x_{8} = -74.3850455717934$$
$$x_{9} = -27.2681932185021$$
$$x_{10} = 98.4096364906533$$
$$x_{11} = 77.990078709455$$
$$x_{12} = 63.853758468634$$
$$x_{13} = 54.4297883675997$$
$$x_{14} = -60.2488305449496$$
$$x_{15} = -71.2436317213696$$
$$x_{16} = -91.6630412793407$$
$$x_{17} = 12.0372918669791$$
$$x_{18} = -83.8093677321176$$
$$x_{19} = 46.5767285387698$$
$$x_{20} = -31.9789399874986$$
$$x_{21} = 82.7022496177044$$
$$x_{22} = 70.1365254526854$$
$$x_{23} = 49.7179176752173$$
$$x_{24} = -63.3901748615295$$
$$x_{25} = -33.54929194441$$
$$x_{26} = -90.0923022635643$$
$$x_{27} = 1.21743661824315$$
$$x_{28} = -69.6729308591578$$
$$x_{29} = 10.4700863363716$$
$$x_{30} = 32.4423379871201$$
$$x_{31} = 5.77961404322637$$
$$x_{32} = -39.8310517723009$$
$$x_{33} = 85.8437101583132$$
$$x_{34} = 62.2830798651494$$
$$x_{35} = 99.9803851183617$$
$$x_{36} = 27.7314984341647$$
$$x_{37} = 19.8817124115812$$
$$x_{38} = -0.905837181017051$$
$$x_{39} = 143.961768689774$$
$$x_{40} = 16.7428843878138$$
$$x_{41} = 104.692639572387$$
$$x_{42} = 40.2945380022353$$
$$x_{43} = -93.2337822301932$$
$$x_{44} = -99.5167635483288$$
$$x_{45} = 68.5658265414413$$
$$x_{46} = 41.8650577909712$$
$$x_{47} = -75.9557580572675$$
$$x_{48} = -6.88153938882236$$
$$x_{49} = 13.605309684597$$
$$x_{50} = -5.32424319445369$$
$$x_{51} = -68.102234412857$$
$$x_{52} = -17.8493252270127$$
$$x_{53} = 71.7072286191551$$
$$x_{54} = 26.161341533004$$
$$x_{55} = 38.72404051969$$
$$x_{56} = 93.6974001819511$$
$$x_{57} = -16.280185477059$$
$$x_{58} = -96.3752695579269$$
$$x_{59} = -19.4187349802935$$
$$x_{60} = -77.5264739484552$$
$$x_{61} = 0.0409142048473795$$
$$x_{62} = -2.2657101507875$$
$$x_{63} = -97.9460157604398$$
$$x_{64} = 18.3121814372645$$
$$x_{65} = -38.2605677226714$$
$$x_{66} = 56.0004312402572$$
$$x_{67} = -53.9662289489669$$
$$x_{68} = -49.2543758469485$$
$$x_{69} = -85.3800978970367$$
$$x_{70} = -24.1280542185133$$
$$x_{71} = -8.44388256158267$$
$$x_{72} = -30.4086341979852$$
$$x_{73} = 84.272978659837$$
$$x_{74} = -41.4015596186877$$
$$x_{75} = 57.5710824552644$$
$$x_{76} = 4.22618247840335$$
$$x_{77} = -61.8194995387526$$
$$x_{78} = -25.6980790089547$$
$$x_{79} = -46.1132015324485$$
$$x_{80} = -55.5368669248221$$
$$x_{81} = 92.1266582086398$$
$$x_{82} = -10.0088987328688$$
$$x_{83} = 24.5912655440908$$
$$x_{84} = 48.1473165545846$$
$$x_{85} = 35.5831242121309$$
$$x_{86} = -11.575496705649$$
$$x_{87} = 34.0127126021886$$
$$x_{88} = -82.2386401004529$$
$$x_{89} = -88.5215652860922$$
$$x_{90} = -47.6837817731732$$
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
$$\left[143.961768689774, \infty\right)$$
Convexa en los intervalos
$$\left(-\infty, -99.5167635483288\right]$$
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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
$$\frac{4 \left(5 x \sin{\left(2 x \right)} + 10 x \cos{\left(2 x \right)} + 7 \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) e^{2}}{25} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = -52.39560050084$$
$$x_{2} = 7.34011082755754$$
$$x_{3} = 90.5559181166057$$
$$x_{4} = 79.5607994828484$$
$$x_{5} = -3.77823446654156$$
$$x_{6} = 76.4193610334537$$
$$x_{7} = 60.712407331793$$
$$x_{8} = -74.3850455717934$$
$$x_{9} = -27.2681932185021$$
$$x_{10} = 98.4096364906533$$
$$x_{11} = 77.990078709455$$
$$x_{12} = 63.853758468634$$
$$x_{13} = 54.4297883675997$$
$$x_{14} = -60.2488305449496$$
$$x_{15} = -71.2436317213696$$
$$x_{16} = -91.6630412793407$$
$$x_{17} = 12.0372918669791$$
$$x_{18} = -83.8093677321176$$
$$x_{19} = 46.5767285387698$$
$$x_{20} = -31.9789399874986$$
$$x_{21} = 82.7022496177044$$
$$x_{22} = 70.1365254526854$$
$$x_{23} = 49.7179176752173$$
$$x_{24} = -63.3901748615295$$
$$x_{25} = -33.54929194441$$
$$x_{26} = -90.0923022635643$$
$$x_{27} = 1.21743661824315$$
$$x_{28} = -69.6729308591578$$
$$x_{29} = 10.4700863363716$$
$$x_{30} = 32.4423379871201$$
$$x_{31} = 5.77961404322637$$
$$x_{32} = -39.8310517723009$$
$$x_{33} = 85.8437101583132$$
$$x_{34} = 62.2830798651494$$
$$x_{35} = 99.9803851183617$$
$$x_{36} = 27.7314984341647$$
$$x_{37} = 19.8817124115812$$
$$x_{38} = -0.905837181017051$$
$$x_{39} = 143.961768689774$$
$$x_{40} = 16.7428843878138$$
$$x_{41} = 104.692639572387$$
$$x_{42} = 40.2945380022353$$
$$x_{43} = -93.2337822301932$$
$$x_{44} = -99.5167635483288$$
$$x_{45} = 68.5658265414413$$
$$x_{46} = 41.8650577909712$$
$$x_{47} = -75.9557580572675$$
$$x_{48} = -6.88153938882236$$
$$x_{49} = 13.605309684597$$
$$x_{50} = -5.32424319445369$$
$$x_{51} = -68.102234412857$$
$$x_{52} = -17.8493252270127$$
$$x_{53} = 71.7072286191551$$
$$x_{54} = 26.161341533004$$
$$x_{55} = 38.72404051969$$
$$x_{56} = 93.6974001819511$$
$$x_{57} = -16.280185477059$$
$$x_{58} = -96.3752695579269$$
$$x_{59} = -19.4187349802935$$
$$x_{60} = -77.5264739484552$$
$$x_{61} = 0.0409142048473795$$
$$x_{62} = -2.2657101507875$$
$$x_{63} = -97.9460157604398$$
$$x_{64} = 18.3121814372645$$
$$x_{65} = -38.2605677226714$$
$$x_{66} = 56.0004312402572$$
$$x_{67} = -53.9662289489669$$
$$x_{68} = -49.2543758469485$$
$$x_{69} = -85.3800978970367$$
$$x_{70} = -24.1280542185133$$
$$x_{71} = -8.44388256158267$$
$$x_{72} = -30.4086341979852$$
$$x_{73} = 84.272978659837$$
$$x_{74} = -41.4015596186877$$
$$x_{75} = 57.5710824552644$$
$$x_{76} = 4.22618247840335$$
$$x_{77} = -61.8194995387526$$
$$x_{78} = -25.6980790089547$$
$$x_{79} = -46.1132015324485$$
$$x_{80} = -55.5368669248221$$
$$x_{81} = 92.1266582086398$$
$$x_{82} = -10.0088987328688$$
$$x_{83} = 24.5912655440908$$
$$x_{84} = 48.1473165545846$$
$$x_{85} = 35.5831242121309$$
$$x_{86} = -11.575496705649$$
$$x_{87} = 34.0127126021886$$
$$x_{88} = -82.2386401004529$$
$$x_{89} = -88.5215652860922$$
$$x_{90} = -47.6837817731732$$
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
$$\left[143.961768689774, \infty\right)$$
Convexa en los intervalos
$$\left(-\infty, -99.5167635483288\right]$$
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \lim_{x \to -\infty}\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25}\right)$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \lim_{x \to \infty}\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \lim_{x \to -\infty}\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \lim_{x \to \infty}\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25}\right)$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función ((-4*cos(2*x) + 3*sin(2*x) - 10*x*cos(2*x) - 5*x*sin(2*x))*exp(2))/25, dividida por x con x->+oo y x ->-oo
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = x \lim_{x \to -\infty}\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25 x}\right)$$
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = x \lim_{x \to \infty}\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25 x}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = x \lim_{x \to -\infty}\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25 x}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = x \lim_{x \to \infty}\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25 x}\right)$$
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:
$$\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25} = \frac{\left(- 5 x \sin{\left(2 x \right)} + 10 x \cos{\left(2 x \right)} - 3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right) e^{2}}{25}$$
- No
$$\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25} = - \frac{\left(- 5 x \sin{\left(2 x \right)} + 10 x \cos{\left(2 x \right)} - 3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right) e^{2}}{25}$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25} = \frac{\left(- 5 x \sin{\left(2 x \right)} + 10 x \cos{\left(2 x \right)} - 3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right) e^{2}}{25}$$
- No
$$\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25} = - \frac{\left(- 5 x \sin{\left(2 x \right)} + 10 x \cos{\left(2 x \right)} - 3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right) e^{2}}{25}$$
- No
es decir, función
no es
par ni impar