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x*(sin(x))^2
Trazado el gráfico de la función/ x*(sin(x))^2

Gráfico de la función y = x*(sin(x))^2

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
            2   
f(x) = x*sin (x)
f(x)=xsin⁡2(x)f{\left(x \right)} = x \sin^{2}{\left(x \right)} 
f = x*sin(x)^2
Gráfico de la función
02468-8-6-4-2-1010-2020
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:
xsin⁡2(x)=0x \sin^{2}{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=πx_{2} = \pi
Solución numérica
x1=3.14159299901751x_{1} = 3.14159299901751
x2=9.42477823217446x_{2} = 9.42477823217446
x3=−3.14159295661011x_{3} = -3.14159295661011
x4=−65.97344576507x_{4} = -65.97344576507
x5=−21.9911485864645x_{5} = -21.9911485864645
x6=−9.42477813384597x_{6} = -9.42477813384597
x7=21.9911485852065x_{7} = 21.9911485852065
x8=−59.6902604576978x_{8} = -59.6902604576978
x9=−81.6814090380603x_{9} = -81.6814090380603
x10=12.5663704571697x_{10} = 12.5663704571697
x11=94.2477796093525x_{11} = 94.2477796093525
x12=87.964594335789x_{12} = 87.964594335789
x13=−28.2743337190252x_{13} = -28.2743337190252
x14=−6.28318514963244x_{14} = -6.28318514963244
x15=−37.6991118772194x_{15} = -37.6991118772194
x16=0x_{16} = 0
x17=−31.4159267074656x_{17} = -31.4159267074656
x18=−43.9822971746086x_{18} = -43.9822971746086
x19=28.2743338652241x_{19} = 28.2743338652241
x20=−87.964594358858x_{20} = -87.964594358858
x21=25.1327410420105x_{21} = 25.1327410420105
x22=3.1415923353488x_{22} = 3.1415923353488
x23=43.9822971694455x_{23} = 43.9822971694455
x24=15.7079634453651x_{24} = 15.7079634453651
x25=72.2566310277197x_{25} = 72.2566310277197
x26=34.5575190322918x_{26} = 34.5575190322918
x27=3.1415931516833x_{27} = 3.1415931516833
x28=37.6991120212708x_{28} = 37.6991120212708
x29=−9.09618852922⋅10−5x_{29} = -9.09618852922 \cdot 10^{-5}
x30=65.9734457529229x_{30} = 65.9734457529229
x31=18.8495556906624x_{31} = 18.8495556906624
x32=6.28318528443896x_{32} = 6.28318528443896
x33=−15.7079632966406x_{33} = -15.7079632966406
x34=−3.14159271719906x_{34} = -3.14159271719906
x35=−18.8495557219808x_{35} = -18.8495557219808
x36=50.2654824463527x_{36} = 50.2654824463527
x37=−18.8495561496377x_{37} = -18.8495561496377
x38=−12.5663703832991x_{38} = -12.5663703832991
x39=3.69946911765974⋅10−5x_{39} = 3.69946911765974 \cdot 10^{-5}
Puntos de cruce con el eje de coordenadas Y
El gráfico cruce el eje Y cuando x es igual a 0:
sustituimos x = 0 en x*sin(x)^2.
0sin⁡2(0)0 \sin^{2}{\left(0 \right)}
Resultado:
f(0)=0f{\left(0 \right)} = 0
Punto:
(0, 0)
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
ddxf(x)=0\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:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
primera derivada
2xsin⁡(x)cos⁡(x)+sin⁡2(x)=02 x \sin{\left(x \right)} \cos{\left(x \right)} + \sin^{2}{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−14.1724320747999x_{1} = -14.1724320747999
x2=51.8459224452234x_{2} = 51.8459224452234
x3=−61.2692172687226x_{3} = -61.2692172687226
x4=67.5516436614121x_{4} = 67.5516436614121
x5=73.8341991854591x_{5} = 73.8341991854591
x6=−36.1421488970061x_{6} = -36.1421488970061
x7=−105.248104538899x_{7} = -105.248104538899
x8=14.1724320747999x_{8} = 14.1724320747999
x9=−89.5409746049841x_{9} = -89.5409746049841
x10=−53.4070751110265x_{10} = -53.4070751110265
x11=−80.1168534696549x_{11} = -80.1168534696549
x12=−7.91705268466621x_{12} = -7.91705268466621
x13=−9.42477796076938x_{13} = -9.42477796076938
x14=28.2743338823081x_{14} = 28.2743338823081
x15=50.2654824574367x_{15} = 50.2654824574367
x16=−97.3893722612836x_{16} = -97.3893722612836
x17=−58.1280655761511x_{17} = -58.1280655761511
x18=70.692907433161x_{18} = 70.692907433161
x19=−84.8230016469244x_{19} = -84.8230016469244
x20=36.1421488970061x_{20} = 36.1421488970061
x21=86.3995849739529x_{21} = 86.3995849739529
x22=92.682377997352x_{22} = 92.682377997352
x23=34.5575191894877x_{23} = 34.5575191894877
x24=20.4448034666183x_{24} = 20.4448034666183
x25=1.83659720315213x_{25} = 1.83659720315213
x26=65.9734457253857x_{26} = 65.9734457253857
x27=0x_{27} = 0
x28=−67.5516436614121x_{28} = -67.5516436614121
x29=58.1280655761511x_{29} = 58.1280655761511
x30=3.14159265358979x_{30} = 3.14159265358979
x31=78.5398163397448x_{31} = 78.5398163397448
x32=−1.83659720315213x_{32} = -1.83659720315213
x33=−20.4448034666183x_{33} = -20.4448034666183
x34=59.6902604182061x_{34} = 59.6902604182061
x35=−42.4232862577008x_{35} = -42.4232862577008
x36=80.1168534696549x_{36} = 80.1168534696549
x37=100.530964914873x_{37} = 100.530964914873
x38=−72.2566310325652x_{38} = -72.2566310325652
x39=278.032748190065x_{39} = 278.032748190065
x40=21.9911485751286x_{40} = 21.9911485751286
x41=−23.5831433102848x_{41} = -23.5831433102848
x42=−37.6991118430775x_{42} = -37.6991118430775
x43=−81.6814089933346x_{43} = -81.6814089933346
x44=−21.9911485751286x_{44} = -21.9911485751286
x45=12.5663706143592x_{45} = 12.5663706143592
x46=−87.9645943005142x_{46} = -87.9645943005142
x47=−51.8459224452234x_{47} = -51.8459224452234
x48=−94.2477796076938x_{48} = -94.2477796076938
x49=−29.861872403816x_{49} = -29.861872403816
x50=26.7222463741877x_{50} = 26.7222463741877
x51=15.707963267949x_{51} = 15.707963267949
x52=−86.3995849739529x_{52} = -86.3995849739529
x53=−43.9822971502571x_{53} = -43.9822971502571
x54=89.5409746049841x_{54} = 89.5409746049841
x55=−6.28318530717959x_{55} = -6.28318530717959
x56=−95.8237937978449x_{56} = -95.8237937978449
x57=−4.81584231784594x_{57} = -4.81584231784594
x58=95.8237937978449x_{58} = 95.8237937978449
x59=−28.2743338823081x_{59} = -28.2743338823081
x60=81.6814089933346x_{60} = 81.6814089933346
x61=−75.398223686155x_{61} = -75.398223686155
x62=29.861872403816x_{62} = 29.861872403816
x63=94.2477796076938x_{63} = 94.2477796076938
x64=−39.2826357527234x_{64} = -39.2826357527234
x65=−59.6902604182061x_{65} = -59.6902604182061
x66=87.9645943005142x_{66} = 87.9645943005142
x67=−45.5640665961997x_{67} = -45.5640665961997
x68=−64.410411962776x_{68} = -64.410411962776
x69=64.410411962776x_{69} = 64.410411962776
x70=−306.306916073247x_{70} = -306.306916073247
x71=−15.707963267949x_{71} = -15.707963267949
x72=23.5831433102848x_{72} = 23.5831433102848
x73=42.4232862577008x_{73} = 42.4232862577008
x74=−73.8341991854591x_{74} = -73.8341991854591
x75=6.28318530717959x_{75} = 6.28318530717959
x76=−50.2654824574367x_{76} = -50.2654824574367
x77=37.6991118430775x_{77} = 37.6991118430775
x78=−17.3076405374146x_{78} = -17.3076405374146
x79=43.9822971502571x_{79} = 43.9822971502571
x80=56.5486677646163x_{80} = 56.5486677646163
x81=−65.9734457253857x_{81} = -65.9734457253857
x82=−83.2582106616487x_{82} = -83.2582106616487
x83=25.1327412287183x_{83} = 25.1327412287183
x84=48.7049516666752x_{84} = 48.7049516666752
x85=7.91705268466621x_{85} = 7.91705268466621
x86=−31.4159265358979x_{86} = -31.4159265358979
x87=45.5640665961997x_{87} = 45.5640665961997
x88=72.2566310325652x_{88} = 72.2566310325652
Signos de extremos en los puntos:
(-14.172432074799941, -14.1548141232633)

(51.84592244522343, 51.8411009136761)

(-61.269217268722585, -61.2651371880071)

(67.5516436614121, 67.5479429919577)

(73.83419918545908, 73.8308133759219)

(-36.142148897006074, -36.135233089007)

(-105.24810453889911, -105.245729252817)

(14.172432074799941, 14.1548141232633)

(-89.54097460498406, -89.5381826741839)

(-53.40707511102649, -1.15535214562331e-28)

(-80.11685346965491, -80.1137331491182)

(-7.917052684666207, -7.88560072412753)

(-9.42477796076938, -1.27214126514718e-30)

(28.274333882308138, 3.43478141589738e-29)

(50.26548245743669, 1.92988541557142e-28)

(-97.3893722612836, -4.58542475390885e-27)

(-58.12806557615112, -58.1237650459065)

(70.692907433161, 70.6893711873986)

(-84.82300164692441, -3.99087542625273e-27)

(36.142148897006074, 36.135233089007)

(86.3995849739529, 86.3966915384367)

(92.68237799735202, 92.6796806914592)

(34.55751918948773, 1.68111309202325e-28)

(20.4448034666183, 20.4325827297121)

(1.8365972031521258, 1.70986852923209)

(65.97344572538566, 6.34844983898999e-29)

(0, 0)

(-67.5516436614121, -67.5479429919577)

(58.12806557615112, 58.1237650459065)

(3.141592653589793, 4.71163431535992e-32)

(78.53981633974483, 1.8941914820334e-29)

(-1.8365972031521258, -1.70986852923209)

(-20.4448034666183, -20.4325827297121)

(59.69026041820607, 8.97021321364436e-29)

(-42.423286257700816, -42.4173940862181)

(80.11685346965491, 80.1137331491182)

(100.53096491487338, 1.54390833245714e-27)

(-72.25663103256524, -2.93139900017185e-27)

(278.0327481900649, 278.031849018319)

(21.991148575128552, 1.61609057016845e-29)

(-23.583143310284843, -23.5725472811462)

(-37.69911184307752, -8.14170409694193e-29)

(-81.68140899333463, -1.25601110053315e-27)

(-21.991148575128552, -1.61609057016845e-29)

(12.566370614359172, 3.01544596183035e-30)

(-87.96459430051421, -1.03429796490781e-27)

(-51.84592244522343, -51.8411009136761)

(-94.2477796076938, -1.10977728956951e-27)

(-29.861872403816044, -29.853502870657)

(26.72224637418772, 26.7128941475173)

(15.707963267948966, 5.8895428941999e-30)

(-86.3995849739529, -86.3966915384367)

(-43.982297150257104, -1.29287245613476e-28)

(89.54097460498406, 89.5381826741839)

(-6.283185307179586, -3.76930745228793e-31)

(-95.82379379784489, -95.8211849135206)

(-4.815842317845935, -4.76448393290203)

(95.82379379784489, 95.8211849135206)

(-28.274333882308138, -3.43478141589738e-29)

(81.68140899333463, 1.25601110053315e-27)

(-75.39822368615503, -6.51336327755355e-28)

(29.861872403816044, 29.853502870657)

(94.2477796076938, 1.10977728956951e-27)

(-39.282635752723394, -39.2762726485285)

(-59.69026041820607, -8.97021321364436e-29)

(87.96459430051421, 1.03429796490781e-27)

(-45.56406659619972, -45.5585804770373)

(-64.41041196277601, -64.4065308365988)

(64.41041196277601, 64.4065308365988)

(-306.30691607324667, -306.306099900576)

(-15.707963267948966, -5.8895428941999e-30)

(23.583143310284843, 23.5725472811462)

(42.423286257700816, 42.4173940862181)

(-73.83419918545908, -73.8308133759219)

(6.283185307179586, 3.76930745228793e-31)

(-50.26548245743669, -1.92988541557142e-28)

(37.69911184307752, 8.14170409694193e-29)

(-17.307640537414635, -17.2932080946897)

(43.982297150257104, 1.29287245613476e-28)

(56.548667764616276, 2.7478251327179e-28)

(-65.97344572538566, -6.34844983898999e-29)

(-83.25821066164869, -83.255208063081)

(25.132741228718345, 2.41235676946428e-29)

(48.70495166667517, 48.6998192592491)

(7.917052684666207, 7.88560072412753)

(-31.41592653589793, -4.71163431535992e-29)

(45.56406659619972, 45.5585804770373)

(72.25663103256524, 2.93139900017185e-27)


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:
x1=−14.1724320747999x_{1} = -14.1724320747999
x2=−61.2692172687226x_{2} = -61.2692172687226
x3=−36.1421488970061x_{3} = -36.1421488970061
x4=−105.248104538899x_{4} = -105.248104538899
x5=−89.5409746049841x_{5} = -89.5409746049841
x6=−80.1168534696549x_{6} = -80.1168534696549
x7=−7.91705268466621x_{7} = -7.91705268466621
x8=28.2743338823081x_{8} = 28.2743338823081
x9=50.2654824574367x_{9} = 50.2654824574367
x10=−58.1280655761511x_{10} = -58.1280655761511
x11=34.5575191894877x_{11} = 34.5575191894877
x12=65.9734457253857x_{12} = 65.9734457253857
x13=−67.5516436614121x_{13} = -67.5516436614121
x14=3.14159265358979x_{14} = 3.14159265358979
x15=78.5398163397448x_{15} = 78.5398163397448
x16=−1.83659720315213x_{16} = -1.83659720315213
x17=−20.4448034666183x_{17} = -20.4448034666183
x18=59.6902604182061x_{18} = 59.6902604182061
x19=−42.4232862577008x_{19} = -42.4232862577008
x20=100.530964914873x_{20} = 100.530964914873
x21=21.9911485751286x_{21} = 21.9911485751286
x22=−23.5831433102848x_{22} = -23.5831433102848
x23=12.5663706143592x_{23} = 12.5663706143592
x24=−51.8459224452234x_{24} = -51.8459224452234
x25=−29.861872403816x_{25} = -29.861872403816
x26=15.707963267949x_{26} = 15.707963267949
x27=−86.3995849739529x_{27} = -86.3995849739529
x28=−95.8237937978449x_{28} = -95.8237937978449
x29=−4.81584231784594x_{29} = -4.81584231784594
x30=81.6814089933346x_{30} = 81.6814089933346
x31=94.2477796076938x_{31} = 94.2477796076938
x32=−39.2826357527234x_{32} = -39.2826357527234
x33=87.9645943005142x_{33} = 87.9645943005142
x34=−45.5640665961997x_{34} = -45.5640665961997
x35=−64.410411962776x_{35} = -64.410411962776
x36=−306.306916073247x_{36} = -306.306916073247
x37=−73.8341991854591x_{37} = -73.8341991854591
x38=6.28318530717959x_{38} = 6.28318530717959
x39=37.6991118430775x_{39} = 37.6991118430775
x40=−17.3076405374146x_{40} = -17.3076405374146
x41=43.9822971502571x_{41} = 43.9822971502571
x42=56.5486677646163x_{42} = 56.5486677646163
x43=−83.2582106616487x_{43} = -83.2582106616487
x44=25.1327412287183x_{44} = 25.1327412287183
x45=72.2566310325652x_{45} = 72.2566310325652
Puntos máximos de la función:
x45=51.8459224452234x_{45} = 51.8459224452234
x45=67.5516436614121x_{45} = 67.5516436614121
x45=73.8341991854591x_{45} = 73.8341991854591
x45=14.1724320747999x_{45} = 14.1724320747999
x45=−53.4070751110265x_{45} = -53.4070751110265
x45=−9.42477796076938x_{45} = -9.42477796076938
x45=−97.3893722612836x_{45} = -97.3893722612836
x45=70.692907433161x_{45} = 70.692907433161
x45=−84.8230016469244x_{45} = -84.8230016469244
x45=36.1421488970061x_{45} = 36.1421488970061
x45=86.3995849739529x_{45} = 86.3995849739529
x45=92.682377997352x_{45} = 92.682377997352
x45=20.4448034666183x_{45} = 20.4448034666183
x45=1.83659720315213x_{45} = 1.83659720315213
x45=58.1280655761511x_{45} = 58.1280655761511
x45=80.1168534696549x_{45} = 80.1168534696549
x45=−72.2566310325652x_{45} = -72.2566310325652
x45=278.032748190065x_{45} = 278.032748190065
x45=−37.6991118430775x_{45} = -37.6991118430775
x45=−81.6814089933346x_{45} = -81.6814089933346
x45=−21.9911485751286x_{45} = -21.9911485751286
x45=−87.9645943005142x_{45} = -87.9645943005142
x45=−94.2477796076938x_{45} = -94.2477796076938
x45=26.7222463741877x_{45} = 26.7222463741877
x45=−43.9822971502571x_{45} = -43.9822971502571
x45=89.5409746049841x_{45} = 89.5409746049841
x45=−6.28318530717959x_{45} = -6.28318530717959
x45=95.8237937978449x_{45} = 95.8237937978449
x45=−28.2743338823081x_{45} = -28.2743338823081
x45=−75.398223686155x_{45} = -75.398223686155
x45=29.861872403816x_{45} = 29.861872403816
x45=−59.6902604182061x_{45} = -59.6902604182061
x45=64.410411962776x_{45} = 64.410411962776
x45=−15.707963267949x_{45} = -15.707963267949
x45=23.5831433102848x_{45} = 23.5831433102848
x45=42.4232862577008x_{45} = 42.4232862577008
x45=−50.2654824574367x_{45} = -50.2654824574367
x45=−65.9734457253857x_{45} = -65.9734457253857
x45=48.7049516666752x_{45} = 48.7049516666752
x45=7.91705268466621x_{45} = 7.91705268466621
x45=−31.4159265358979x_{45} = -31.4159265358979
x45=45.5640665961997x_{45} = 45.5640665961997
Decrece en los intervalos
[100.530964914873,∞)\left[100.530964914873, \infty\right)
Crece en los intervalos
(−∞,−306.306916073247]\left(-\infty, -306.306916073247\right]
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
d2dx2f(x)=0\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:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
segunda derivada
2(−x(sin⁡2(x)−cos⁡2(x))+2sin⁡(x)cos⁡(x))=02 \left(- x \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=62.0545116429054x_{1} = 62.0545116429054
x2=−55.7722336752062x_{2} = -55.7722336752062
x3=−19.6603640661261x_{3} = -19.6603640661261
x4=−68.3369563786298x_{4} = -68.3369563786298
x5=−66.766332133246x_{5} = -66.766332133246
x6=−38.4974949445838x_{6} = -38.4974949445838
x7=24.3678503974527x_{7} = 24.3678503974527
x8=−21.2292853858495x_{8} = -21.2292853858495
x9=120.170079673253x_{9} = 120.170079673253
x10=−10.2587614549708x_{10} = -10.2587614549708
x11=−47.9197205706165x_{11} = -47.9197205706165
x12=−62.0545116429054x_{12} = -62.0545116429054
x13=−11.8231619098018x_{13} = -11.8231619098018
x14=63.6251091208926x_{14} = 63.6251091208926
x15=11.8231619098018x_{15} = 11.8231619098018
x16=49.4901859325761x_{16} = 49.4901859325761
x17=47.9197205706165x_{17} = 47.9197205706165
x18=−33.7869153354295x_{18} = -33.7869153354295
x19=−60.4839244878466x_{19} = -60.4839244878466
x20=85.6142396947314x_{20} = 85.6142396947314
x21=69.9075883539626x_{21} = 69.9075883539626
x22=96.6091494063022x_{22} = 96.6091494063022
x23=55.7722336752062x_{23} = 55.7722336752062
x24=−40.0677825970372x_{24} = -40.0677825970372
x25=−46.3492776216985x_{25} = -46.3492776216985
x26=−93.4677306800165x_{26} = -93.4677306800165
x27=2.54349254705114x_{27} = 2.54349254705114
x28=68.3369563786298x_{28} = 68.3369563786298
x29=91.8970257752571x_{29} = 91.8970257752571
x30=27.5071048394191x_{30} = 27.5071048394191
x31=0x_{31} = 0
x32=−1.1444648640517x_{32} = -1.1444648640517
x33=−63.6251091208926x_{33} = -63.6251091208926
x34=−84.0435524991391x_{34} = -84.0435524991391
x35=82.4728694594266x_{35} = 82.4728694594266
x36=88.7556256712795x_{36} = 88.7556256712795
x37=84.0435524991391x_{37} = 84.0435524991391
x38=16.5235843473527x_{38} = 16.5235843473527
x39=−5.58635293416499x_{39} = -5.58635293416499
x40=5.58635293416499x_{40} = 5.58635293416499
x41=98.1798629425939x_{41} = 98.1798629425939
x42=71.4782275499213x_{42} = 71.4782275499213
x43=−27.5071048394191x_{43} = -27.5071048394191
x44=−69.9075883539626x_{44} = -69.9075883539626
x45=8.69662198229738x_{45} = 8.69662198229738
x46=−13.3890435377793x_{46} = -13.3890435377793
x47=−54.2016970313842x_{47} = -54.2016970313842
x48=40.0677825970372x_{48} = 40.0677825970372
x49=−49.4901859325761x_{49} = -49.4901859325761
x50=30.6468374831214x_{50} = 30.6468374831214
x51=−58.9133484807877x_{51} = -58.9133484807877
x52=−24.3678503974527x_{52} = -24.3678503974527
x53=66.766332133246x_{53} = 66.766332133246
x54=77.760847792972x_{54} = 77.760847792972
x55=−85.6142396947314x_{55} = -85.6142396947314
x56=25.9374070267134x_{56} = 25.9374070267134
x57=−25.9374070267134x_{57} = -25.9374070267134
x58=−41.6381085824888x_{58} = -41.6381085824888
x59=−77.760847792972x_{59} = -77.760847792972
x60=74.6195257807054x_{60} = 74.6195257807054
x61=−91.8970257752571x_{61} = -91.8970257752571
x62=−32.2168395518658x_{62} = -32.2168395518658
x63=60.4839244878466x_{63} = 60.4839244878466
x64=−98.1798629425939x_{64} = -98.1798629425939
x65=38.4974949445838x_{65} = 38.4974949445838
x66=99.7505790857949x_{66} = 99.7505790857949
x67=41.6381085824888x_{67} = 41.6381085824888
x68=4.04808180161146x_{68} = 4.04808180161146
x69=−57.3427845371101x_{69} = -57.3427845371101
x70=−4.04808180161146x_{70} = -4.04808180161146
x71=46.3492776216985x_{71} = 46.3492776216985
x72=−18.0917665453763x_{72} = -18.0917665453763
x73=90.3263240494369x_{73} = 90.3263240494369
x74=19.6603640661261x_{74} = 19.6603640661261
x75=52.6311758774383x_{75} = 52.6311758774383
x76=10.2587614549708x_{76} = 10.2587614549708
x77=76.1901839979235x_{77} = 76.1901839979235
x78=54.2016970313842x_{78} = 54.2016970313842
x79=−90.3263240494369x_{79} = -90.3263240494369
x80=33.7869153354295x_{80} = 33.7869153354295
x81=−35.3570550332742x_{81} = -35.3570550332742
x82=−79.3315168346756x_{82} = -79.3315168346756
x83=−76.1901839979235x_{83} = -76.1901839979235
x84=18.0917665453763x_{84} = 18.0917665453763
x85=−99.7505790857949x_{85} = -99.7505790857949
x86=32.2168395518658x_{86} = 32.2168395518658
x87=−82.4728694594266x_{87} = -82.4728694594266
x88=−71.4782275499213x_{88} = -71.4782275499213

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
[99.7505790857949,∞)\left[99.7505790857949, \infty\right)
Convexa en los intervalos
(−∞,−99.7505790857949]\left(-\infty, -99.7505790857949\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(xsin⁡2(x))=⟨−∞,0⟩\lim_{x \to -\infty}\left(x \sin^{2}{\left(x \right)}\right) = \left\langle -\infty, 0\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−∞,0⟩y = \left\langle -\infty, 0\right\rangle
lim⁡x→∞(xsin⁡2(x))=⟨0,∞⟩\lim_{x \to \infty}\left(x \sin^{2}{\left(x \right)}\right) = \left\langle 0, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨0,∞⟩y = \left\langle 0, \infty\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función x*sin(x)^2, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞sin⁡2(x)=⟨0,1⟩\lim_{x \to -\infty} \sin^{2}{\left(x \right)} = \left\langle 0, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨0,1⟩xy = \left\langle 0, 1\right\rangle x
lim⁡x→∞sin⁡2(x)=⟨0,1⟩\lim_{x \to \infty} \sin^{2}{\left(x \right)} = \left\langle 0, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨0,1⟩xy = \left\langle 0, 1\right\rangle x
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:
xsin⁡2(x)=−xsin⁡2(x)x \sin^{2}{\left(x \right)} = - x \sin^{2}{\left(x \right)}
- No
xsin⁡2(x)=xsin⁡2(x)x \sin^{2}{\left(x \right)} = x \sin^{2}{\left(x \right)}
- Sí
es decir, función
es
impar
Gráfico
Gráfico de la función y = x*(sin(x))^2
    © Sr Examen – Калькулятор